dt/interface/dtds.c

#include <petsc/private/petscdsimpl.h> /*I "petscds.h" I*/

PetscClassId PETSCDS_CLASSID = 0;

PetscFunctionList PetscDSList              = NULL;
PetscBool         PetscDSRegisterAllCalled = PETSC_FALSE;

/* A PetscDS (Discrete System) encodes a set of equations posed in a discrete space, which represents a set of
   nonlinear continuum equations. The equations can have multiple fields, each field having a different
   discretization. In addition, different pieces of the domain can have different field combinations and equations.

   The DS provides the user a description of the approximation space on any given cell. It also gives pointwise
   functions representing the equations.

   Each field is associated with a label, marking the cells on which it is supported. Note that a field can be
   supported on the closure of a cell not in the label due to overlap of the boundary of neighboring cells. The DM
   then creates a DS for each set of cells with identical approximation spaces. When assembling, the user asks for
   the space associated with a given cell. DMPlex uses the labels associated with each DS in the default integration loop.
*/

/*@C
  PetscDSRegister - Adds a new `PetscDS` implementation

  Not Collective; No Fortran Support

  Input Parameters:
+ sname        - The name of a new user-defined creation routine
- function - The creation routine itself

  Sample usage:
.vb
    PetscDSRegister("my_ds", MyPetscDSCreate);
.ve

  Then, your PetscDS type can be chosen with the procedural interface via
.vb
    PetscDSCreate(MPI_Comm, PetscDS *);
    PetscDSSetType(PetscDS, "my_ds");
.ve
   or at runtime via the option
.vb
    -petscds_type my_ds
.ve

  Level: advanced

  Note:
  `PetscDSRegister()` may be called multiple times to add several user-defined `PetscDSs`

.seealso: `PetscDSType`, `PetscDS`, `PetscDSRegisterAll()`, `PetscDSRegisterDestroy()`
@*/
PetscErrorCode PetscDSRegister(const char sname[], PetscErrorCode (*function)(PetscDS))
{
  PetscFunctionBegin;
  PetscCall(PetscFunctionListAdd(&PetscDSList, sname, function));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSSetType - Builds a particular `PetscDS`

  Collective; No Fortran Support

  Input Parameters:
+ prob - The `PetscDS` object
- name - The `PetscDSType`

  Options Database Key:
. -petscds_type <type> - Sets the PetscDS type; use -help for a list of available types

  Level: intermediate

.seealso: `PetscDSType`, `PetscDS`, `PetscDSGetType()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSSetType(PetscDS prob, PetscDSType name)
{
  PetscErrorCode (*r)(PetscDS);
  PetscBool match;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  PetscCall(PetscObjectTypeCompare((PetscObject)prob, name, &match));
  if (match) PetscFunctionReturn(PETSC_SUCCESS);

  PetscCall(PetscDSRegisterAll());
  PetscCall(PetscFunctionListFind(PetscDSList, name, &r));
  PetscCheck(r, PetscObjectComm((PetscObject)prob), PETSC_ERR_ARG_UNKNOWN_TYPE, "Unknown PetscDS type: %s", name);

  PetscTryTypeMethod(prob, destroy);
  prob->ops->destroy = NULL;

  PetscCall((*r)(prob));
  PetscCall(PetscObjectChangeTypeName((PetscObject)prob, name));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSGetType - Gets the `PetscDSType` name (as a string) from the `PetscDS`

  Not Collective; No Fortran Support

  Input Parameter:
. prob  - The `PetscDS`

  Output Parameter:
. name - The `PetscDSType` name

  Level: intermediate

.seealso: `PetscDSType`, `PetscDS`, `PetscDSSetType()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSGetType(PetscDS prob, PetscDSType *name)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  PetscValidPointer(name, 2);
  PetscCall(PetscDSRegisterAll());
  *name = ((PetscObject)prob)->type_name;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PetscDSView_Ascii(PetscDS ds, PetscViewer viewer)
{
  PetscViewerFormat  format;
  const PetscScalar *constants;
  PetscInt           Nf, numConstants, f;

  PetscFunctionBegin;
  PetscCall(PetscDSGetNumFields(ds, &Nf));
  PetscCall(PetscViewerGetFormat(viewer, &format));
  PetscCall(PetscViewerASCIIPrintf(viewer, "Discrete System with %" PetscInt_FMT " fields\n", Nf));
  PetscCall(PetscViewerASCIIPushTab(viewer));
  PetscCall(PetscViewerASCIIPrintf(viewer, "  cell total dim %" PetscInt_FMT " total comp %" PetscInt_FMT "\n", ds->totDim, ds->totComp));
  if (ds->isCohesive) PetscCall(PetscViewerASCIIPrintf(viewer, "  cohesive cell\n"));
  for (f = 0; f < Nf; ++f) {
    DSBoundary      b;
    PetscObject     obj;
    PetscClassId    id;
    PetscQuadrature q;
    const char     *name;
    PetscInt        Nc, Nq, Nqc;

    PetscCall(PetscDSGetDiscretization(ds, f, &obj));
    PetscCall(PetscObjectGetClassId(obj, &id));
    PetscCall(PetscObjectGetName(obj, &name));
    PetscCall(PetscViewerASCIIPrintf(viewer, "Field %s", name ? name : "<unknown>"));
    PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
    if (id == PETSCFE_CLASSID) {
      PetscCall(PetscFEGetNumComponents((PetscFE)obj, &Nc));
      PetscCall(PetscFEGetQuadrature((PetscFE)obj, &q));
      PetscCall(PetscViewerASCIIPrintf(viewer, " FEM"));
    } else if (id == PETSCFV_CLASSID) {
      PetscCall(PetscFVGetNumComponents((PetscFV)obj, &Nc));
      PetscCall(PetscFVGetQuadrature((PetscFV)obj, &q));
      PetscCall(PetscViewerASCIIPrintf(viewer, " FVM"));
    } else SETERRQ(PetscObjectComm((PetscObject)ds), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %" PetscInt_FMT, f);
    if (Nc > 1) PetscCall(PetscViewerASCIIPrintf(viewer, " %" PetscInt_FMT " components", Nc));
    else PetscCall(PetscViewerASCIIPrintf(viewer, " %" PetscInt_FMT " component ", Nc));
    if (ds->implicit[f]) PetscCall(PetscViewerASCIIPrintf(viewer, " (implicit)"));
    else PetscCall(PetscViewerASCIIPrintf(viewer, " (explicit)"));
    if (q) {
      PetscCall(PetscQuadratureGetData(q, NULL, &Nqc, &Nq, NULL, NULL));
      PetscCall(PetscViewerASCIIPrintf(viewer, " (Nq %" PetscInt_FMT " Nqc %" PetscInt_FMT ")", Nq, Nqc));
    }
    PetscCall(PetscViewerASCIIPrintf(viewer, " %" PetscInt_FMT "-jet", ds->jetDegree[f]));
    PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
    PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
    PetscCall(PetscViewerASCIIPushTab(viewer));
    if (id == PETSCFE_CLASSID) PetscCall(PetscFEView((PetscFE)obj, viewer));
    else if (id == PETSCFV_CLASSID) PetscCall(PetscFVView((PetscFV)obj, viewer));
    PetscCall(PetscViewerASCIIPopTab(viewer));

    for (b = ds->boundary; b; b = b->next) {
      char    *name;
      PetscInt c, i;

      if (b->field != f) continue;
      PetscCall(PetscViewerASCIIPushTab(viewer));
      PetscCall(PetscViewerASCIIPrintf(viewer, "Boundary %s (%s) %s\n", b->name, b->lname, DMBoundaryConditionTypes[b->type]));
      if (!b->Nc) {
        PetscCall(PetscViewerASCIIPrintf(viewer, "  all components\n"));
      } else {
        PetscCall(PetscViewerASCIIPrintf(viewer, "  components: "));
        PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
        for (c = 0; c < b->Nc; ++c) {
          if (c > 0) PetscCall(PetscViewerASCIIPrintf(viewer, ", "));
          PetscCall(PetscViewerASCIIPrintf(viewer, "%" PetscInt_FMT, b->comps[c]));
        }
        PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
        PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
      }
      PetscCall(PetscViewerASCIIPrintf(viewer, "  values: "));
      PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
      for (i = 0; i < b->Nv; ++i) {
        if (i > 0) PetscCall(PetscViewerASCIIPrintf(viewer, ", "));
        PetscCall(PetscViewerASCIIPrintf(viewer, "%" PetscInt_FMT, b->values[i]));
      }
      PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
      PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
#if defined(__clang__)
      PETSC_PRAGMA_DIAGNOSTIC_IGNORED_BEGIN("-Wformat-pedantic");
#elif defined(__GNUC__) || defined(__GNUG__)
      PETSC_PRAGMA_DIAGNOSTIC_IGNORED_BEGIN("-Wformat");
#endif
      if (b->func) {
        PetscCall(PetscDLAddr(b->func, &name));
        if (name) PetscCall(PetscViewerASCIIPrintf(viewer, "  func: %s\n", name));
        else PetscCall(PetscViewerASCIIPrintf(viewer, "  func: %p\n", b->func));
        PetscCall(PetscFree(name));
      }
      if (b->func_t) {
        PetscCall(PetscDLAddr(b->func_t, &name));
        if (name) PetscCall(PetscViewerASCIIPrintf(viewer, "  func_t: %s\n", name));
        else PetscCall(PetscViewerASCIIPrintf(viewer, "  func_t: %p\n", b->func_t));
        PetscCall(PetscFree(name));
      }
      PETSC_PRAGMA_DIAGNOSTIC_IGNORED_END();
      PetscCall(PetscWeakFormView(b->wf, viewer));
      PetscCall(PetscViewerASCIIPopTab(viewer));
    }
  }
  PetscCall(PetscDSGetConstants(ds, &numConstants, &constants));
  if (numConstants) {
    PetscCall(PetscViewerASCIIPrintf(viewer, "%" PetscInt_FMT " constants\n", numConstants));
    PetscCall(PetscViewerASCIIPushTab(viewer));
    for (f = 0; f < numConstants; ++f) PetscCall(PetscViewerASCIIPrintf(viewer, "%g\n", (double)PetscRealPart(constants[f])));
    PetscCall(PetscViewerASCIIPopTab(viewer));
  }
  PetscCall(PetscWeakFormView(ds->wf, viewer));
  PetscCall(PetscViewerASCIIPopTab(viewer));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
   PetscDSViewFromOptions - View a `PetscDS` based on values in the options database

   Collective

   Input Parameters:
+  A - the `PetscDS` object
.  obj - Optional object that provides the options prefix used in the search
-  name - command line option

   Level: intermediate

.seealso: `PetscDSType`, `PetscDS`, `PetscDSView()`, `PetscObjectViewFromOptions()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSViewFromOptions(PetscDS A, PetscObject obj, const char name[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(A, PETSCDS_CLASSID, 1);
  PetscCall(PetscObjectViewFromOptions((PetscObject)A, obj, name));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSView - Views a `PetscDS`

  Collective

  Input Parameters:
+ prob - the `PetscDS` object to view
- v  - the viewer

  Level: developer

.seealso: `PetscDSType`, `PetscDS`, `PetscViewer`, `PetscDSDestroy()`, `PetscDSViewFromOptions()`
@*/
PetscErrorCode PetscDSView(PetscDS prob, PetscViewer v)
{
  PetscBool iascii;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  if (!v) PetscCall(PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject)prob), &v));
  else PetscValidHeaderSpecific(v, PETSC_VIEWER_CLASSID, 2);
  PetscCall(PetscObjectTypeCompare((PetscObject)v, PETSCVIEWERASCII, &iascii));
  if (iascii) PetscCall(PetscDSView_Ascii(prob, v));
  PetscTryTypeMethod(prob, view, v);
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSSetFromOptions - sets parameters in a `PetscDS` from the options database

  Collective

  Input Parameter:
. prob - the `PetscDS` object to set options for

  Options Database Keys:
+ -petscds_type <type>     - Set the `PetscDS` type
. -petscds_view <view opt> - View the `PetscDS`
. -petscds_jac_pre         - Turn formation of a separate Jacobian preconditioner on or off
. -bc_<name> <ids>         - Specify a list of label ids for a boundary condition
- -bc_<name>_comp <comps>  - Specify a list of field components to constrain for a boundary condition

  Level: intermediate

.seealso: `PetscDS`, `PetscDSView()`
@*/
PetscErrorCode PetscDSSetFromOptions(PetscDS prob)
{
  DSBoundary  b;
  const char *defaultType;
  char        name[256];
  PetscBool   flg;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  if (!((PetscObject)prob)->type_name) {
    defaultType = PETSCDSBASIC;
  } else {
    defaultType = ((PetscObject)prob)->type_name;
  }
  PetscCall(PetscDSRegisterAll());

  PetscObjectOptionsBegin((PetscObject)prob);
  for (b = prob->boundary; b; b = b->next) {
    char      optname[1024];
    PetscInt  ids[1024], len = 1024;
    PetscBool flg;

    PetscCall(PetscSNPrintf(optname, sizeof(optname), "-bc_%s", b->name));
    PetscCall(PetscMemzero(ids, sizeof(ids)));
    PetscCall(PetscOptionsIntArray(optname, "List of boundary IDs", "", ids, &len, &flg));
    if (flg) {
      b->Nv = len;
      PetscCall(PetscFree(b->values));
      PetscCall(PetscMalloc1(len, &b->values));
      PetscCall(PetscArraycpy(b->values, ids, len));
      PetscCall(PetscWeakFormRewriteKeys(b->wf, b->label, len, b->values));
    }
    len = 1024;
    PetscCall(PetscSNPrintf(optname, sizeof(optname), "-bc_%s_comp", b->name));
    PetscCall(PetscMemzero(ids, sizeof(ids)));
    PetscCall(PetscOptionsIntArray(optname, "List of boundary field components", "", ids, &len, &flg));
    if (flg) {
      b->Nc = len;
      PetscCall(PetscFree(b->comps));
      PetscCall(PetscMalloc1(len, &b->comps));
      PetscCall(PetscArraycpy(b->comps, ids, len));
    }
  }
  PetscCall(PetscOptionsFList("-petscds_type", "Discrete System", "PetscDSSetType", PetscDSList, defaultType, name, 256, &flg));
  if (flg) {
    PetscCall(PetscDSSetType(prob, name));
  } else if (!((PetscObject)prob)->type_name) {
    PetscCall(PetscDSSetType(prob, defaultType));
  }
  PetscCall(PetscOptionsBool("-petscds_jac_pre", "Discrete System", "PetscDSUseJacobianPreconditioner", prob->useJacPre, &prob->useJacPre, &flg));
  PetscCall(PetscOptionsBool("-petscds_force_quad", "Discrete System", "PetscDSSetForceQuad", prob->forceQuad, &prob->forceQuad, &flg));
  PetscTryTypeMethod(prob, setfromoptions);
  /* process any options handlers added with PetscObjectAddOptionsHandler() */
  PetscCall(PetscObjectProcessOptionsHandlers((PetscObject)prob, PetscOptionsObject));
  PetscOptionsEnd();
  if (prob->Nf) PetscCall(PetscDSViewFromOptions(prob, NULL, "-petscds_view"));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSSetUp - Construct data structures for the `PetscDS`

  Collective

  Input Parameter:
. prob - the `PetscDS` object to setup

  Level: developer

.seealso: `PetscDS`, `PetscDSView()`, `PetscDSDestroy()`
@*/
PetscErrorCode PetscDSSetUp(PetscDS prob)
{
  const PetscInt Nf          = prob->Nf;
  PetscBool      hasH        = PETSC_FALSE;
  PetscInt       maxOrder[4] = {-1, -1, -1, -1};
  PetscInt       dim, dimEmbed, NbMax = 0, NcMax = 0, NqMax = 0, NsMax = 1, f;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  if (prob->setup) PetscFunctionReturn(PETSC_SUCCESS);
  /* Calculate sizes */
  PetscCall(PetscDSGetSpatialDimension(prob, &dim));
  PetscCall(PetscDSGetCoordinateDimension(prob, &dimEmbed));
  prob->totDim = prob->totComp = 0;
  PetscCall(PetscMalloc2(Nf, &prob->Nc, Nf, &prob->Nb));
  PetscCall(PetscCalloc2(Nf + 1, &prob->off, Nf + 1, &prob->offDer));
  PetscCall(PetscCalloc6(Nf + 1, &prob->offCohesive[0], Nf + 1, &prob->offCohesive[1], Nf + 1, &prob->offCohesive[2], Nf + 1, &prob->offDerCohesive[0], Nf + 1, &prob->offDerCohesive[1], Nf + 1, &prob->offDerCohesive[2]));
  PetscCall(PetscMalloc2(Nf, &prob->T, Nf, &prob->Tf));
  if (prob->forceQuad) {
    // Note: This assumes we have one kind of cell at each dimension.
    //       We can fix this by having quadrature hold the celltype
    PetscQuadrature maxQuad[4] = {NULL, NULL, NULL, NULL};

    for (f = 0; f < Nf; ++f) {
      PetscObject     obj;
      PetscClassId    id;
      PetscQuadrature q = NULL, fq = NULL;
      PetscInt        dim = -1, order = -1, forder = -1;

      PetscCall(PetscDSGetDiscretization(prob, f, &obj));
      if (!obj) continue;
      PetscCall(PetscObjectGetClassId(obj, &id));
      if (id == PETSCFE_CLASSID) {
        PetscFE fe = (PetscFE)obj;

        PetscCall(PetscFEGetQuadrature(fe, &q));
        PetscCall(PetscFEGetFaceQuadrature(fe, &fq));
      } else if (id == PETSCFV_CLASSID) {
        PetscFV fv = (PetscFV)obj;

        PetscCall(PetscFVGetQuadrature(fv, &q));
      }
      if (q) {
        PetscCall(PetscQuadratureGetData(q, &dim, NULL, NULL, NULL, NULL));
        PetscCall(PetscQuadratureGetOrder(q, &order));
        if (order > maxOrder[dim]) {
          maxOrder[dim] = order;
          maxQuad[dim]  = q;
        }
      }
      if (fq) {
        PetscCall(PetscQuadratureGetData(fq, &dim, NULL, NULL, NULL, NULL));
        PetscCall(PetscQuadratureGetOrder(fq, &forder));
        if (forder > maxOrder[dim]) {
          maxOrder[dim] = forder;
          maxQuad[dim]  = fq;
        }
      }
    }
    for (f = 0; f < Nf; ++f) {
      PetscObject     obj;
      PetscClassId    id;
      PetscQuadrature q;
      PetscInt        dim;

      PetscCall(PetscDSGetDiscretization(prob, f, &obj));
      if (!obj) continue;
      PetscCall(PetscObjectGetClassId(obj, &id));
      if (id == PETSCFE_CLASSID) {
        PetscFE fe = (PetscFE)obj;

        PetscCall(PetscFEGetQuadrature(fe, &q));
        PetscCall(PetscQuadratureGetData(q, &dim, NULL, NULL, NULL, NULL));
        PetscCall(PetscFESetQuadrature(fe, maxQuad[dim]));
        PetscCall(PetscFESetFaceQuadrature(fe, maxQuad[dim - 1]));
      } else if (id == PETSCFV_CLASSID) {
        PetscFV fv = (PetscFV)obj;

        PetscCall(PetscFVGetQuadrature(fv, &q));
        PetscCall(PetscQuadratureGetData(q, &dim, NULL, NULL, NULL, NULL));
        PetscCall(PetscFVSetQuadrature(fv, maxQuad[dim]));
      }
    }
  }
  for (f = 0; f < Nf; ++f) {
    PetscObject     obj;
    PetscClassId    id;
    PetscQuadrature q  = NULL;
    PetscInt        Nq = 0, Nb, Nc;

    PetscCall(PetscDSGetDiscretization(prob, f, &obj));
    if (prob->jetDegree[f] > 1) hasH = PETSC_TRUE;
    if (!obj) {
      /* Empty mesh */
      Nb = Nc    = 0;
      prob->T[f] = prob->Tf[f] = NULL;
    } else {
      PetscCall(PetscObjectGetClassId(obj, &id));
      if (id == PETSCFE_CLASSID) {
        PetscFE fe = (PetscFE)obj;

        PetscCall(PetscFEGetQuadrature(fe, &q));
        {
          PetscQuadrature fq;
          PetscInt        dim, order;

          PetscCall(PetscQuadratureGetData(q, &dim, NULL, NULL, NULL, NULL));
          PetscCall(PetscQuadratureGetOrder(q, &order));
          if (maxOrder[dim] < 0) maxOrder[dim] = order;
          PetscCheck(order == maxOrder[dim], PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Field %" PetscInt_FMT " cell quadrature order %" PetscInt_FMT " != %" PetscInt_FMT " DS cell quadrature order", f, order, maxOrder[dim]);
          PetscCall(PetscFEGetFaceQuadrature(fe, &fq));
          if (fq) {
            PetscCall(PetscQuadratureGetData(fq, &dim, NULL, NULL, NULL, NULL));
            PetscCall(PetscQuadratureGetOrder(fq, &order));
            if (maxOrder[dim] < 0) maxOrder[dim] = order;
            PetscCheck(order == maxOrder[dim], PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Field %" PetscInt_FMT " face quadrature order %" PetscInt_FMT " != %" PetscInt_FMT " DS face quadrature order", f, order, maxOrder[dim]);
          }
        }
        PetscCall(PetscFEGetDimension(fe, &Nb));
        PetscCall(PetscFEGetNumComponents(fe, &Nc));
        PetscCall(PetscFEGetCellTabulation(fe, prob->jetDegree[f], &prob->T[f]));
        PetscCall(PetscFEGetFaceTabulation(fe, prob->jetDegree[f], &prob->Tf[f]));
      } else if (id == PETSCFV_CLASSID) {
        PetscFV fv = (PetscFV)obj;

        PetscCall(PetscFVGetQuadrature(fv, &q));
        PetscCall(PetscFVGetNumComponents(fv, &Nc));
        Nb = Nc;
        PetscCall(PetscFVGetCellTabulation(fv, &prob->T[f]));
        /* TODO: should PetscFV also have face tabulation? Otherwise there will be a null pointer in prob->basisFace */
      } else SETERRQ(PetscObjectComm((PetscObject)prob), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %" PetscInt_FMT, f);
    }
    prob->Nc[f]                    = Nc;
    prob->Nb[f]                    = Nb;
    prob->off[f + 1]               = Nc + prob->off[f];
    prob->offDer[f + 1]            = Nc * dim + prob->offDer[f];
    prob->offCohesive[0][f + 1]    = (prob->cohesive[f] ? Nc : Nc * 2) + prob->offCohesive[0][f];
    prob->offDerCohesive[0][f + 1] = (prob->cohesive[f] ? Nc : Nc * 2) * dimEmbed + prob->offDerCohesive[0][f];
    prob->offCohesive[1][f]        = (prob->cohesive[f] ? 0 : Nc) + prob->offCohesive[0][f];
    prob->offDerCohesive[1][f]     = (prob->cohesive[f] ? 0 : Nc) * dimEmbed + prob->offDerCohesive[0][f];
    prob->offCohesive[2][f + 1]    = (prob->cohesive[f] ? Nc : Nc * 2) + prob->offCohesive[2][f];
    prob->offDerCohesive[2][f + 1] = (prob->cohesive[f] ? Nc : Nc * 2) * dimEmbed + prob->offDerCohesive[2][f];
    if (q) PetscCall(PetscQuadratureGetData(q, NULL, NULL, &Nq, NULL, NULL));
    NqMax = PetscMax(NqMax, Nq);
    NbMax = PetscMax(NbMax, Nb);
    NcMax = PetscMax(NcMax, Nc);
    prob->totDim += Nb;
    prob->totComp += Nc;
    /* There are two faces for all fields on a cohesive cell, except for cohesive fields */
    if (prob->isCohesive && !prob->cohesive[f]) prob->totDim += Nb;
  }
  prob->offCohesive[1][Nf]    = prob->offCohesive[0][Nf];
  prob->offDerCohesive[1][Nf] = prob->offDerCohesive[0][Nf];
  /* Allocate works space */
  NsMax = 2; /* A non-cohesive discretizations can be used on a cohesive cell, so we need this extra workspace for all DS */
  PetscCall(PetscMalloc3(NsMax * prob->totComp, &prob->u, NsMax * prob->totComp, &prob->u_t, NsMax * prob->totComp * dimEmbed + (hasH ? NsMax * prob->totComp * dimEmbed * dimEmbed : 0), &prob->u_x));
  PetscCall(PetscMalloc5(dimEmbed, &prob->x, NbMax * NcMax, &prob->basisReal, NbMax * NcMax * dimEmbed, &prob->basisDerReal, NbMax * NcMax, &prob->testReal, NbMax * NcMax * dimEmbed, &prob->testDerReal));
  PetscCall(PetscMalloc6(NsMax * NqMax * NcMax, &prob->f0, NsMax * NqMax * NcMax * dimEmbed, &prob->f1, NsMax * NsMax * NqMax * NcMax * NcMax, &prob->g0, NsMax * NsMax * NqMax * NcMax * NcMax * dimEmbed, &prob->g1, NsMax * NsMax * NqMax * NcMax * NcMax * dimEmbed,
                         &prob->g2, NsMax * NsMax * NqMax * NcMax * NcMax * dimEmbed * dimEmbed, &prob->g3));
  PetscTryTypeMethod(prob, setup);
  prob->setup = PETSC_TRUE;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PetscDSDestroyStructs_Static(PetscDS prob)
{
  PetscFunctionBegin;
  PetscCall(PetscFree2(prob->Nc, prob->Nb));
  PetscCall(PetscFree2(prob->off, prob->offDer));
  PetscCall(PetscFree6(prob->offCohesive[0], prob->offCohesive[1], prob->offCohesive[2], prob->offDerCohesive[0], prob->offDerCohesive[1], prob->offDerCohesive[2]));
  PetscCall(PetscFree2(prob->T, prob->Tf));
  PetscCall(PetscFree3(prob->u, prob->u_t, prob->u_x));
  PetscCall(PetscFree5(prob->x, prob->basisReal, prob->basisDerReal, prob->testReal, prob->testDerReal));
  PetscCall(PetscFree6(prob->f0, prob->f1, prob->g0, prob->g1, prob->g2, prob->g3));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PetscDSEnlarge_Static(PetscDS prob, PetscInt NfNew)
{
  PetscObject          *tmpd;
  PetscBool            *tmpi;
  PetscInt             *tmpk;
  PetscBool            *tmpc;
  PetscPointFunc       *tmpup;
  PetscSimplePointFunc *tmpexactSol, *tmpexactSol_t;
  void                **tmpexactCtx, **tmpexactCtx_t;
  void                **tmpctx;
  PetscInt              Nf = prob->Nf, f;

  PetscFunctionBegin;
  if (Nf >= NfNew) PetscFunctionReturn(PETSC_SUCCESS);
  prob->setup = PETSC_FALSE;
  PetscCall(PetscDSDestroyStructs_Static(prob));
  PetscCall(PetscMalloc4(NfNew, &tmpd, NfNew, &tmpi, NfNew, &tmpc, NfNew, &tmpk));
  for (f = 0; f < Nf; ++f) {
    tmpd[f] = prob->disc[f];
    tmpi[f] = prob->implicit[f];
    tmpc[f] = prob->cohesive[f];
    tmpk[f] = prob->jetDegree[f];
  }
  for (f = Nf; f < NfNew; ++f) {
    tmpd[f] = NULL;
    tmpi[f] = PETSC_TRUE, tmpc[f] = PETSC_FALSE;
    tmpk[f] = 1;
  }
  PetscCall(PetscFree4(prob->disc, prob->implicit, prob->cohesive, prob->jetDegree));
  PetscCall(PetscWeakFormSetNumFields(prob->wf, NfNew));
  prob->Nf        = NfNew;
  prob->disc      = tmpd;
  prob->implicit  = tmpi;
  prob->cohesive  = tmpc;
  prob->jetDegree = tmpk;
  PetscCall(PetscCalloc2(NfNew, &tmpup, NfNew, &tmpctx));
  for (f = 0; f < Nf; ++f) tmpup[f] = prob->update[f];
  for (f = 0; f < Nf; ++f) tmpctx[f] = prob->ctx[f];
  for (f = Nf; f < NfNew; ++f) tmpup[f] = NULL;
  for (f = Nf; f < NfNew; ++f) tmpctx[f] = NULL;
  PetscCall(PetscFree2(prob->update, prob->ctx));
  prob->update = tmpup;
  prob->ctx    = tmpctx;
  PetscCall(PetscCalloc4(NfNew, &tmpexactSol, NfNew, &tmpexactCtx, NfNew, &tmpexactSol_t, NfNew, &tmpexactCtx_t));
  for (f = 0; f < Nf; ++f) tmpexactSol[f] = prob->exactSol[f];
  for (f = 0; f < Nf; ++f) tmpexactCtx[f] = prob->exactCtx[f];
  for (f = 0; f < Nf; ++f) tmpexactSol_t[f] = prob->exactSol_t[f];
  for (f = 0; f < Nf; ++f) tmpexactCtx_t[f] = prob->exactCtx_t[f];
  for (f = Nf; f < NfNew; ++f) tmpexactSol[f] = NULL;
  for (f = Nf; f < NfNew; ++f) tmpexactCtx[f] = NULL;
  for (f = Nf; f < NfNew; ++f) tmpexactSol_t[f] = NULL;
  for (f = Nf; f < NfNew; ++f) tmpexactCtx_t[f] = NULL;
  PetscCall(PetscFree4(prob->exactSol, prob->exactCtx, prob->exactSol_t, prob->exactCtx_t));
  prob->exactSol   = tmpexactSol;
  prob->exactCtx   = tmpexactCtx;
  prob->exactSol_t = tmpexactSol_t;
  prob->exactCtx_t = tmpexactCtx_t;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSDestroy - Destroys a `PetscDS` object

  Collective

  Input Parameter:
. prob - the `PetscDS` object to destroy

  Level: developer

.seealso: `PetscDSView()`
@*/
PetscErrorCode PetscDSDestroy(PetscDS *ds)
{
  PetscInt f;

  PetscFunctionBegin;
  if (!*ds) PetscFunctionReturn(PETSC_SUCCESS);
  PetscValidHeaderSpecific((*ds), PETSCDS_CLASSID, 1);

  if (--((PetscObject)(*ds))->refct > 0) {
    *ds = NULL;
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  ((PetscObject)(*ds))->refct = 0;
  if ((*ds)->subprobs) {
    PetscInt dim, d;

    PetscCall(PetscDSGetSpatialDimension(*ds, &dim));
    for (d = 0; d < dim; ++d) PetscCall(PetscDSDestroy(&(*ds)->subprobs[d]));
  }
  PetscCall(PetscFree((*ds)->subprobs));
  PetscCall(PetscDSDestroyStructs_Static(*ds));
  for (f = 0; f < (*ds)->Nf; ++f) PetscCall(PetscObjectDereference((*ds)->disc[f]));
  PetscCall(PetscFree4((*ds)->disc, (*ds)->implicit, (*ds)->cohesive, (*ds)->jetDegree));
  PetscCall(PetscWeakFormDestroy(&(*ds)->wf));
  PetscCall(PetscFree2((*ds)->update, (*ds)->ctx));
  PetscCall(PetscFree4((*ds)->exactSol, (*ds)->exactCtx, (*ds)->exactSol_t, (*ds)->exactCtx_t));
  PetscTryTypeMethod((*ds), destroy);
  PetscCall(PetscDSDestroyBoundary(*ds));
  PetscCall(PetscFree((*ds)->constants));
  for (PetscInt c = 0; c < DM_NUM_POLYTOPES; ++c) {
    const PetscInt Na = DMPolytopeTypeGetNumArrangments((DMPolytopeType)c);
    if ((*ds)->quadPerm[c])
      for (PetscInt o = 0; o < Na; ++o) PetscCall(ISDestroy(&(*ds)->quadPerm[c][o]));
    PetscCall(PetscFree((*ds)->quadPerm[c]));
    (*ds)->quadPerm[c] = NULL;
  }
  PetscCall(PetscHeaderDestroy(ds));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSCreate - Creates an empty `PetscDS` object. The type can then be set with `PetscDSSetType()`.

  Collective

  Input Parameter:
. comm - The communicator for the `PetscDS` object

  Output Parameter:
. ds   - The `PetscDS` object

  Level: beginner

.seealso: `PetscDS`, `PetscDSSetType()`, `PETSCDSBASIC`, `PetscDSType`
@*/
PetscErrorCode PetscDSCreate(MPI_Comm comm, PetscDS *ds)
{
  PetscDS p;

  PetscFunctionBegin;
  PetscValidPointer(ds, 2);
  *ds = NULL;
  PetscCall(PetscDSInitializePackage());

  PetscCall(PetscHeaderCreate(p, PETSCDS_CLASSID, "PetscDS", "Discrete System", "PetscDS", comm, PetscDSDestroy, PetscDSView));

  p->Nf           = 0;
  p->setup        = PETSC_FALSE;
  p->numConstants = 0;
  p->constants    = NULL;
  p->dimEmbed     = -1;
  p->useJacPre    = PETSC_TRUE;
  p->forceQuad    = PETSC_TRUE;
  PetscCall(PetscWeakFormCreate(comm, &p->wf));
  PetscCall(PetscArrayzero(p->quadPerm, DM_NUM_POLYTOPES));

  *ds = p;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSGetNumFields - Returns the number of fields in the `PetscDS`

  Not Collective

  Input Parameter:
. prob - The `PetscDS` object

  Output Parameter:
. Nf - The number of fields

  Level: beginner

.seealso: `PetscDS`, `PetscDSGetSpatialDimension()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSGetNumFields(PetscDS prob, PetscInt *Nf)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  PetscValidIntPointer(Nf, 2);
  *Nf = prob->Nf;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSGetSpatialDimension - Returns the spatial dimension of the `PetscDS`, meaning the topological dimension of the discretizations

  Not Collective

  Input Parameter:
. prob - The `PetscDS` object

  Output Parameter:
. dim - The spatial dimension

  Level: beginner

.seealso: `PetscDS`, `PetscDSGetCoordinateDimension()`, `PetscDSGetNumFields()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSGetSpatialDimension(PetscDS prob, PetscInt *dim)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  PetscValidIntPointer(dim, 2);
  *dim = 0;
  if (prob->Nf) {
    PetscObject  obj;
    PetscClassId id;

    PetscCall(PetscDSGetDiscretization(prob, 0, &obj));
    if (obj) {
      PetscCall(PetscObjectGetClassId(obj, &id));
      if (id == PETSCFE_CLASSID) PetscCall(PetscFEGetSpatialDimension((PetscFE)obj, dim));
      else if (id == PETSCFV_CLASSID) PetscCall(PetscFVGetSpatialDimension((PetscFV)obj, dim));
      else SETERRQ(PetscObjectComm((PetscObject)prob), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", 0);
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSGetCoordinateDimension - Returns the coordinate dimension of the `PetscDS`, meaning the dimension of the space into which the discretiaztions are embedded

  Not Collective

  Input Parameter:
. prob - The `PetscDS` object

  Output Parameter:
. dimEmbed - The coordinate dimension

  Level: beginner

.seealso: `PetscDS`, `PetscDSSetCoordinateDimension()`, `PetscDSGetSpatialDimension()`, `PetscDSGetNumFields()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSGetCoordinateDimension(PetscDS prob, PetscInt *dimEmbed)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  PetscValidIntPointer(dimEmbed, 2);
  PetscCheck(prob->dimEmbed >= 0, PetscObjectComm((PetscObject)prob), PETSC_ERR_ARG_WRONGSTATE, "No coordinate dimension set for this DS");
  *dimEmbed = prob->dimEmbed;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSSetCoordinateDimension - Set the coordinate dimension of the `PetscDS`, meaning the dimension of the space into which the discretiaztions are embedded

  Logically Collective

  Input Parameters:
+ prob - The `PetscDS` object
- dimEmbed - The coordinate dimension

  Level: beginner

.seealso: `PetscDS`, `PetscDSGetCoordinateDimension()`, `PetscDSGetSpatialDimension()`, `PetscDSGetNumFields()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSSetCoordinateDimension(PetscDS prob, PetscInt dimEmbed)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  PetscCheck(dimEmbed >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Coordinate dimension must be non-negative, not %" PetscInt_FMT, dimEmbed);
  prob->dimEmbed = dimEmbed;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSGetForceQuad - Returns the flag to force matching quadratures among the field discretizations

  Not collective

  Input Parameter:
. prob - The `PetscDS` object

  Output Parameter:
. forceQuad - The flag

  Level: intermediate

.seealso: `PetscDS`, `PetscDSSetForceQuad()`, `PetscDSGetDiscretization()`, `PetscDSGetNumFields()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSGetForceQuad(PetscDS ds, PetscBool *forceQuad)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  PetscValidBoolPointer(forceQuad, 2);
  *forceQuad = ds->forceQuad;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSSetForceQuad - Set the flag to force matching quadratures among the field discretizations

  Logically collective on ds

  Input Parameters:
+ ds - The `PetscDS` object
- forceQuad - The flag

  Level: intermediate

.seealso: `PetscDS`, `PetscDSGetForceQuad()`, `PetscDSGetDiscretization()`, `PetscDSGetNumFields()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSSetForceQuad(PetscDS ds, PetscBool forceQuad)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  ds->forceQuad = forceQuad;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSIsCohesive - Returns the flag indicating that this `PetscDS` is for a cohesive cell

  Not Collective

  Input Parameter:
. ds - The `PetscDS` object

  Output Parameter:
. isCohesive - The flag

  Level: developer

.seealso: `PetscDS`, `PetscDSGetNumCohesive()`, `PetscDSGetCohesive()`, `PetscDSSetCohesive()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSIsCohesive(PetscDS ds, PetscBool *isCohesive)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  PetscValidBoolPointer(isCohesive, 2);
  *isCohesive = ds->isCohesive;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSGetNumCohesive - Returns the number of cohesive fields, meaning those defined on the interior of a cohesive cell

  Not Collective

  Input Parameter:
. ds - The `PetscDS` object

  Output Parameter:
. numCohesive - The number of cohesive fields

  Level: developer

.seealso: `PetscDS`, `PetscDSSetCohesive()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSGetNumCohesive(PetscDS ds, PetscInt *numCohesive)
{
  PetscInt f;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  PetscValidIntPointer(numCohesive, 2);
  *numCohesive = 0;
  for (f = 0; f < ds->Nf; ++f) *numCohesive += ds->cohesive[f] ? 1 : 0;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSGetCohesive - Returns the flag indicating that a field is cohesive, meaning it is defined on the interior of a cohesive cell

  Not Collective

  Input Parameters:
+ ds - The `PetscDS` object
- f  - The field index

  Output Parameter:
. isCohesive - The flag

  Level: developer

.seealso: `PetscDS`, `PetscDSSetCohesive()`, `PetscDSIsCohesive()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSGetCohesive(PetscDS ds, PetscInt f, PetscBool *isCohesive)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  PetscValidBoolPointer(isCohesive, 3);
  PetscCheck(!(f < 0) && !(f >= ds->Nf), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be in [0, %" PetscInt_FMT ")", f, ds->Nf);
  *isCohesive = ds->cohesive[f];
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSSetCohesive - Set the flag indicating that a field is cohesive, meaning it is defined on the interior of a cohesive cell

  Not Collective

  Input Parameters:
+ ds - The `PetscDS` object
. f  - The field index
- isCohesive - The flag for a cohesive field

  Level: developer

.seealso: `PetscDS`, `PetscDSGetCohesive()`, `PetscDSIsCohesive()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSSetCohesive(PetscDS ds, PetscInt f, PetscBool isCohesive)
{
  PetscInt i;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  PetscCheck(!(f < 0) && !(f >= ds->Nf), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be in [0, %" PetscInt_FMT ")", f, ds->Nf);
  ds->cohesive[f] = isCohesive;
  ds->isCohesive  = PETSC_FALSE;
  for (i = 0; i < ds->Nf; ++i) ds->isCohesive = ds->isCohesive || ds->cohesive[f] ? PETSC_TRUE : PETSC_FALSE;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSGetTotalDimension - Returns the total size of the approximation space for this system

  Not Collective

  Input Parameter:
. prob - The `PetscDS` object

  Output Parameter:
. dim - The total problem dimension

  Level: beginner

.seealso: `PetscDS`, `PetscDSGetNumFields()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSGetTotalDimension(PetscDS prob, PetscInt *dim)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  PetscCall(PetscDSSetUp(prob));
  PetscValidIntPointer(dim, 2);
  *dim = prob->totDim;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSGetTotalComponents - Returns the total number of components in this system

  Not Collective

  Input Parameter:
. prob - The `PetscDS` object

  Output Parameter:
. dim - The total number of components

  Level: beginner

.seealso: `PetscDS`, `PetscDSGetNumFields()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSGetTotalComponents(PetscDS prob, PetscInt *Nc)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  PetscCall(PetscDSSetUp(prob));
  PetscValidIntPointer(Nc, 2);
  *Nc = prob->totComp;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSGetDiscretization - Returns the discretization object for the given field

  Not Collective

  Input Parameters:
+ prob - The `PetscDS` object
- f - The field number

  Output Parameter:
. disc - The discretization object

  Level: beginner

.seealso: `PetscDS`, `PetscFE`, `PetscFV`, `PetscDSSetDiscretization()`, `PetscDSAddDiscretization()`, `PetscDSGetNumFields()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSGetDiscretization(PetscDS prob, PetscInt f, PetscObject *disc)
{
  PetscFunctionBeginHot;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  PetscValidPointer(disc, 3);
  PetscCheck(!(f < 0) && !(f >= prob->Nf), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be in [0, %" PetscInt_FMT ")", f, prob->Nf);
  *disc = prob->disc[f];
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSSetDiscretization - Sets the discretization object for the given field

  Not Collective

  Input Parameters:
+ prob - The `PetscDS` object
. f - The field number
- disc - The discretization object

  Level: beginner

.seealso: `PetscDS`, `PetscFE`, `PetscFV`, `PetscDSGetDiscretization()`, `PetscDSAddDiscretization()`, `PetscDSGetNumFields()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSSetDiscretization(PetscDS prob, PetscInt f, PetscObject disc)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  if (disc) PetscValidPointer(disc, 3);
  PetscCheck(f >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be non-negative", f);
  PetscCall(PetscDSEnlarge_Static(prob, f + 1));
  PetscCall(PetscObjectDereference(prob->disc[f]));
  prob->disc[f] = disc;
  PetscCall(PetscObjectReference(disc));
  if (disc) {
    PetscClassId id;

    PetscCall(PetscObjectGetClassId(disc, &id));
    if (id == PETSCFE_CLASSID) {
      PetscCall(PetscDSSetImplicit(prob, f, PETSC_TRUE));
    } else if (id == PETSCFV_CLASSID) {
      PetscCall(PetscDSSetImplicit(prob, f, PETSC_FALSE));
    }
    PetscCall(PetscDSSetJetDegree(prob, f, 1));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSGetWeakForm - Returns the weak form object

  Not Collective

  Input Parameter:
. ds - The `PetscDS` object

  Output Parameter:
. wf - The weak form object

  Level: beginner

.seealso: `PetscWeakForm`, `PetscDSSetWeakForm()`, `PetscDSGetNumFields()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSGetWeakForm(PetscDS ds, PetscWeakForm *wf)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  PetscValidPointer(wf, 2);
  *wf = ds->wf;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSSetWeakForm - Sets the weak form object

  Not Collective

  Input Parameters:
+ ds - The `PetscDS` object
- wf - The weak form object

  Level: beginner

.seealso: `PetscWeakForm`, `PetscDSGetWeakForm()`, `PetscDSGetNumFields()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSSetWeakForm(PetscDS ds, PetscWeakForm wf)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  PetscValidHeaderSpecific(wf, PETSCWEAKFORM_CLASSID, 2);
  PetscCall(PetscObjectDereference((PetscObject)ds->wf));
  ds->wf = wf;
  PetscCall(PetscObjectReference((PetscObject)wf));
  PetscCall(PetscWeakFormSetNumFields(wf, ds->Nf));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSAddDiscretization - Adds a discretization object

  Not Collective

  Input Parameters:
+ prob - The `PetscDS` object
- disc - The boundary discretization object

  Level: beginner

.seealso: `PetscWeakForm`, `PetscDSGetDiscretization()`, `PetscDSSetDiscretization()`, `PetscDSGetNumFields()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSAddDiscretization(PetscDS prob, PetscObject disc)
{
  PetscFunctionBegin;
  PetscCall(PetscDSSetDiscretization(prob, prob->Nf, disc));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSGetQuadrature - Returns the quadrature, which must agree for all fields in the `PetscDS`

  Not Collective

  Input Parameter:
. prob - The `PetscDS` object

  Output Parameter:
. q - The quadrature object

  Level: intermediate

.seealso: `PetscDS`, `PetscQuadrature`, `PetscDSSetImplicit()`, `PetscDSSetDiscretization()`, `PetscDSAddDiscretization()`, `PetscDSGetNumFields()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSGetQuadrature(PetscDS prob, PetscQuadrature *q)
{
  PetscObject  obj;
  PetscClassId id;

  PetscFunctionBegin;
  *q = NULL;
  if (!prob->Nf) PetscFunctionReturn(PETSC_SUCCESS);
  PetscCall(PetscDSGetDiscretization(prob, 0, &obj));
  PetscCall(PetscObjectGetClassId(obj, &id));
  if (id == PETSCFE_CLASSID) PetscCall(PetscFEGetQuadrature((PetscFE)obj, q));
  else if (id == PETSCFV_CLASSID) PetscCall(PetscFVGetQuadrature((PetscFV)obj, q));
  else SETERRQ(PetscObjectComm((PetscObject)prob), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", 0);
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSGetImplicit - Returns the flag for implicit solve for this field. This is just a guide for `TSIMEX`

  Not Collective

  Input Parameters:
+ prob - The `PetscDS` object
- f - The field number

  Output Parameter:
. implicit - The flag indicating what kind of solve to use for this field

  Level: developer

.seealso: `TSIMEX`, `PetscDS`, `PetscDSSetImplicit()`, `PetscDSSetDiscretization()`, `PetscDSAddDiscretization()`, `PetscDSGetNumFields()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSGetImplicit(PetscDS prob, PetscInt f, PetscBool *implicit)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  PetscValidBoolPointer(implicit, 3);
  PetscCheck(!(f < 0) && !(f >= prob->Nf), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be in [0, %" PetscInt_FMT ")", f, prob->Nf);
  *implicit = prob->implicit[f];
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSSetImplicit - Set the flag for implicit solve for this field. This is just a guide for `TSIMEX`

  Not Collective

  Input Parameters:
+ prob - The `PetscDS` object
. f - The field number
- implicit - The flag indicating what kind of solve to use for this field

  Level: developer

.seealso: `TSIMEX`, `PetscDSGetImplicit()`, `PetscDSSetDiscretization()`, `PetscDSAddDiscretization()`, `PetscDSGetNumFields()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSSetImplicit(PetscDS prob, PetscInt f, PetscBool implicit)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  PetscCheck(!(f < 0) && !(f >= prob->Nf), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be in [0, %" PetscInt_FMT ")", f, prob->Nf);
  prob->implicit[f] = implicit;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSGetJetDegree - Returns the highest derivative for this field equation, or the k-jet that the discretization needs to tabulate.

  Not Collective

  Input Parameters:
+ ds - The `PetscDS` object
- f  - The field number

  Output Parameter:
. k  - The highest derivative we need to tabulate

  Level: developer

.seealso: `PetscDS`, `PetscDSSetJetDegree()`, `PetscDSSetDiscretization()`, `PetscDSAddDiscretization()`, `PetscDSGetNumFields()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSGetJetDegree(PetscDS ds, PetscInt f, PetscInt *k)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  PetscValidIntPointer(k, 3);
  PetscCheck(!(f < 0) && !(f >= ds->Nf), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be in [0, %" PetscInt_FMT ")", f, ds->Nf);
  *k = ds->jetDegree[f];
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSSetJetDegree - Set the highest derivative for this field equation, or the k-jet that the discretization needs to tabulate.

  Not Collective

  Input Parameters:
+ ds - The `PetscDS` object
. f  - The field number
- k  - The highest derivative we need to tabulate

  Level: developer

.seealso: ``PetscDS`, PetscDSGetJetDegree()`, `PetscDSSetDiscretization()`, `PetscDSAddDiscretization()`, `PetscDSGetNumFields()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSSetJetDegree(PetscDS ds, PetscInt f, PetscInt k)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  PetscCheck(!(f < 0) && !(f >= ds->Nf), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be in [0, %" PetscInt_FMT ")", f, ds->Nf);
  ds->jetDegree[f] = k;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSGetObjective - Get the pointwise objective function for a given test field

  Not Collective

  Input Parameters:
+ ds - The `PetscDS`
- f  - The test field number

  Output Parameters:
. obj - integrand for the test function term

  Calling sequence of `obj`:
.vb
  void f0(PetscInt dim, PetscInt Nf, PetscInt NfAux,
          const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
          const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
          PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar obj[])
.ve
+ dim - the spatial dimension
. Nf - the number of fields
. uOff - the offset into u[] and u_t[] for each field
. uOff_x - the offset into u_x[] for each field
. u - each field evaluated at the current point
. u_t - the time derivative of each field evaluated at the current point
. u_x - the gradient of each field evaluated at the current point
. aOff - the offset into a[] and a_t[] for each auxiliary field
. aOff_x - the offset into a_x[] for each auxiliary field
. a - each auxiliary field evaluated at the current point
. a_t - the time derivative of each auxiliary field evaluated at the current point
. a_x - the gradient of auxiliary each field evaluated at the current point
. t - current time
. x - coordinates of the current point
. numConstants - number of constant parameters
. constants - constant parameters
- obj - output values at the current point

  Level: intermediate

  Note:
  We are using a first order FEM model for the weak form:  \int_\Omega \phi obj(u, u_t, \nabla u, x, t)

.seealso: `PetscDS`, `PetscDSSetObjective()`, `PetscDSGetResidual()`
@*/
PetscErrorCode PetscDSGetObjective(PetscDS ds, PetscInt f, void (**obj)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar obj[]))
{
  PetscPointFunc *tmp;
  PetscInt        n;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  PetscValidPointer(obj, 3);
  PetscCheck(!(f < 0) && !(f >= ds->Nf), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be in [0, %" PetscInt_FMT ")", f, ds->Nf);
  PetscCall(PetscWeakFormGetObjective(ds->wf, NULL, 0, f, 0, &n, &tmp));
  *obj = tmp ? tmp[0] : NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSSetObjective - Set the pointwise objective function for a given test field

  Not Collective

  Input Parameters:
+ ds  - The `PetscDS`
. f   - The test field number
- obj - integrand for the test function term

  Calling sequence of `obj`:
.vb
  void f0(PetscInt dim, PetscInt Nf, PetscInt NfAux,
          const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
          const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
          PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar obj[])
.ve
+ dim - the spatial dimension
. Nf - the number of fields
. uOff - the offset into u[] and u_t[] for each field
. uOff_x - the offset into u_x[] for each field
. u - each field evaluated at the current point
. u_t - the time derivative of each field evaluated at the current point
. u_x - the gradient of each field evaluated at the current point
. aOff - the offset into a[] and a_t[] for each auxiliary field
. aOff_x - the offset into a_x[] for each auxiliary field
. a - each auxiliary field evaluated at the current point
. a_t - the time derivative of each auxiliary field evaluated at the current point
. a_x - the gradient of auxiliary each field evaluated at the current point
. t - current time
. x - coordinates of the current point
. numConstants - number of constant parameters
. constants - constant parameters
- obj - output values at the current point

  Level: intermediate

  Note:
  We are using a first order FEM model for the weak form:  \int_\Omega \phi obj(u, u_t, \nabla u, x, t)

.seealso: `PetscDS`, `PetscDSGetObjective()`, `PetscDSSetResidual()`
@*/
PetscErrorCode PetscDSSetObjective(PetscDS ds, PetscInt f, void (*obj)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar obj[]))
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  if (obj) PetscValidFunction(obj, 3);
  PetscCheck(f >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be non-negative", f);
  PetscCall(PetscWeakFormSetIndexObjective(ds->wf, NULL, 0, f, 0, 0, obj));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSGetResidual - Get the pointwise residual function for a given test field

  Not Collective

  Input Parameters:
+ ds - The `PetscDS`
- f  - The test field number

  Output Parameters:
+ f0 - integrand for the test function term
- f1 - integrand for the test function gradient term

  Calling sequence of `f0` and `f1`:
.vb
  void f0(PetscInt dim, PetscInt Nf, PetscInt NfAux,
          const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
          const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
          PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
.ve
+ dim - the spatial dimension
. Nf - the number of fields
. uOff - the offset into u[] and u_t[] for each field
. uOff_x - the offset into u_x[] for each field
. u - each field evaluated at the current point
. u_t - the time derivative of each field evaluated at the current point
. u_x - the gradient of each field evaluated at the current point
. aOff - the offset into a[] and a_t[] for each auxiliary field
. aOff_x - the offset into a_x[] for each auxiliary field
. a - each auxiliary field evaluated at the current point
. a_t - the time derivative of each auxiliary field evaluated at the current point
. a_x - the gradient of auxiliary each field evaluated at the current point
. t - current time
. x - coordinates of the current point
. numConstants - number of constant parameters
. constants - constant parameters
- f0 - output values at the current point

  Level: intermediate

  Note:
  We are using a first order FEM model for the weak form:  \int_\Omega \phi f_0(u, u_t, \nabla u, x, t) + \nabla\phi \cdot {\vec f}_1(u, u_t, \nabla u, x, t)

.seealso: `PetscDS`, `PetscDSSetResidual()`
@*/
PetscErrorCode PetscDSGetResidual(PetscDS ds, PetscInt f, void (**f0)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]), void (**f1)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[]))
{
  PetscPointFunc *tmp0, *tmp1;
  PetscInt        n0, n1;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  PetscCheck(!(f < 0) && !(f >= ds->Nf), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be in [0, %" PetscInt_FMT ")", f, ds->Nf);
  PetscCall(PetscWeakFormGetResidual(ds->wf, NULL, 0, f, 0, &n0, &tmp0, &n1, &tmp1));
  *f0 = tmp0 ? tmp0[0] : NULL;
  *f1 = tmp1 ? tmp1[0] : NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSSetResidual - Set the pointwise residual function for a given test field

  Not Collective

  Input Parameters:
+ ds - The `PetscDS`
. f  - The test field number
. f0 - integrand for the test function term
- f1 - integrand for the test function gradient term

  Calling sequence of `f0` and `f1`:
.vb
  void f0(PetscInt dim, PetscInt Nf, PetscInt NfAux,
          const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
          const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
          PetscReal t, const PetscReal x[], PetscScalar f0[])
.ve
+ dim - the spatial dimension
. Nf - the number of fields
. uOff - the offset into u[] and u_t[] for each field
. uOff_x - the offset into u_x[] for each field
. u - each field evaluated at the current point
. u_t - the time derivative of each field evaluated at the current point
. u_x - the gradient of each field evaluated at the current point
. aOff - the offset into a[] and a_t[] for each auxiliary field
. aOff_x - the offset into a_x[] for each auxiliary field
. a - each auxiliary field evaluated at the current point
. a_t - the time derivative of each auxiliary field evaluated at the current point
. a_x - the gradient of auxiliary each field evaluated at the current point
. t - current time
. x - coordinates of the current point
. numConstants - number of constant parameters
. constants - constant parameters
- f0 - output values at the current point

  Level: intermediate

  Note:
  We are using a first order FEM model for the weak form:  \int_\Omega \phi f_0(u, u_t, \nabla u, x, t) + \nabla\phi \cdot {\vec f}_1(u, u_t, \nabla u, x, t)

.seealso: `PetscDS`, `PetscDSGetResidual()`
@*/
PetscErrorCode PetscDSSetResidual(PetscDS ds, PetscInt f, void (*f0)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]), void (*f1)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[]))
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  if (f0) PetscValidFunction(f0, 3);
  if (f1) PetscValidFunction(f1, 4);
  PetscCheck(f >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be non-negative", f);
  PetscCall(PetscWeakFormSetIndexResidual(ds->wf, NULL, 0, f, 0, 0, f0, 0, f1));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSGetRHSResidual - Get the pointwise RHS residual function for explicit timestepping for a given test field

  Not Collective

  Input Parameters:
+ ds - The `PetscDS`
- f  - The test field number

  Output Parameters:
+ f0 - integrand for the test function term
- f1 - integrand for the test function gradient term

  Calling sequence of `f0` and `f1`:
.vb
  void f0(PetscInt dim, PetscInt Nf, PetscInt NfAux,
          const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
          const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
          PetscReal t, const PetscReal x[], PetscScalar f0[])
.ve
+ dim - the spatial dimension
. Nf - the number of fields
. uOff - the offset into u[] and u_t[] for each field
. uOff_x - the offset into u_x[] for each field
. u - each field evaluated at the current point
. u_t - the time derivative of each field evaluated at the current point
. u_x - the gradient of each field evaluated at the current point
. aOff - the offset into a[] and a_t[] for each auxiliary field
. aOff_x - the offset into a_x[] for each auxiliary field
. a - each auxiliary field evaluated at the current point
. a_t - the time derivative of each auxiliary field evaluated at the current point
. a_x - the gradient of auxiliary each field evaluated at the current point
. t - current time
. x - coordinates of the current point
. numConstants - number of constant parameters
. constants - constant parameters
- f0 - output values at the current point

  Level: intermediate

  Note:
  We are using a first order FEM model for the weak form: \int_\Omega \phi f_0(u, u_t, \nabla u, x, t) + \nabla\phi \cdot {\vec f}_1(u, u_t, \nabla u, x, t)

.seealso: `PetscDS`, `PetscDSSetRHSResidual()`
@*/
PetscErrorCode PetscDSGetRHSResidual(PetscDS ds, PetscInt f, void (**f0)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]), void (**f1)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[]))
{
  PetscPointFunc *tmp0, *tmp1;
  PetscInt        n0, n1;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  PetscCheck(!(f < 0) && !(f >= ds->Nf), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be in [0, %" PetscInt_FMT ")", f, ds->Nf);
  PetscCall(PetscWeakFormGetResidual(ds->wf, NULL, 0, f, 100, &n0, &tmp0, &n1, &tmp1));
  *f0 = tmp0 ? tmp0[0] : NULL;
  *f1 = tmp1 ? tmp1[0] : NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSSetRHSResidual - Set the pointwise residual function for explicit timestepping for a given test field

  Not Collective

  Input Parameters:
+ ds - The `PetscDS`
. f  - The test field number
. f0 - integrand for the test function term
- f1 - integrand for the test function gradient term

  Clling sequence for the callbacks f0 and f1:
.vb
  f0(PetscInt dim, PetscInt Nf, PetscInt NfAux,
     const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
     const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
     PetscReal t, const PetscReal x[], PetscScalar f0[])
.ve
+ dim - the spatial dimension
. Nf - the number of fields
. uOff - the offset into u[] and u_t[] for each field
. uOff_x - the offset into u_x[] for each field
. u - each field evaluated at the current point
. u_t - the time derivative of each field evaluated at the current point
. u_x - the gradient of each field evaluated at the current point
. aOff - the offset into a[] and a_t[] for each auxiliary field
. aOff_x - the offset into a_x[] for each auxiliary field
. a - each auxiliary field evaluated at the current point
. a_t - the time derivative of each auxiliary field evaluated at the current point
. a_x - the gradient of auxiliary each field evaluated at the current point
. t - current time
. x - coordinates of the current point
. numConstants - number of constant parameters
. constants - constant parameters
- f0 - output values at the current point

  Level: intermediate

  Note:
  We are using a first order FEM model for the weak form:  \int_\Omega \phi f_0(u, u_t, \nabla u, x, t) + \nabla\phi \cdot {\vec f}_1(u, u_t, \nabla u, x, t)

.seealso: `PetscDS`, `PetscDSGetResidual()`
@*/
PetscErrorCode PetscDSSetRHSResidual(PetscDS ds, PetscInt f, void (*f0)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]), void (*f1)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[]))
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  if (f0) PetscValidFunction(f0, 3);
  if (f1) PetscValidFunction(f1, 4);
  PetscCheck(f >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be non-negative", f);
  PetscCall(PetscWeakFormSetIndexResidual(ds->wf, NULL, 0, f, 100, 0, f0, 0, f1));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSHasJacobian - Checks that the Jacobian functions have been set

  Not Collective

  Input Parameter:
. prob - The `PetscDS`

  Output Parameter:
. hasJac - flag that pointwise function for the Jacobian has been set

  Level: intermediate

.seealso: `PetscDS`, `PetscDSGetJacobianPreconditioner()`, `PetscDSSetJacobianPreconditioner()`, `PetscDSGetJacobian()`
@*/
PetscErrorCode PetscDSHasJacobian(PetscDS ds, PetscBool *hasJac)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  PetscCall(PetscWeakFormHasJacobian(ds->wf, hasJac));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSGetJacobian - Get the pointwise Jacobian function for given test and basis field

  Not Collective

  Input Parameters:
+ ds - The `PetscDS`
. f  - The test field number
- g  - The field number

  Output Parameters:
+ g0 - integrand for the test and basis function term
. g1 - integrand for the test function and basis function gradient term
. g2 - integrand for the test function gradient and basis function term
- g3 - integrand for the test function gradient and basis function gradient term

  Calling sequence of `g0`, `g1`, `g2` and `g3`:
.vb
  void g0(PetscInt dim, PetscInt Nf, PetscInt NfAux,
          const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
          const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
          PetscReal t, const PetscReal u_tShift, const PetscReal x[], PetscScalar g0[])
.ve
+ dim - the spatial dimension
. Nf - the number of fields
. uOff - the offset into u[] and u_t[] for each field
. uOff_x - the offset into u_x[] for each field
. u - each field evaluated at the current point
. u_t - the time derivative of each field evaluated at the current point
. u_x - the gradient of each field evaluated at the current point
. aOff - the offset into a[] and a_t[] for each auxiliary field
. aOff_x - the offset into a_x[] for each auxiliary field
. a - each auxiliary field evaluated at the current point
. a_t - the time derivative of each auxiliary field evaluated at the current point
. a_x - the gradient of auxiliary each field evaluated at the current point
. t - current time
. u_tShift - the multiplier a for dF/dU_t
. x - coordinates of the current point
. numConstants - number of constant parameters
. constants - constant parameters
- g0 - output values at the current point

  Level: intermediate

  Note:
  We are using a first order FEM model for the weak form:
  \int_\Omega \phi g_0(u, u_t, \nabla u, x, t) \psi + \phi {\vec g}_1(u, u_t, \nabla u, x, t) \nabla \psi + \nabla\phi \cdot {\vec g}_2(u, u_t, \nabla u, x, t) \psi + \nabla\phi \cdot {\overleftrightarrow g}_3(u, u_t, \nabla u, x, t) \cdot \nabla \psi

.seealso: `PetscDS`, `PetscDSSetJacobian()`
@*/
PetscErrorCode PetscDSGetJacobian(PetscDS ds, PetscInt f, PetscInt g, void (**g0)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[]), void (**g1)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g1[]), void (**g2)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g2[]), void (**g3)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[]))
{
  PetscPointJac *tmp0, *tmp1, *tmp2, *tmp3;
  PetscInt       n0, n1, n2, n3;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  PetscCheck(!(f < 0) && !(f >= ds->Nf), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be in [0, %" PetscInt_FMT ")", f, ds->Nf);
  PetscCheck(!(g < 0) && !(g >= ds->Nf), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be in [0, %" PetscInt_FMT ")", g, ds->Nf);
  PetscCall(PetscWeakFormGetJacobian(ds->wf, NULL, 0, f, g, 0, &n0, &tmp0, &n1, &tmp1, &n2, &tmp2, &n3, &tmp3));
  *g0 = tmp0 ? tmp0[0] : NULL;
  *g1 = tmp1 ? tmp1[0] : NULL;
  *g2 = tmp2 ? tmp2[0] : NULL;
  *g3 = tmp3 ? tmp3[0] : NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSSetJacobian - Set the pointwise Jacobian function for given test and basis fields

  Not Collective

  Input Parameters:
+ ds - The `PetscDS`
. f  - The test field number
. g  - The field number
. g0 - integrand for the test and basis function term
. g1 - integrand for the test function and basis function gradient term
. g2 - integrand for the test function gradient and basis function term
- g3 - integrand for the test function gradient and basis function gradient term

  Calling sequence of `g0`, `g1`, `g2` and `g3`:
.vb
  void g0(PetscInt dim, PetscInt Nf, PetscInt NfAux,
          const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
          const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
          PetscReal t, const PetscReal x[], PetscScalar g0[])
.ve
+ dim - the spatial dimension
. Nf - the number of fields
. uOff - the offset into u[] and u_t[] for each field
. uOff_x - the offset into u_x[] for each field
. u - each field evaluated at the current point
. u_t - the time derivative of each field evaluated at the current point
. u_x - the gradient of each field evaluated at the current point
. aOff - the offset into a[] and a_t[] for each auxiliary field
. aOff_x - the offset into a_x[] for each auxiliary field
. a - each auxiliary field evaluated at the current point
. a_t - the time derivative of each auxiliary field evaluated at the current point
. a_x - the gradient of auxiliary each field evaluated at the current point
. t - current time
. u_tShift - the multiplier a for dF/dU_t
. x - coordinates of the current point
. numConstants - number of constant parameters
. constants - constant parameters
- g0 - output values at the current point

  Level: intermediate

  Note:
   We are using a first order FEM model for the weak form:
  \int_\Omega \phi g_0(u, u_t, \nabla u, x, t) \psi + \phi {\vec g}_1(u, u_t, \nabla u, x, t) \nabla \psi + \nabla\phi \cdot {\vec g}_2(u, u_t, \nabla u, x, t) \psi + \nabla\phi \cdot {\overleftrightarrow g}_3(u, u_t, \nabla u, x, t) \cdot \nabla \psi

.seealso: `PetscDS`, `PetscDSGetJacobian()`
@*/
PetscErrorCode PetscDSSetJacobian(PetscDS ds, PetscInt f, PetscInt g, void (*g0)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[]), void (*g1)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g1[]), void (*g2)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g2[]), void (*g3)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[]))
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  if (g0) PetscValidFunction(g0, 4);
  if (g1) PetscValidFunction(g1, 5);
  if (g2) PetscValidFunction(g2, 6);
  if (g3) PetscValidFunction(g3, 7);
  PetscCheck(f >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be non-negative", f);
  PetscCheck(g >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be non-negative", g);
  PetscCall(PetscWeakFormSetIndexJacobian(ds->wf, NULL, 0, f, g, 0, 0, g0, 0, g1, 0, g2, 0, g3));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSUseJacobianPreconditioner - Set whether to construct a Jacobian preconditioner

  Not Collective

  Input Parameters:
+ prob - The `PetscDS`
- useJacPre - flag that enables construction of a Jacobian preconditioner

  Level: intermediate

.seealso: `PetscDS`, `PetscDSGetJacobianPreconditioner()`, `PetscDSSetJacobianPreconditioner()`, `PetscDSGetJacobian()`
@*/
PetscErrorCode PetscDSUseJacobianPreconditioner(PetscDS prob, PetscBool useJacPre)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  prob->useJacPre = useJacPre;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSHasJacobianPreconditioner - Checks if a Jacobian preconditioner matrix has been set

  Not Collective

  Input Parameter:
. prob - The `PetscDS`

  Output Parameter:
. hasJacPre - flag that pointwise function for Jacobian preconditioner matrix has been set

  Level: intermediate

.seealso: `PetscDS`, `PetscDSGetJacobianPreconditioner()`, `PetscDSSetJacobianPreconditioner()`, `PetscDSGetJacobian()`
@*/
PetscErrorCode PetscDSHasJacobianPreconditioner(PetscDS ds, PetscBool *hasJacPre)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  *hasJacPre = PETSC_FALSE;
  if (!ds->useJacPre) PetscFunctionReturn(PETSC_SUCCESS);
  PetscCall(PetscWeakFormHasJacobianPreconditioner(ds->wf, hasJacPre));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSGetJacobianPreconditioner - Get the pointwise Jacobian preconditioner function for given test and basis field. If this is missing,
   the system matrix is used to build the preconditioner.

  Not Collective

  Input Parameters:
+ ds - The `PetscDS`
. f  - The test field number
- g  - The field number

  Output Parameters:
+ g0 - integrand for the test and basis function term
. g1 - integrand for the test function and basis function gradient term
. g2 - integrand for the test function gradient and basis function term
- g3 - integrand for the test function gradient and basis function gradient term

  Calling sequence of `g0`, `g1`, `g2` and `g3`:
.vb
  void g0(PetscInt dim, PetscInt Nf, PetscInt NfAux,
          const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
          const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
          PetscReal t, const PetscReal u_tShift, const PetscReal x[], PetscScalar g0[])
.ve
+ dim - the spatial dimension
. Nf - the number of fields
. uOff - the offset into u[] and u_t[] for each field
. uOff_x - the offset into u_x[] for each field
. u - each field evaluated at the current point
. u_t - the time derivative of each field evaluated at the current point
. u_x - the gradient of each field evaluated at the current point
. aOff - the offset into a[] and a_t[] for each auxiliary field
. aOff_x - the offset into a_x[] for each auxiliary field
. a - each auxiliary field evaluated at the current point
. a_t - the time derivative of each auxiliary field evaluated at the current point
. a_x - the gradient of auxiliary each field evaluated at the current point
. t - current time
. u_tShift - the multiplier a for dF/dU_t
. x - coordinates of the current point
. numConstants - number of constant parameters
. constants - constant parameters
- g0 - output values at the current point

  Level: intermediate

  Note:
  We are using a first order FEM model for the weak form:
  \int_\Omega \phi g_0(u, u_t, \nabla u, x, t) \psi + \phi {\vec g}_1(u, u_t, \nabla u, x, t) \nabla \psi + \nabla\phi \cdot {\vec g}_2(u, u_t, \nabla u, x, t) \psi + \nabla\phi \cdot {\overleftrightarrow g}_3(u, u_t, \nabla u, x, t) \cdot \nabla \psi

.seealso: `PetscDS`, `PetscDSSetJacobianPreconditioner()`, `PetscDSGetJacobian()`
@*/
PetscErrorCode PetscDSGetJacobianPreconditioner(PetscDS ds, PetscInt f, PetscInt g, void (**g0)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[]), void (**g1)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g1[]), void (**g2)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g2[]), void (**g3)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[]))
{
  PetscPointJac *tmp0, *tmp1, *tmp2, *tmp3;
  PetscInt       n0, n1, n2, n3;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  PetscCheck(!(f < 0) && !(f >= ds->Nf), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be in [0, %" PetscInt_FMT ")", f, ds->Nf);
  PetscCheck(!(g < 0) && !(g >= ds->Nf), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be in [0, %" PetscInt_FMT ")", g, ds->Nf);
  PetscCall(PetscWeakFormGetJacobianPreconditioner(ds->wf, NULL, 0, f, g, 0, &n0, &tmp0, &n1, &tmp1, &n2, &tmp2, &n3, &tmp3));
  *g0 = tmp0 ? tmp0[0] : NULL;
  *g1 = tmp1 ? tmp1[0] : NULL;
  *g2 = tmp2 ? tmp2[0] : NULL;
  *g3 = tmp3 ? tmp3[0] : NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSSetJacobianPreconditioner - Set the pointwise Jacobian preconditioner function for given test and basis fields.
  If this is missing, the system matrix is used to build the preconditioner.

  Not Collective

  Input Parameters:
+ ds - The `PetscDS`
. f  - The test field number
. g  - The field number
. g0 - integrand for the test and basis function term
. g1 - integrand for the test function and basis function gradient term
. g2 - integrand for the test function gradient and basis function term
- g3 - integrand for the test function gradient and basis function gradient term

  Calling sequence of `g0`, `g1`, `g2` and `g3`:
.vb
  void g0(PetscInt dim, PetscInt Nf, PetscInt NfAux,
          const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
          const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
          PetscReal t, const PetscReal x[], PetscScalar g0[])
.ve
+ dim - the spatial dimension
. Nf - the number of fields
. uOff - the offset into u[] and u_t[] for each field
. uOff_x - the offset into u_x[] for each field
. u - each field evaluated at the current point
. u_t - the time derivative of each field evaluated at the current point
. u_x - the gradient of each field evaluated at the current point
. aOff - the offset into a[] and a_t[] for each auxiliary field
. aOff_x - the offset into a_x[] for each auxiliary field
. a - each auxiliary field evaluated at the current point
. a_t - the time derivative of each auxiliary field evaluated at the current point
. a_x - the gradient of auxiliary each field evaluated at the current point
. t - current time
. u_tShift - the multiplier a for dF/dU_t
. x - coordinates of the current point
. numConstants - number of constant parameters
. constants - constant parameters
- g0 - output values at the current point

  Level: intermediate

  Note:
  We are using a first order FEM model for the weak form:
  \int_\Omega \phi g_0(u, u_t, \nabla u, x, t) \psi + \phi {\vec g}_1(u, u_t, \nabla u, x, t) \nabla \psi + \nabla\phi \cdot {\vec g}_2(u, u_t, \nabla u, x, t) \psi + \nabla\phi \cdot {\overleftrightarrow g}_3(u, u_t, \nabla u, x, t) \cdot \nabla \psi

.seealso: `PetscDS`, `PetscDSGetJacobianPreconditioner()`, `PetscDSSetJacobian()`
@*/
PetscErrorCode PetscDSSetJacobianPreconditioner(PetscDS ds, PetscInt f, PetscInt g, void (*g0)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[]), void (*g1)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g1[]), void (*g2)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g2[]), void (*g3)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[]))
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  if (g0) PetscValidFunction(g0, 4);
  if (g1) PetscValidFunction(g1, 5);
  if (g2) PetscValidFunction(g2, 6);
  if (g3) PetscValidFunction(g3, 7);
  PetscCheck(f >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be non-negative", f);
  PetscCheck(g >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be non-negative", g);
  PetscCall(PetscWeakFormSetIndexJacobianPreconditioner(ds->wf, NULL, 0, f, g, 0, 0, g0, 0, g1, 0, g2, 0, g3));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSHasDynamicJacobian - Signals that a dynamic Jacobian, dF/du_t, has been set

  Not Collective

  Input Parameter:
. ds - The `PetscDS`

  Output Parameter:
. hasDynJac - flag that pointwise function for dynamic Jacobian has been set

  Level: intermediate

.seealso: `PetscDS`, `PetscDSGetDynamicJacobian()`, `PetscDSSetDynamicJacobian()`, `PetscDSGetJacobian()`
@*/
PetscErrorCode PetscDSHasDynamicJacobian(PetscDS ds, PetscBool *hasDynJac)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  PetscCall(PetscWeakFormHasDynamicJacobian(ds->wf, hasDynJac));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSGetDynamicJacobian - Get the pointwise dynamic Jacobian, dF/du_t, function for given test and basis field

  Not Collective

  Input Parameters:
+ ds - The `PetscDS`
. f  - The test field number
- g  - The field number

  Output Parameters:
+ g0 - integrand for the test and basis function term
. g1 - integrand for the test function and basis function gradient term
. g2 - integrand for the test function gradient and basis function term
- g3 - integrand for the test function gradient and basis function gradient term

   Calling sequence of `g0`, `g1`, `g2` and `g3`:
.vb
  void g0(PetscInt dim, PetscInt Nf, PetscInt NfAux,
          const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
          const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
          PetscReal t, const PetscReal u_tShift, const PetscReal x[], PetscScalar g0[])
.ve
+ dim - the spatial dimension
. Nf - the number of fields
. uOff - the offset into u[] and u_t[] for each field
. uOff_x - the offset into u_x[] for each field
. u - each field evaluated at the current point
. u_t - the time derivative of each field evaluated at the current point
. u_x - the gradient of each field evaluated at the current point
. aOff - the offset into a[] and a_t[] for each auxiliary field
. aOff_x - the offset into a_x[] for each auxiliary field
. a - each auxiliary field evaluated at the current point
. a_t - the time derivative of each auxiliary field evaluated at the current point
. a_x - the gradient of auxiliary each field evaluated at the current point
. t - current time
. u_tShift - the multiplier a for dF/dU_t
. x - coordinates of the current point
. numConstants - number of constant parameters
. constants - constant parameters
- g0 - output values at the current point

  Level: intermediate

  Note:
  We are using a first order FEM model for the weak form:
  \int_\Omega \phi g_0(u, u_t, \nabla u, x, t) \psi + \phi {\vec g}_1(u, u_t, \nabla u, x, t) \nabla \psi + \nabla\phi \cdot {\vec g}_2(u, u_t, \nabla u, x, t) \psi + \nabla\phi \cdot {\overleftrightarrow g}_3(u, u_t, \nabla u, x, t) \cdot \nabla \psi

.seealso: `PetscDS`, `PetscDSSetJacobian()`
@*/
PetscErrorCode PetscDSGetDynamicJacobian(PetscDS ds, PetscInt f, PetscInt g, void (**g0)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[]), void (**g1)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g1[]), void (**g2)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g2[]), void (**g3)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[]))
{
  PetscPointJac *tmp0, *tmp1, *tmp2, *tmp3;
  PetscInt       n0, n1, n2, n3;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  PetscCheck(!(f < 0) && !(f >= ds->Nf), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be in [0, %" PetscInt_FMT ")", f, ds->Nf);
  PetscCheck(!(g < 0) && !(g >= ds->Nf), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be in [0, %" PetscInt_FMT ")", g, ds->Nf);
  PetscCall(PetscWeakFormGetDynamicJacobian(ds->wf, NULL, 0, f, g, 0, &n0, &tmp0, &n1, &tmp1, &n2, &tmp2, &n3, &tmp3));
  *g0 = tmp0 ? tmp0[0] : NULL;
  *g1 = tmp1 ? tmp1[0] : NULL;
  *g2 = tmp2 ? tmp2[0] : NULL;
  *g3 = tmp3 ? tmp3[0] : NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSSetDynamicJacobian - Set the pointwise dynamic Jacobian, dF/du_t, function for given test and basis fields

  Not Collective

  Input Parameters:
+ ds - The `PetscDS`
. f  - The test field number
. g  - The field number
. g0 - integrand for the test and basis function term
. g1 - integrand for the test function and basis function gradient term
. g2 - integrand for the test function gradient and basis function term
- g3 - integrand for the test function gradient and basis function gradient term

  Calling sequence of `g0`, `g1`, `g2` and `g3`:
.vb
   void g0(PetscInt dim, PetscInt Nf, PetscInt NfAux,
           const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
           const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
           PetscReal t, const PetscReal x[], PetscScalar g0[])
.ve
+ dim - the spatial dimension
. Nf - the number of fields
. uOff - the offset into u[] and u_t[] for each field
. uOff_x - the offset into u_x[] for each field
. u - each field evaluated at the current point
. u_t - the time derivative of each field evaluated at the current point
. u_x - the gradient of each field evaluated at the current point
. aOff - the offset into a[] and a_t[] for each auxiliary field
. aOff_x - the offset into a_x[] for each auxiliary field
. a - each auxiliary field evaluated at the current point
. a_t - the time derivative of each auxiliary field evaluated at the current point
. a_x - the gradient of auxiliary each field evaluated at the current point
. t - current time
. u_tShift - the multiplier a for dF/dU_t
. x - coordinates of the current point
. numConstants - number of constant parameters
. constants - constant parameters
- g0 - output values at the current point

  Level: intermediate

  Note:
  We are using a first order FEM model for the weak form:
  \int_\Omega \phi g_0(u, u_t, \nabla u, x, t) \psi + \phi {\vec g}_1(u, u_t, \nabla u, x, t) \nabla \psi + \nabla\phi \cdot {\vec g}_2(u, u_t, \nabla u, x, t) \psi + \nabla\phi \cdot {\overleftrightarrow g}_3(u, u_t, \nabla u, x, t) \cdot \nabla \psi

.seealso: `PetscDS`, `PetscDSGetJacobian()`
@*/
PetscErrorCode PetscDSSetDynamicJacobian(PetscDS ds, PetscInt f, PetscInt g, void (*g0)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[]), void (*g1)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g1[]), void (*g2)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g2[]), void (*g3)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[]))
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  if (g0) PetscValidFunction(g0, 4);
  if (g1) PetscValidFunction(g1, 5);
  if (g2) PetscValidFunction(g2, 6);
  if (g3) PetscValidFunction(g3, 7);
  PetscCheck(f >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be non-negative", f);
  PetscCheck(g >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be non-negative", g);
  PetscCall(PetscWeakFormSetIndexDynamicJacobian(ds->wf, NULL, 0, f, g, 0, 0, g0, 0, g1, 0, g2, 0, g3));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSGetRiemannSolver - Returns the Riemann solver for the given field

  Not Collective

  Input Parameters:
+ ds - The `PetscDS` object
- f  - The field number

  Output Parameter:
. r    - Riemann solver

  Calling sequence of `r`:
.vb
  void r(PetscInt dim, PetscInt Nf, const PetscReal x[], const PetscReal n[], const PetscScalar uL[], const PetscScalar uR[], PetscScalar flux[], void *ctx)
.ve
+ dim  - The spatial dimension
. Nf   - The number of fields
. x    - The coordinates at a point on the interface
. n    - The normal vector to the interface
. uL   - The state vector to the left of the interface
. uR   - The state vector to the right of the interface
. flux - output array of flux through the interface
. numConstants - number of constant parameters
. constants - constant parameters
- ctx  - optional user context

  Level: intermediate

.seealso: `PetscDS`, `PetscDSSetRiemannSolver()`
@*/
PetscErrorCode PetscDSGetRiemannSolver(PetscDS ds, PetscInt f, void (**r)(PetscInt dim, PetscInt Nf, const PetscReal x[], const PetscReal n[], const PetscScalar uL[], const PetscScalar uR[], PetscInt numConstants, const PetscScalar constants[], PetscScalar flux[], void *ctx))
{
  PetscRiemannFunc *tmp;
  PetscInt          n;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  PetscValidPointer(r, 3);
  PetscCheck(!(f < 0) && !(f >= ds->Nf), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be in [0, %" PetscInt_FMT ")", f, ds->Nf);
  PetscCall(PetscWeakFormGetRiemannSolver(ds->wf, NULL, 0, f, 0, &n, &tmp));
  *r = tmp ? tmp[0] : NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSSetRiemannSolver - Sets the Riemann solver for the given field

  Not Collective

  Input Parameters:
+ ds - The `PetscDS` object
. f  - The field number
- r  - Riemann solver

  Calling sequence of `r`:
.vb
   void r(PetscInt dim, PetscInt Nf, const PetscReal x[], const PetscReal n[], const PetscScalar uL[], const PetscScalar uR[], PetscScalar flux[], void *ctx)
.ve
+ dim  - The spatial dimension
. Nf   - The number of fields
. x    - The coordinates at a point on the interface
. n    - The normal vector to the interface
. uL   - The state vector to the left of the interface
. uR   - The state vector to the right of the interface
. flux - output array of flux through the interface
. numConstants - number of constant parameters
. constants - constant parameters
- ctx  - optional user context

  Level: intermediate

.seealso: `PetscDS`, `PetscDSGetRiemannSolver()`
@*/
PetscErrorCode PetscDSSetRiemannSolver(PetscDS ds, PetscInt f, void (*r)(PetscInt dim, PetscInt Nf, const PetscReal x[], const PetscReal n[], const PetscScalar uL[], const PetscScalar uR[], PetscInt numConstants, const PetscScalar constants[], PetscScalar flux[], void *ctx))
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  if (r) PetscValidFunction(r, 3);
  PetscCheck(f >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be non-negative", f);
  PetscCall(PetscWeakFormSetIndexRiemannSolver(ds->wf, NULL, 0, f, 0, 0, r));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSGetUpdate - Get the pointwise update function for a given field

  Not Collective

  Input Parameters:
+ ds - The `PetscDS`
- f  - The field number

  Output Parameter:
. update - update function

  Calling sequence of `update`:
.vb
  void update(PetscInt dim, PetscInt Nf, PetscInt NfAux,
              const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
              const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
              PetscReal t, const PetscReal x[], PetscScalar uNew[])
.ve
+ dim - the spatial dimension
. Nf - the number of fields
. uOff - the offset into u[] and u_t[] for each field
. uOff_x - the offset into u_x[] for each field
. u - each field evaluated at the current point
. u_t - the time derivative of each field evaluated at the current point
. u_x - the gradient of each field evaluated at the current point
. aOff - the offset into a[] and a_t[] for each auxiliary field
. aOff_x - the offset into a_x[] for each auxiliary field
. a - each auxiliary field evaluated at the current point
. a_t - the time derivative of each auxiliary field evaluated at the current point
. a_x - the gradient of auxiliary each field evaluated at the current point
. t - current time
. x - coordinates of the current point
- uNew - new value for field at the current point

  Level: intermediate

.seealso: `PetscDS`, `PetscDSSetUpdate()`, `PetscDSSetResidual()`
@*/
PetscErrorCode PetscDSGetUpdate(PetscDS ds, PetscInt f, void (**update)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar uNew[]))
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  PetscCheck(!(f < 0) && !(f >= ds->Nf), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be in [0, %" PetscInt_FMT ")", f, ds->Nf);
  if (update) {
    PetscValidPointer(update, 3);
    *update = ds->update[f];
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSSetUpdate - Set the pointwise update function for a given field

  Not Collective

  Input Parameters:
+ ds     - The `PetscDS`
. f      - The field number
- update - update function

  Calling sequence of `update`:
.vb
  void update(PetscInt dim, PetscInt Nf, PetscInt NfAux,
              const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
              const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
              PetscReal t, const PetscReal x[], PetscScalar uNew[])
.ve
+ dim - the spatial dimension
. Nf - the number of fields
. uOff - the offset into u[] and u_t[] for each field
. uOff_x - the offset into u_x[] for each field
. u - each field evaluated at the current point
. u_t - the time derivative of each field evaluated at the current point
. u_x - the gradient of each field evaluated at the current point
. aOff - the offset into a[] and a_t[] for each auxiliary field
. aOff_x - the offset into a_x[] for each auxiliary field
. a - each auxiliary field evaluated at the current point
. a_t - the time derivative of each auxiliary field evaluated at the current point
. a_x - the gradient of auxiliary each field evaluated at the current point
. t - current time
. x - coordinates of the current point
- uNew - new field values at the current point

  Level: intermediate

.seealso: `PetscDS`, `PetscDSGetResidual()`
@*/
PetscErrorCode PetscDSSetUpdate(PetscDS ds, PetscInt f, void (*update)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar uNew[]))
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  if (update) PetscValidFunction(update, 3);
  PetscCheck(f >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be non-negative", f);
  PetscCall(PetscDSEnlarge_Static(ds, f + 1));
  ds->update[f] = update;
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode PetscDSGetContext(PetscDS ds, PetscInt f, void *ctx)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  PetscCheck(!(f < 0) && !(f >= ds->Nf), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be in [0, %" PetscInt_FMT ")", f, ds->Nf);
  PetscValidPointer(ctx, 3);
  *(void **)ctx = ds->ctx[f];
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode PetscDSSetContext(PetscDS ds, PetscInt f, void *ctx)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  PetscCheck(f >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be non-negative", f);
  PetscCall(PetscDSEnlarge_Static(ds, f + 1));
  ds->ctx[f] = ctx;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSGetBdResidual - Get the pointwise boundary residual function for a given test field

  Not Collective

  Input Parameters:
+ ds - The PetscDS
- f  - The test field number

  Output Parameters:
+ f0 - boundary integrand for the test function term
- f1 - boundary integrand for the test function gradient term

  Calling sequence of `f0` and `f1`:
.vb
  void f0(PetscInt dim, PetscInt Nf, PetscInt NfAux,
          const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
          const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
          PetscReal t, const PetscReal x[], const PetscReal n[], PetscScalar f0[])
.ve
+ dim - the spatial dimension
. Nf - the number of fields
. uOff - the offset into u[] and u_t[] for each field
. uOff_x - the offset into u_x[] for each field
. u - each field evaluated at the current point
. u_t - the time derivative of each field evaluated at the current point
. u_x - the gradient of each field evaluated at the current point
. aOff - the offset into a[] and a_t[] for each auxiliary field
. aOff_x - the offset into a_x[] for each auxiliary field
. a - each auxiliary field evaluated at the current point
. a_t - the time derivative of each auxiliary field evaluated at the current point
. a_x - the gradient of auxiliary each field evaluated at the current point
. t - current time
. x - coordinates of the current point
. n - unit normal at the current point
. numConstants - number of constant parameters
. constants - constant parameters
- f0 - output values at the current point

  Level: intermediate

  Note:
  We are using a first order FEM model for the weak form:
  \int_\Gamma \phi {\vec f}_0(u, u_t, \nabla u, x, t) \cdot \hat n + \nabla\phi \cdot {\overleftrightarrow f}_1(u, u_t, \nabla u, x, t) \cdot \hat n

.seealso: `PetscDS`, `PetscDSSetBdResidual()`
@*/
PetscErrorCode PetscDSGetBdResidual(PetscDS ds, PetscInt f, void (**f0)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], const PetscReal n[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]), void (**f1)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], const PetscReal n[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[]))
{
  PetscBdPointFunc *tmp0, *tmp1;
  PetscInt          n0, n1;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  PetscCheck(!(f < 0) && !(f >= ds->Nf), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be in [0, %" PetscInt_FMT ")", f, ds->Nf);
  PetscCall(PetscWeakFormGetBdResidual(ds->wf, NULL, 0, f, 0, &n0, &tmp0, &n1, &tmp1));
  *f0 = tmp0 ? tmp0[0] : NULL;
  *f1 = tmp1 ? tmp1[0] : NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSSetBdResidual - Get the pointwise boundary residual function for a given test field

  Not Collective

  Input Parameters:
+ ds - The `PetscDS`
. f  - The test field number
. f0 - boundary integrand for the test function term
- f1 - boundary integrand for the test function gradient term

  Calling sequence of `f0` and `f1`:
.vb
  void f0(PetscInt dim, PetscInt Nf, PetscInt NfAux,
          const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
          const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
          PetscReal t, const PetscReal x[], const PetscReal n[], PetscScalar f0[])
.ve
+ dim - the spatial dimension
. Nf - the number of fields
. uOff - the offset into u[] and u_t[] for each field
. uOff_x - the offset into u_x[] for each field
. u - each field evaluated at the current point
. u_t - the time derivative of each field evaluated at the current point
. u_x - the gradient of each field evaluated at the current point
. aOff - the offset into a[] and a_t[] for each auxiliary field
. aOff_x - the offset into a_x[] for each auxiliary field
. a - each auxiliary field evaluated at the current point
. a_t - the time derivative of each auxiliary field evaluated at the current point
. a_x - the gradient of auxiliary each field evaluated at the current point
. t - current time
. x - coordinates of the current point
. n - unit normal at the current point
. numConstants - number of constant parameters
. constants - constant parameters
- f0 - output values at the current point

  Level: intermediate

  Note:
  We are using a first order FEM model for the weak form:
  \int_\Gamma \phi {\vec f}_0(u, u_t, \nabla u, x, t) \cdot \hat n + \nabla\phi \cdot {\overleftrightarrow f}_1(u, u_t, \nabla u, x, t) \cdot \hat n

.seealso: `PetscDS`, `PetscDSGetBdResidual()`
@*/
PetscErrorCode PetscDSSetBdResidual(PetscDS ds, PetscInt f, void (*f0)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], const PetscReal n[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]), void (*f1)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], const PetscReal n[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[]))
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  PetscCheck(f >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be non-negative", f);
  PetscCall(PetscWeakFormSetIndexBdResidual(ds->wf, NULL, 0, f, 0, 0, f0, 0, f1));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSHasBdJacobian - Indicates that boundary Jacobian functions have been set

  Not Collective

  Input Parameter:
. ds - The `PetscDS`

  Output Parameter:
. hasBdJac - flag that pointwise function for the boundary Jacobian has been set

  Level: intermediate

.seealso: `PetscDS`, `PetscDSHasJacobian()`, `PetscDSSetBdJacobian()`, `PetscDSGetBdJacobian()`
@*/
PetscErrorCode PetscDSHasBdJacobian(PetscDS ds, PetscBool *hasBdJac)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  PetscValidBoolPointer(hasBdJac, 2);
  PetscCall(PetscWeakFormHasBdJacobian(ds->wf, hasBdJac));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSGetBdJacobian - Get the pointwise boundary Jacobian function for given test and basis field

  Not Collective

  Input Parameters:
+ ds - The `PetscDS`
. f  - The test field number
- g  - The field number

  Output Parameters:
+ g0 - integrand for the test and basis function term
. g1 - integrand for the test function and basis function gradient term
. g2 - integrand for the test function gradient and basis function term
- g3 - integrand for the test function gradient and basis function gradient term

  Calling sequence of `g0`, `g1`, `g2` and `g3`:
.vb
  void g0(PetscInt dim, PetscInt Nf, PetscInt NfAux,
          const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
          const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
          PetscReal t, const PetscReal x[], const PetscReal n[], PetscScalar g0[])
.ve
+ dim - the spatial dimension
. Nf - the number of fields
. uOff - the offset into u[] and u_t[] for each field
. uOff_x - the offset into u_x[] for each field
. u - each field evaluated at the current point
. u_t - the time derivative of each field evaluated at the current point
. u_x - the gradient of each field evaluated at the current point
. aOff - the offset into a[] and a_t[] for each auxiliary field
. aOff_x - the offset into a_x[] for each auxiliary field
. a - each auxiliary field evaluated at the current point
. a_t - the time derivative of each auxiliary field evaluated at the current point
. a_x - the gradient of auxiliary each field evaluated at the current point
. t - current time
. u_tShift - the multiplier a for dF/dU_t
. x - coordinates of the current point
. n - normal at the current point
. numConstants - number of constant parameters
. constants - constant parameters
- g0 - output values at the current point

  Level: intermediate

  Note:
  We are using a first order FEM model for the weak form:
  \int_\Gamma \phi {\vec g}_0(u, u_t, \nabla u, x, t) \cdot \hat n \psi + \phi {\vec g}_1(u, u_t, \nabla u, x, t) \cdot \hat n \nabla \psi + \nabla\phi \cdot {\vec g}_2(u, u_t, \nabla u, x, t) \cdot \hat n \psi + \nabla\phi \cdot {\overleftrightarrow g}_3(u, u_t, \nabla u, x, t) \cdot \hat n \cdot \nabla \psi

.seealso: `PetscDS`, `PetscDSSetBdJacobian()`
@*/
PetscErrorCode PetscDSGetBdJacobian(PetscDS ds, PetscInt f, PetscInt g, void (**g0)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], const PetscReal n[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[]), void (**g1)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], const PetscReal n[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g1[]), void (**g2)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], const PetscReal n[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g2[]), void (**g3)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], const PetscReal n[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[]))
{
  PetscBdPointJac *tmp0, *tmp1, *tmp2, *tmp3;
  PetscInt         n0, n1, n2, n3;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  PetscCheck(!(f < 0) && !(f >= ds->Nf), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be in [0, %" PetscInt_FMT ")", f, ds->Nf);
  PetscCheck(!(g < 0) && !(g >= ds->Nf), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be in [0, %" PetscInt_FMT ")", g, ds->Nf);
  PetscCall(PetscWeakFormGetBdJacobian(ds->wf, NULL, 0, f, g, 0, &n0, &tmp0, &n1, &tmp1, &n2, &tmp2, &n3, &tmp3));
  *g0 = tmp0 ? tmp0[0] : NULL;
  *g1 = tmp1 ? tmp1[0] : NULL;
  *g2 = tmp2 ? tmp2[0] : NULL;
  *g3 = tmp3 ? tmp3[0] : NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSSetBdJacobian - Set the pointwise boundary Jacobian function for given test and basis field

  Not Collective

  Input Parameters:
+ ds - The PetscDS
. f  - The test field number
. g  - The field number
. g0 - integrand for the test and basis function term
. g1 - integrand for the test function and basis function gradient term
. g2 - integrand for the test function gradient and basis function term
- g3 - integrand for the test function gradient and basis function gradient term

  Calling sequence of `g0`, `g1`, `g2` and `g3`:
.vb
  void g0(PetscInt dim, PetscInt Nf, PetscInt NfAux,
       const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
       const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
       PetscReal t, const PetscReal x[], const PetscReal n[], PetscScalar g0[])
.ve
+ dim - the spatial dimension
. Nf - the number of fields
. uOff - the offset into u[] and u_t[] for each field
. uOff_x - the offset into u_x[] for each field
. u - each field evaluated at the current point
. u_t - the time derivative of each field evaluated at the current point
. u_x - the gradient of each field evaluated at the current point
. aOff - the offset into a[] and a_t[] for each auxiliary field
. aOff_x - the offset into a_x[] for each auxiliary field
. a - each auxiliary field evaluated at the current point
. a_t - the time derivative of each auxiliary field evaluated at the current point
. a_x - the gradient of auxiliary each field evaluated at the current point
. t - current time
. u_tShift - the multiplier a for dF/dU_t
. x - coordinates of the current point
. n - normal at the current point
. numConstants - number of constant parameters
. constants - constant parameters
- g0 - output values at the current point

  Level: intermediate

  Note:
  We are using a first order FEM model for the weak form:
  \int_\Gamma \phi {\vec g}_0(u, u_t, \nabla u, x, t) \cdot \hat n \psi + \phi {\vec g}_1(u, u_t, \nabla u, x, t) \cdot \hat n \nabla \psi + \nabla\phi \cdot {\vec g}_2(u, u_t, \nabla u, x, t) \cdot \hat n \psi + \nabla\phi \cdot {\overleftrightarrow g}_3(u, u_t, \nabla u, x, t) \cdot \hat n \cdot \nabla \psi

.seealso: `PetscDS`, `PetscDSGetBdJacobian()`
@*/
PetscErrorCode PetscDSSetBdJacobian(PetscDS ds, PetscInt f, PetscInt g, void (*g0)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], const PetscReal n[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[]), void (*g1)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], const PetscReal n[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g1[]), void (*g2)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], const PetscReal n[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g2[]), void (*g3)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], const PetscReal n[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[]))
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  if (g0) PetscValidFunction(g0, 4);
  if (g1) PetscValidFunction(g1, 5);
  if (g2) PetscValidFunction(g2, 6);
  if (g3) PetscValidFunction(g3, 7);
  PetscCheck(f >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be non-negative", f);
  PetscCheck(g >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be non-negative", g);
  PetscCall(PetscWeakFormSetIndexBdJacobian(ds->wf, NULL, 0, f, g, 0, 0, g0, 0, g1, 0, g2, 0, g3));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSHasBdJacobianPreconditioner - Signals that boundary Jacobian preconditioner functions have been set

  Not Collective

  Input Parameter:
. ds - The `PetscDS`

  Output Parameter:
. hasBdJac - flag that pointwise function for the boundary Jacobian preconditioner has been set

  Level: intermediate

.seealso: `PetscDS`, `PetscDSHasJacobian()`, `PetscDSSetBdJacobian()`, `PetscDSGetBdJacobian()`
@*/
PetscErrorCode PetscDSHasBdJacobianPreconditioner(PetscDS ds, PetscBool *hasBdJacPre)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  PetscValidBoolPointer(hasBdJacPre, 2);
  PetscCall(PetscWeakFormHasBdJacobianPreconditioner(ds->wf, hasBdJacPre));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSGetBdJacobianPreconditioner - Get the pointwise boundary Jacobian preconditioner function for given test and basis field

  Not Collective; No Fortran Support

  Input Parameters:
+ ds - The `PetscDS`
. f  - The test field number
- g  - The field number

  Output Parameters:
+ g0 - integrand for the test and basis function term
. g1 - integrand for the test function and basis function gradient term
. g2 - integrand for the test function gradient and basis function term
- g3 - integrand for the test function gradient and basis function gradient term

   Calling sequence of `g0`, `g1`, `g2` and `g3`:
.vb
  void g0(PetscInt dim, PetscInt Nf, PetscInt NfAux,
          const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
          const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
          PetscReal t, const PetscReal x[], const PetscReal n[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
.ve
+ dim - the spatial dimension
. Nf - the number of fields
. NfAux - the number of auxiliary fields
. uOff - the offset into u[] and u_t[] for each field
. uOff_x - the offset into u_x[] for each field
. u - each field evaluated at the current point
. u_t - the time derivative of each field evaluated at the current point
. u_x - the gradient of each field evaluated at the current point
. aOff - the offset into a[] and a_t[] for each auxiliary field
. aOff_x - the offset into a_x[] for each auxiliary field
. a - each auxiliary field evaluated at the current point
. a_t - the time derivative of each auxiliary field evaluated at the current point
. a_x - the gradient of auxiliary each field evaluated at the current point
. t - current time
. u_tShift - the multiplier a for dF/dU_t
. x - coordinates of the current point
. n - normal at the current point
. numConstants - number of constant parameters
. constants - constant parameters
- g0 - output values at the current point

  Level: intermediate

  Note:
  We are using a first order FEM model for the weak form:
  \int_\Gamma \phi {\vec g}_0(u, u_t, \nabla u, x, t) \cdot \hat n \psi + \phi {\vec g}_1(u, u_t, \nabla u, x, t) \cdot \hat n \nabla \psi + \nabla\phi \cdot {\vec g}_2(u, u_t, \nabla u, x, t) \cdot \hat n \psi + \nabla\phi \cdot {\overleftrightarrow g}_3(u, u_t, \nabla u, x, t) \cdot \hat n \cdot \nabla \psi

.seealso: `PetscDS`, `PetscDSSetBdJacobianPreconditioner()`
@*/
PetscErrorCode PetscDSGetBdJacobianPreconditioner(PetscDS ds, PetscInt f, PetscInt g, void (**g0)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], const PetscReal n[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[]), void (**g1)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], const PetscReal n[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g1[]), void (**g2)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], const PetscReal n[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g2[]), void (**g3)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], const PetscReal n[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[]))
{
  PetscBdPointJac *tmp0, *tmp1, *tmp2, *tmp3;
  PetscInt         n0, n1, n2, n3;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  PetscCheck(!(f < 0) && !(f >= ds->Nf), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be in [0, %" PetscInt_FMT ")", f, ds->Nf);
  PetscCheck(!(g < 0) && !(g >= ds->Nf), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be in [0, %" PetscInt_FMT ")", g, ds->Nf);
  PetscCall(PetscWeakFormGetBdJacobianPreconditioner(ds->wf, NULL, 0, f, g, 0, &n0, &tmp0, &n1, &tmp1, &n2, &tmp2, &n3, &tmp3));
  *g0 = tmp0 ? tmp0[0] : NULL;
  *g1 = tmp1 ? tmp1[0] : NULL;
  *g2 = tmp2 ? tmp2[0] : NULL;
  *g3 = tmp3 ? tmp3[0] : NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSSetBdJacobianPreconditioner - Set the pointwise boundary Jacobian preconditioner function for given test and basis field

  Not Collective; No Fortran Support

  Input Parameters:
+ ds - The `PetscDS`
. f  - The test field number
. g  - The field number
. g0 - integrand for the test and basis function term
. g1 - integrand for the test function and basis function gradient term
. g2 - integrand for the test function gradient and basis function term
- g3 - integrand for the test function gradient and basis function gradient term

   Calling sequence of `g0`, `g1`, `g2` and `g3`:
.vb
  void g0(PetscInt dim, PetscInt Nf, PetscInt NfAux,
          const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
          const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
          PetscReal t, const PetscReal x[], const PetscReal n[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
.ve
+ dim - the spatial dimension
. Nf - the number of fields
. NfAux - the number of auxiliary fields
. uOff - the offset into u[] and u_t[] for each field
. uOff_x - the offset into u_x[] for each field
. u - each field evaluated at the current point
. u_t - the time derivative of each field evaluated at the current point
. u_x - the gradient of each field evaluated at the current point
. aOff - the offset into a[] and a_t[] for each auxiliary field
. aOff_x - the offset into a_x[] for each auxiliary field
. a - each auxiliary field evaluated at the current point
. a_t - the time derivative of each auxiliary field evaluated at the current point
. a_x - the gradient of auxiliary each field evaluated at the current point
. t - current time
. u_tShift - the multiplier a for dF/dU_t
. x - coordinates of the current point
. n - normal at the current point
. numConstants - number of constant parameters
. constants - constant parameters
- g0 - output values at the current point

  Level: intermediate

  Note:
  We are using a first order FEM model for the weak form:
  \int_\Gamma \phi {\vec g}_0(u, u_t, \nabla u, x, t) \cdot \hat n \psi + \phi {\vec g}_1(u, u_t, \nabla u, x, t) \cdot \hat n \nabla \psi + \nabla\phi \cdot {\vec g}_2(u, u_t, \nabla u, x, t) \cdot \hat n \psi + \nabla\phi \cdot {\overleftrightarrow g}_3(u, u_t, \nabla u, x, t) \cdot \hat n \cdot \nabla \psi

.seealso: `PetscDS`, `PetscDSGetBdJacobianPreconditioner()`
@*/
PetscErrorCode PetscDSSetBdJacobianPreconditioner(PetscDS ds, PetscInt f, PetscInt g, void (*g0)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], const PetscReal n[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[]), void (*g1)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], const PetscReal n[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g1[]), void (*g2)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], const PetscReal n[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g2[]), void (*g3)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], const PetscReal n[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[]))
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  if (g0) PetscValidFunction(g0, 4);
  if (g1) PetscValidFunction(g1, 5);
  if (g2) PetscValidFunction(g2, 6);
  if (g3) PetscValidFunction(g3, 7);
  PetscCheck(f >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be non-negative", f);
  PetscCheck(g >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be non-negative", g);
  PetscCall(PetscWeakFormSetIndexBdJacobianPreconditioner(ds->wf, NULL, 0, f, g, 0, 0, g0, 0, g1, 0, g2, 0, g3));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSGetExactSolution - Get the pointwise exact solution function for a given test field

  Not Collective

  Input Parameters:
+ prob - The PetscDS
- f    - The test field number

  Output Parameters:
+ exactSol - exact solution for the test field
- exactCtx - exact solution context

  Calling sequence of `exactSol`:
.vb
  PetscErrorCode sol(PetscInt dim, PetscReal t, const PetscReal x[], PetscInt Nc, PetscScalar u[], void *ctx)
.ve
+ dim - the spatial dimension
. t - current time
. x - coordinates of the current point
. Nc - the number of field components
. u - the solution field evaluated at the current point
- ctx - a user context

  Level: intermediate

.seealso: `PetscDS`, `PetscDSSetExactSolution()`, `PetscDSGetExactSolutionTimeDerivative()`
@*/
PetscErrorCode PetscDSGetExactSolution(PetscDS prob, PetscInt f, PetscErrorCode (**sol)(PetscInt dim, PetscReal t, const PetscReal x[], PetscInt Nc, PetscScalar u[], void *ctx), void **ctx)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  PetscCheck(!(f < 0) && !(f >= prob->Nf), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be in [0, %" PetscInt_FMT ")", f, prob->Nf);
  if (sol) {
    PetscValidPointer(sol, 3);
    *sol = prob->exactSol[f];
  }
  if (ctx) {
    PetscValidPointer(ctx, 4);
    *ctx = prob->exactCtx[f];
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSSetExactSolution - Set the pointwise exact solution function for a given test field

  Not Collective

  Input Parameters:
+ prob - The `PetscDS`
. f    - The test field number
. sol  - solution function for the test fields
- ctx  - solution context or `NULL`

  Calling sequence of `sol`:
.vb
  PetscErrorCode sol(PetscInt dim, PetscReal t, const PetscReal x[], PetscInt Nc, PetscScalar u[], void *ctx)
.ve
+ dim - the spatial dimension
. t - current time
. x - coordinates of the current point
. Nc - the number of field components
. u - the solution field evaluated at the current point
- ctx - a user context

  Level: intermediate

.seealso: `PetscDS`, `PetscDSGetExactSolution()`
@*/
PetscErrorCode PetscDSSetExactSolution(PetscDS prob, PetscInt f, PetscErrorCode (*sol)(PetscInt dim, PetscReal t, const PetscReal x[], PetscInt Nc, PetscScalar u[], void *ctx), void *ctx)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  PetscCheck(f >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be non-negative", f);
  PetscCall(PetscDSEnlarge_Static(prob, f + 1));
  if (sol) {
    PetscValidFunction(sol, 3);
    prob->exactSol[f] = sol;
  }
  if (ctx) {
    PetscValidFunction(ctx, 4);
    prob->exactCtx[f] = ctx;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSGetExactSolutionTimeDerivative - Get the pointwise time derivative of the exact solution function for a given test field

  Not Collective

  Input Parameters:
+ prob - The `PetscDS`
- f    - The test field number

  Output Parameters:
+ exactSol - time derivative of the exact solution for the test field
- exactCtx - time derivative of the exact solution context

  Calling sequence of `exactSol`:
.vb
  PetscErrorCode sol(PetscInt dim, PetscReal t, const PetscReal x[], PetscInt Nc, PetscScalar u[], void *ctx)
.ve
+ dim - the spatial dimension
. t - current time
. x - coordinates of the current point
. Nc - the number of field components
. u - the solution field evaluated at the current point
- ctx - a user context

  Level: intermediate

.seealso: `PetscDS`, `PetscDSSetExactSolutionTimeDerivative()`, `PetscDSGetExactSolution()`
@*/
PetscErrorCode PetscDSGetExactSolutionTimeDerivative(PetscDS prob, PetscInt f, PetscErrorCode (**sol)(PetscInt dim, PetscReal t, const PetscReal x[], PetscInt Nc, PetscScalar u[], void *ctx), void **ctx)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  PetscCheck(!(f < 0) && !(f >= prob->Nf), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be in [0, %" PetscInt_FMT ")", f, prob->Nf);
  if (sol) {
    PetscValidPointer(sol, 3);
    *sol = prob->exactSol_t[f];
  }
  if (ctx) {
    PetscValidPointer(ctx, 4);
    *ctx = prob->exactCtx_t[f];
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSSetExactSolutionTimeDerivative - Set the pointwise time derivative of the exact solution function for a given test field

  Not Collective

  Input Parameters:
+ prob - The `PetscDS`
. f    - The test field number
. sol  - time derivative of the solution function for the test fields
- ctx  - time derivative of the solution context or `NULL`

  Calling sequence of `sol`:
.vb
  PetscErrorCode sol(PetscInt dim, PetscReal t, const PetscReal x[], PetscInt Nc, PetscScalar u[], void *ctx)
.ve
+ dim - the spatial dimension
. t - current time
. x - coordinates of the current point
. Nc - the number of field components
. u - the solution field evaluated at the current point
- ctx - a user context

  Level: intermediate

.seealso: `PetscDS`, `PetscDSGetExactSolutionTimeDerivative()`, `PetscDSSetExactSolution()`
@*/
PetscErrorCode PetscDSSetExactSolutionTimeDerivative(PetscDS prob, PetscInt f, PetscErrorCode (*sol)(PetscInt dim, PetscReal t, const PetscReal x[], PetscInt Nc, PetscScalar u[], void *ctx), void *ctx)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  PetscCheck(f >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be non-negative", f);
  PetscCall(PetscDSEnlarge_Static(prob, f + 1));
  if (sol) {
    PetscValidFunction(sol, 3);
    prob->exactSol_t[f] = sol;
  }
  if (ctx) {
    PetscValidFunction(ctx, 4);
    prob->exactCtx_t[f] = ctx;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSGetConstants - Returns the array of constants passed to point functions

  Not Collective

  Input Parameter:
. prob - The `PetscDS` object

  Output Parameters:
+ numConstants - The number of constants
- constants    - The array of constants, NULL if there are none

  Level: intermediate

.seealso: `PetscDS`, `PetscDSSetConstants()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSGetConstants(PetscDS prob, PetscInt *numConstants, const PetscScalar *constants[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  if (numConstants) {
    PetscValidIntPointer(numConstants, 2);
    *numConstants = prob->numConstants;
  }
  if (constants) {
    PetscValidPointer(constants, 3);
    *constants = prob->constants;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSSetConstants - Set the array of constants passed to point functions

  Not Collective

  Input Parameters:
+ prob         - The `PetscDS` object
. numConstants - The number of constants
- constants    - The array of constants, NULL if there are none

  Level: intermediate

.seealso: `PetscDS`, `PetscDSGetConstants()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSSetConstants(PetscDS prob, PetscInt numConstants, PetscScalar constants[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  if (numConstants != prob->numConstants) {
    PetscCall(PetscFree(prob->constants));
    prob->numConstants = numConstants;
    if (prob->numConstants) {
      PetscCall(PetscMalloc1(prob->numConstants, &prob->constants));
    } else {
      prob->constants = NULL;
    }
  }
  if (prob->numConstants) {
    PetscValidScalarPointer(constants, 3);
    PetscCall(PetscArraycpy(prob->constants, constants, prob->numConstants));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSGetFieldIndex - Returns the index of the given field

  Not Collective

  Input Parameters:
+ prob - The `PetscDS` object
- disc - The discretization object

  Output Parameter:
. f - The field number

  Level: beginner

.seealso: `PetscDS`, `PetscGetDiscretization()`, `PetscDSGetNumFields()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSGetFieldIndex(PetscDS prob, PetscObject disc, PetscInt *f)
{
  PetscInt g;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  PetscValidIntPointer(f, 3);
  *f = -1;
  for (g = 0; g < prob->Nf; ++g) {
    if (disc == prob->disc[g]) break;
  }
  PetscCheck(g != prob->Nf, PetscObjectComm((PetscObject)prob), PETSC_ERR_ARG_WRONG, "Field not found in PetscDS.");
  *f = g;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSGetFieldSize - Returns the size of the given field in the full space basis

  Not Collective

  Input Parameters:
+ prob - The `PetscDS` object
- f - The field number

  Output Parameter:
. size - The size

  Level: beginner

.seealso: `PetscDS`, `PetscDSGetFieldOffset()`, `PetscDSGetNumFields()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSGetFieldSize(PetscDS prob, PetscInt f, PetscInt *size)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  PetscValidIntPointer(size, 3);
  PetscCheck(!(f < 0) && !(f >= prob->Nf), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be in [0, %" PetscInt_FMT ")", f, prob->Nf);
  PetscCall(PetscDSSetUp(prob));
  *size = prob->Nb[f];
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSGetFieldOffset - Returns the offset of the given field in the full space basis

  Not Collective

  Input Parameters:
+ prob - The `PetscDS` object
- f - The field number

  Output Parameter:
. off - The offset

  Level: beginner

.seealso: `PetscDS`, `PetscDSGetFieldSize()`, `PetscDSGetNumFields()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSGetFieldOffset(PetscDS prob, PetscInt f, PetscInt *off)
{
  PetscInt size, g;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  PetscValidIntPointer(off, 3);
  PetscCheck(!(f < 0) && !(f >= prob->Nf), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be in [0, %" PetscInt_FMT ")", f, prob->Nf);
  *off = 0;
  for (g = 0; g < f; ++g) {
    PetscCall(PetscDSGetFieldSize(prob, g, &size));
    *off += size;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSGetFieldOffsetCohesive - Returns the offset of the given field in the full space basis on a cohesive cell

  Not Collective

  Input Parameters:
+ prob - The `PetscDS` object
- f - The field number

  Output Parameter:
. off - The offset

  Level: beginner

.seealso: `PetscDS`, `PetscDSGetFieldSize()`, `PetscDSGetNumFields()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSGetFieldOffsetCohesive(PetscDS ds, PetscInt f, PetscInt *off)
{
  PetscInt size, g;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  PetscValidIntPointer(off, 3);
  PetscCheck(!(f < 0) && !(f >= ds->Nf), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be in [0, %" PetscInt_FMT ")", f, ds->Nf);
  *off = 0;
  for (g = 0; g < f; ++g) {
    PetscBool cohesive;

    PetscCall(PetscDSGetCohesive(ds, g, &cohesive));
    PetscCall(PetscDSGetFieldSize(ds, g, &size));
    *off += cohesive ? size : size * 2;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSGetDimensions - Returns the size of the approximation space for each field on an evaluation point

  Not Collective

  Input Parameter:
. prob - The `PetscDS` object

  Output Parameter:
. dimensions - The number of dimensions

  Level: beginner

.seealso: `PetscDS`, `PetscDSGetComponentOffsets()`, `PetscDSGetNumFields()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSGetDimensions(PetscDS prob, PetscInt *dimensions[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  PetscCall(PetscDSSetUp(prob));
  PetscValidPointer(dimensions, 2);
  *dimensions = prob->Nb;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSGetComponents - Returns the number of components for each field on an evaluation point

  Not Collective

  Input Parameter:
. prob - The `PetscDS` object

  Output Parameter:
. components - The number of components

  Level: beginner

.seealso: `PetscDS`, `PetscDSGetComponentOffsets()`, `PetscDSGetNumFields()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSGetComponents(PetscDS prob, PetscInt *components[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  PetscCall(PetscDSSetUp(prob));
  PetscValidPointer(components, 2);
  *components = prob->Nc;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSGetComponentOffset - Returns the offset of the given field on an evaluation point

  Not Collective

  Input Parameters:
+ prob - The `PetscDS` object
- f - The field number

  Output Parameter:
. off - The offset

  Level: beginner

.seealso: `PetscDS`, `PetscDSGetNumFields()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSGetComponentOffset(PetscDS prob, PetscInt f, PetscInt *off)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  PetscValidIntPointer(off, 3);
  PetscCheck(!(f < 0) && !(f >= prob->Nf), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field number %" PetscInt_FMT " must be in [0, %" PetscInt_FMT ")", f, prob->Nf);
  PetscCall(PetscDSSetUp(prob));
  *off = prob->off[f];
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSGetComponentOffsets - Returns the offset of each field on an evaluation point

  Not Collective

  Input Parameter:
. prob - The `PetscDS` object

  Output Parameter:
. offsets - The offsets

  Level: beginner

.seealso: `PetscDS`, `PetscDSGetNumFields()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSGetComponentOffsets(PetscDS prob, PetscInt *offsets[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  PetscValidPointer(offsets, 2);
  PetscCall(PetscDSSetUp(prob));
  *offsets = prob->off;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSGetComponentDerivativeOffsets - Returns the offset of each field derivative on an evaluation point

  Not Collective

  Input Parameter:
. prob - The `PetscDS` object

  Output Parameter:
. offsets - The offsets

  Level: beginner

.seealso: `PetscDS`, `PetscDSGetNumFields()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSGetComponentDerivativeOffsets(PetscDS prob, PetscInt *offsets[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  PetscValidPointer(offsets, 2);
  PetscCall(PetscDSSetUp(prob));
  *offsets = prob->offDer;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSGetComponentOffsetsCohesive - Returns the offset of each field on an evaluation point

  Not Collective

  Input Parameters:
+ ds - The `PetscDS` object
- s  - The cohesive side, 0 for negative, 1 for positive, 2 for cohesive

  Output Parameter:
. offsets - The offsets

  Level: beginner

.seealso: `PetscDS`, `PetscDSGetNumFields()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSGetComponentOffsetsCohesive(PetscDS ds, PetscInt s, PetscInt *offsets[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  PetscValidPointer(offsets, 3);
  PetscCheck(ds->isCohesive, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Cohesive offsets are only valid for a cohesive DS");
  PetscCheck(!(s < 0) && !(s > 2), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Cohesive side %" PetscInt_FMT " is not in [0, 2]", s);
  PetscCall(PetscDSSetUp(ds));
  *offsets = ds->offCohesive[s];
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSGetComponentDerivativeOffsetsCohesive - Returns the offset of each field derivative on an evaluation point

  Not Collective

  Input Parameters:
+ ds - The `PetscDS` object
- s  - The cohesive side, 0 for negative, 1 for positive, 2 for cohesive

  Output Parameter:
. offsets - The offsets

  Level: beginner

.seealso: `PetscDS`, `PetscDSGetNumFields()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSGetComponentDerivativeOffsetsCohesive(PetscDS ds, PetscInt s, PetscInt *offsets[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  PetscValidPointer(offsets, 3);
  PetscCheck(ds->isCohesive, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Cohesive offsets are only valid for a cohesive DS");
  PetscCheck(!(s < 0) && !(s > 2), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Cohesive side %" PetscInt_FMT " is not in [0, 2]", s);
  PetscCall(PetscDSSetUp(ds));
  *offsets = ds->offDerCohesive[s];
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSGetTabulation - Return the basis tabulation at quadrature points for the volume discretization

  Not Collective

  Input Parameter:
. prob - The `PetscDS` object

  Output Parameter:
. T - The basis function and derivatives tabulation at quadrature points for each field

  Level: intermediate

.seealso: `PetscDS`, `PetscTabulation`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSGetTabulation(PetscDS prob, PetscTabulation *T[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  PetscValidPointer(T, 2);
  PetscCall(PetscDSSetUp(prob));
  *T = prob->T;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSGetFaceTabulation - Return the basis tabulation at quadrature points on the faces

  Not Collective

  Input Parameter:
. prob - The `PetscDS` object

  Output Parameter:
. Tf - The basis function and derivative tabulation on each local face at quadrature points for each and field

  Level: intermediate

.seealso: `PetscTabulation`, `PetscDS`, `PetscDSGetTabulation()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSGetFaceTabulation(PetscDS prob, PetscTabulation *Tf[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  PetscValidPointer(Tf, 2);
  PetscCall(PetscDSSetUp(prob));
  *Tf = prob->Tf;
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode PetscDSGetEvaluationArrays(PetscDS prob, PetscScalar **u, PetscScalar **u_t, PetscScalar **u_x)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  PetscCall(PetscDSSetUp(prob));
  if (u) {
    PetscValidPointer(u, 2);
    *u = prob->u;
  }
  if (u_t) {
    PetscValidPointer(u_t, 3);
    *u_t = prob->u_t;
  }
  if (u_x) {
    PetscValidPointer(u_x, 4);
    *u_x = prob->u_x;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode PetscDSGetWeakFormArrays(PetscDS prob, PetscScalar **f0, PetscScalar **f1, PetscScalar **g0, PetscScalar **g1, PetscScalar **g2, PetscScalar **g3)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  PetscCall(PetscDSSetUp(prob));
  if (f0) {
    PetscValidPointer(f0, 2);
    *f0 = prob->f0;
  }
  if (f1) {
    PetscValidPointer(f1, 3);
    *f1 = prob->f1;
  }
  if (g0) {
    PetscValidPointer(g0, 4);
    *g0 = prob->g0;
  }
  if (g1) {
    PetscValidPointer(g1, 5);
    *g1 = prob->g1;
  }
  if (g2) {
    PetscValidPointer(g2, 6);
    *g2 = prob->g2;
  }
  if (g3) {
    PetscValidPointer(g3, 7);
    *g3 = prob->g3;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode PetscDSGetWorkspace(PetscDS prob, PetscReal **x, PetscScalar **basisReal, PetscScalar **basisDerReal, PetscScalar **testReal, PetscScalar **testDerReal)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  PetscCall(PetscDSSetUp(prob));
  if (x) {
    PetscValidPointer(x, 2);
    *x = prob->x;
  }
  if (basisReal) {
    PetscValidPointer(basisReal, 3);
    *basisReal = prob->basisReal;
  }
  if (basisDerReal) {
    PetscValidPointer(basisDerReal, 4);
    *basisDerReal = prob->basisDerReal;
  }
  if (testReal) {
    PetscValidPointer(testReal, 5);
    *testReal = prob->testReal;
  }
  if (testDerReal) {
    PetscValidPointer(testDerReal, 6);
    *testDerReal = prob->testDerReal;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSAddBoundary - Add a boundary condition to the model. The pointwise functions are used to provide boundary values for essential boundary conditions.
  In FEM, they are acting upon by dual basis functionals to generate FEM coefficients which are fixed. Natural boundary conditions signal to PETSc that boundary
  integrals should be performed, using the kernels from `PetscDSSetBdResidual()`.

  Collective

  Input Parameters:
+ ds       - The PetscDS object
. type     - The type of condition, e.g. `DM_BC_ESSENTIAL`/`DM_BC_ESSENTIAL_FIELD` (Dirichlet), or `DM_BC_NATURAL` (Neumann)
. name     - The BC name
. label    - The label defining constrained points
. Nv       - The number of `DMLabel` values for constrained points
. values   - An array of label values for constrained points
. field    - The field to constrain
. Nc       - The number of constrained field components (0 will constrain all fields)
. comps    - An array of constrained component numbers
. bcFunc   - A pointwise function giving boundary values
. bcFunc_t - A pointwise function giving the time derivative of the boundary values, or NULL
- ctx      - An optional user context for bcFunc

  Output Parameter:
- bd       - The boundary number

  Options Database Keys:
+ -bc_<boundary name> <num> - Overrides the boundary ids
- -bc_<boundary name>_comp <num> - Overrides the boundary components

  Level: developer

  Note:
  Both `bcFunc` and `bcFunc_t` will depend on the boundary condition type. If the type if `DM_BC_ESSENTIAL`, Then the calling sequence is:

$ void bcFunc(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar bcval[])

  If the type is `DM_BC_ESSENTIAL_FIELD` or other _FIELD value, then the calling sequence is:
.vb
  void bcFunc(PetscInt dim, PetscInt Nf, PetscInt NfAux,
              const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
              const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
              PetscReal time, const PetscReal x[], PetscScalar bcval[])
.ve
+ dim - the spatial dimension
. Nf - the number of fields
. uOff - the offset into u[] and u_t[] for each field
. uOff_x - the offset into u_x[] for each field
. u - each field evaluated at the current point
. u_t - the time derivative of each field evaluated at the current point
. u_x - the gradient of each field evaluated at the current point
. aOff - the offset into a[] and a_t[] for each auxiliary field
. aOff_x - the offset into a_x[] for each auxiliary field
. a - each auxiliary field evaluated at the current point
. a_t - the time derivative of each auxiliary field evaluated at the current point
. a_x - the gradient of auxiliary each field evaluated at the current point
. t - current time
. x - coordinates of the current point
. numConstants - number of constant parameters
. constants - constant parameters
- bcval - output values at the current point

.seealso: `PetscDS`, `PetscWeakForm`, `DMLabel`, `DMBoundaryConditionType`, `PetscDSAddBoundaryByName()`, `PetscDSGetBoundary()`, `PetscDSSetResidual()`, `PetscDSSetBdResidual()`
@*/
PetscErrorCode PetscDSAddBoundary(PetscDS ds, DMBoundaryConditionType type, const char name[], DMLabel label, PetscInt Nv, const PetscInt values[], PetscInt field, PetscInt Nc, const PetscInt comps[], void (*bcFunc)(void), void (*bcFunc_t)(void), void *ctx, PetscInt *bd)
{
  DSBoundary  head = ds->boundary, b;
  PetscInt    n    = 0;
  const char *lname;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  PetscValidLogicalCollectiveEnum(ds, type, 2);
  PetscValidCharPointer(name, 3);
  PetscValidHeaderSpecific(label, DMLABEL_CLASSID, 4);
  PetscValidLogicalCollectiveInt(ds, Nv, 5);
  PetscValidLogicalCollectiveInt(ds, field, 7);
  PetscValidLogicalCollectiveInt(ds, Nc, 8);
  PetscCheck(field >= 0 && field < ds->Nf, PetscObjectComm((PetscObject)ds), PETSC_ERR_ARG_OUTOFRANGE, "Field %" PetscInt_FMT " is not in [0, %" PetscInt_FMT ")", field, ds->Nf);
  if (Nc > 0) {
    PetscInt *fcomps;
    PetscInt  c;

    PetscCall(PetscDSGetComponents(ds, &fcomps));
    PetscCheck(Nc <= fcomps[field], PetscObjectComm((PetscObject)ds), PETSC_ERR_ARG_OUTOFRANGE, "Number of constrained components %" PetscInt_FMT " > %" PetscInt_FMT " components for field %" PetscInt_FMT, Nc, fcomps[field], field);
    for (c = 0; c < Nc; ++c) {
      PetscCheck(comps[c] >= 0 && comps[c] < fcomps[field], PetscObjectComm((PetscObject)ds), PETSC_ERR_ARG_OUTOFRANGE, "Constrained component[%" PetscInt_FMT "] %" PetscInt_FMT " not in [0, %" PetscInt_FMT ") components for field %" PetscInt_FMT, c, comps[c], fcomps[field], field);
    }
  }
  PetscCall(PetscNew(&b));
  PetscCall(PetscStrallocpy(name, (char **)&b->name));
  PetscCall(PetscWeakFormCreate(PETSC_COMM_SELF, &b->wf));
  PetscCall(PetscWeakFormSetNumFields(b->wf, ds->Nf));
  PetscCall(PetscMalloc1(Nv, &b->values));
  if (Nv) PetscCall(PetscArraycpy(b->values, values, Nv));
  PetscCall(PetscMalloc1(Nc, &b->comps));
  if (Nc) PetscCall(PetscArraycpy(b->comps, comps, Nc));
  PetscCall(PetscObjectGetName((PetscObject)label, &lname));
  PetscCall(PetscStrallocpy(lname, (char **)&b->lname));
  b->type   = type;
  b->label  = label;
  b->Nv     = Nv;
  b->field  = field;
  b->Nc     = Nc;
  b->func   = bcFunc;
  b->func_t = bcFunc_t;
  b->ctx    = ctx;
  b->next   = NULL;
  /* Append to linked list so that we can preserve the order */
  if (!head) ds->boundary = b;
  while (head) {
    if (!head->next) {
      head->next = b;
      head       = b;
    }
    head = head->next;
    ++n;
  }
  if (bd) {
    PetscValidIntPointer(bd, 13);
    *bd = n;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSAddBoundaryByName - Add a boundary condition to the model. The pointwise functions are used to provide boundary values for essential boundary conditions.
  In FEM, they are acting upon by dual basis functionals to generate FEM coefficients which are fixed. Natural boundary conditions signal to PETSc that
  boundary integrals should be performed, using the kernels from `PetscDSSetBdResidual()`.

  Collective

  Input Parameters:
+ ds       - The `PetscDS` object
. type     - The type of condition, e.g. `DM_BC_ESSENTIAL`/`DM_BC_ESSENTIAL_FIELD` (Dirichlet), or `DM_BC_NATURAL` (Neumann)
. name     - The BC name
. lname    - The naem of the label defining constrained points
. Nv       - The number of `DMLabel` values for constrained points
. values   - An array of label values for constrained points
. field    - The field to constrain
. Nc       - The number of constrained field components (0 will constrain all fields)
. comps    - An array of constrained component numbers
. bcFunc   - A pointwise function giving boundary values
. bcFunc_t - A pointwise function giving the time derivative of the boundary values, or NULL
- ctx      - An optional user context for bcFunc

  Output Parameter:
- bd       - The boundary number

  Options Database Keys:
+ -bc_<boundary name> <num> - Overrides the boundary ids
- -bc_<boundary name>_comp <num> - Overrides the boundary components

  Calling Sequence of `bcFunc` and `bcFunc_t`:
  If the type is `DM_BC_ESSENTIAL`
.vb
  void bcFunc(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar bcval[])
.ve
  If the type is `DM_BC_ESSENTIAL_FIELD` or other _FIELD value,
.vb
  void bcFunc(PetscInt dim, PetscInt Nf, PetscInt NfAux,
              const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
              const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
              PetscReal time, const PetscReal x[], PetscScalar bcval[])
.ve
+ dim - the spatial dimension
. Nf - the number of fields
. uOff - the offset into u[] and u_t[] for each field
. uOff_x - the offset into u_x[] for each field
. u - each field evaluated at the current point
. u_t - the time derivative of each field evaluated at the current point
. u_x - the gradient of each field evaluated at the current point
. aOff - the offset into a[] and a_t[] for each auxiliary field
. aOff_x - the offset into a_x[] for each auxiliary field
. a - each auxiliary field evaluated at the current point
. a_t - the time derivative of each auxiliary field evaluated at the current point
. a_x - the gradient of auxiliary each field evaluated at the current point
. t - current time
. x - coordinates of the current point
. numConstants - number of constant parameters
. constants - constant parameters
- bcval - output values at the current point

  Level: developer

  Note:
  This function should only be used with `DMFOREST` currently, since labels cannot be defined before the underlying `DMPLEX` is built.

.seealso: `PetscDS`, `PetscWeakForm`, `DMLabel`, `DMBoundaryConditionType`, `PetscDSAddBoundary()`, `PetscDSGetBoundary()`, `PetscDSSetResidual()`, `PetscDSSetBdResidual()`
@*/
PetscErrorCode PetscDSAddBoundaryByName(PetscDS ds, DMBoundaryConditionType type, const char name[], const char lname[], PetscInt Nv, const PetscInt values[], PetscInt field, PetscInt Nc, const PetscInt comps[], void (*bcFunc)(void), void (*bcFunc_t)(void), void *ctx, PetscInt *bd)
{
  DSBoundary head = ds->boundary, b;
  PetscInt   n    = 0;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  PetscValidLogicalCollectiveEnum(ds, type, 2);
  PetscValidCharPointer(name, 3);
  PetscValidCharPointer(lname, 4);
  PetscValidLogicalCollectiveInt(ds, Nv, 5);
  PetscValidLogicalCollectiveInt(ds, field, 7);
  PetscValidLogicalCollectiveInt(ds, Nc, 8);
  PetscCall(PetscNew(&b));
  PetscCall(PetscStrallocpy(name, (char **)&b->name));
  PetscCall(PetscWeakFormCreate(PETSC_COMM_SELF, &b->wf));
  PetscCall(PetscWeakFormSetNumFields(b->wf, ds->Nf));
  PetscCall(PetscMalloc1(Nv, &b->values));
  if (Nv) PetscCall(PetscArraycpy(b->values, values, Nv));
  PetscCall(PetscMalloc1(Nc, &b->comps));
  if (Nc) PetscCall(PetscArraycpy(b->comps, comps, Nc));
  PetscCall(PetscStrallocpy(lname, (char **)&b->lname));
  b->type   = type;
  b->label  = NULL;
  b->Nv     = Nv;
  b->field  = field;
  b->Nc     = Nc;
  b->func   = bcFunc;
  b->func_t = bcFunc_t;
  b->ctx    = ctx;
  b->next   = NULL;
  /* Append to linked list so that we can preserve the order */
  if (!head) ds->boundary = b;
  while (head) {
    if (!head->next) {
      head->next = b;
      head       = b;
    }
    head = head->next;
    ++n;
  }
  if (bd) {
    PetscValidIntPointer(bd, 13);
    *bd = n;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSUpdateBoundary - Change a boundary condition for the model. The pointwise functions are used to provide boundary values for essential boundary conditions.
  In FEM, they are acting upon by dual basis functionals to generate FEM coefficients which are fixed. Natural boundary conditions signal to PETSc that boundary integrals
  should be performed, using the kernels from `PetscDSSetBdResidual()`.

  Input Parameters:
+ ds       - The `PetscDS` object
. bd       - The boundary condition number
. type     - The type of condition, e.g. `DM_BC_ESSENTIAL`/`DM_BC_ESSENTIAL_FIELD` (Dirichlet), or `DM_BC_NATURAL` (Neumann)
. name     - The BC name
. label    - The label defining constrained points
. Nv       - The number of `DMLabel` ids for constrained points
. values   - An array of ids for constrained points
. field    - The field to constrain
. Nc       - The number of constrained field components
. comps    - An array of constrained component numbers
. bcFunc   - A pointwise function giving boundary values
. bcFunc_t - A pointwise function giving the time derivative of the boundary values, or NULL
- ctx      - An optional user context for bcFunc

  Level: developer

  Note:
  The boundary condition number is the order in which it was registered. The user can get the number of boundary conditions from `PetscDSGetNumBoundary()`.
  See `PetscDSAddBoundary()` for a description of the calling sequences for the callbacks.

.seealso: `PetscDS`, `PetscWeakForm`, `DMBoundaryConditionType`, `PetscDSAddBoundary()`, `PetscDSGetBoundary()`, `PetscDSGetNumBoundary()`, `DMLabel`
@*/
PetscErrorCode PetscDSUpdateBoundary(PetscDS ds, PetscInt bd, DMBoundaryConditionType type, const char name[], DMLabel label, PetscInt Nv, const PetscInt values[], PetscInt field, PetscInt Nc, const PetscInt comps[], void (*bcFunc)(void), void (*bcFunc_t)(void), void *ctx)
{
  DSBoundary b = ds->boundary;
  PetscInt   n = 0;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  while (b) {
    if (n == bd) break;
    b = b->next;
    ++n;
  }
  PetscCheck(b, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Boundary %" PetscInt_FMT " is not in [0, %" PetscInt_FMT ")", bd, n);
  if (name) {
    PetscCall(PetscFree(b->name));
    PetscCall(PetscStrallocpy(name, (char **)&b->name));
  }
  b->type = type;
  if (label) {
    const char *name;

    b->label = label;
    PetscCall(PetscFree(b->lname));
    PetscCall(PetscObjectGetName((PetscObject)label, &name));
    PetscCall(PetscStrallocpy(name, (char **)&b->lname));
  }
  if (Nv >= 0) {
    b->Nv = Nv;
    PetscCall(PetscFree(b->values));
    PetscCall(PetscMalloc1(Nv, &b->values));
    if (Nv) PetscCall(PetscArraycpy(b->values, values, Nv));
  }
  if (field >= 0) b->field = field;
  if (Nc >= 0) {
    b->Nc = Nc;
    PetscCall(PetscFree(b->comps));
    PetscCall(PetscMalloc1(Nc, &b->comps));
    if (Nc) PetscCall(PetscArraycpy(b->comps, comps, Nc));
  }
  if (bcFunc) b->func = bcFunc;
  if (bcFunc_t) b->func_t = bcFunc_t;
  if (ctx) b->ctx = ctx;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSGetNumBoundary - Get the number of registered BC

  Input Parameter:
. ds - The `PetscDS` object

  Output Parameter:
. numBd - The number of BC

  Level: intermediate

.seealso: `PetscDS`, `PetscDSAddBoundary()`, `PetscDSGetBoundary()`
@*/
PetscErrorCode PetscDSGetNumBoundary(PetscDS ds, PetscInt *numBd)
{
  DSBoundary b = ds->boundary;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  PetscValidIntPointer(numBd, 2);
  *numBd = 0;
  while (b) {
    ++(*numBd);
    b = b->next;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PetscDSGetBoundary - Gets a boundary condition to the model

  Input Parameters:
+ ds          - The `PetscDS` object
- bd          - The BC number

  Output Parameters:
+ wf       - The `PetscWeakForm` holding the pointwise functions
. type     - The type of condition, e.g. `DM_BC_ESSENTIAL`/`DM_BC_ESSENTIAL_FIELD` (Dirichlet), or `DM_BC_NATURAL` (Neumann)
. name     - The BC name
. label    - The label defining constrained points
. Nv       - The number of `DMLabel` ids for constrained points
. values   - An array of ids for constrained points
. field    - The field to constrain
. Nc       - The number of constrained field components
. comps    - An array of constrained component numbers
. bcFunc   - A pointwise function giving boundary values
. bcFunc_t - A pointwise function giving the time derivative of the boundary values
- ctx      - An optional user context for bcFunc

  Options Database Keys:
+ -bc_<boundary name> <num> - Overrides the boundary ids
- -bc_<boundary name>_comp <num> - Overrides the boundary components

  Level: developer

.seealso: `PetscDS`, `PetscWeakForm`, `DMBoundaryConditionType`, `PetscDSAddBoundary()`, `DMLabel`
@*/
PetscErrorCode PetscDSGetBoundary(PetscDS ds, PetscInt bd, PetscWeakForm *wf, DMBoundaryConditionType *type, const char *name[], DMLabel *label, PetscInt *Nv, const PetscInt *values[], PetscInt *field, PetscInt *Nc, const PetscInt *comps[], void (**func)(void), void (**func_t)(void), void **ctx)
{
  DSBoundary b = ds->boundary;
  PetscInt   n = 0;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  while (b) {
    if (n == bd) break;
    b = b->next;
    ++n;
  }
  PetscCheck(b, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Boundary %" PetscInt_FMT " is not in [0, %" PetscInt_FMT ")", bd, n);
  if (wf) {
    PetscValidPointer(wf, 3);
    *wf = b->wf;
  }
  if (type) {
    PetscValidPointer(type, 4);
    *type = b->type;
  }
  if (name) {
    PetscValidPointer(name, 5);
    *name = b->name;
  }
  if (label) {
    PetscValidPointer(label, 6);
    *label = b->label;
  }
  if (Nv) {
    PetscValidIntPointer(Nv, 7);
    *Nv = b->Nv;
  }
  if (values) {
    PetscValidPointer(values, 8);
    *values = b->values;
  }
  if (field) {
    PetscValidIntPointer(field, 9);
    *field = b->field;
  }
  if (Nc) {
    PetscValidIntPointer(Nc, 10);
    *Nc = b->Nc;
  }
  if (comps) {
    PetscValidPointer(comps, 11);
    *comps = b->comps;
  }
  if (func) {
    PetscValidPointer(func, 12);
    *func = b->func;
  }
  if (func_t) {
    PetscValidPointer(func_t, 13);
    *func_t = b->func_t;
  }
  if (ctx) {
    PetscValidPointer(ctx, 14);
    *ctx = b->ctx;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode DSBoundaryDuplicate_Internal(DSBoundary b, DSBoundary *bNew)
{
  PetscFunctionBegin;
  PetscCall(PetscNew(bNew));
  PetscCall(PetscWeakFormCreate(PETSC_COMM_SELF, &(*bNew)->wf));
  PetscCall(PetscWeakFormCopy(b->wf, (*bNew)->wf));
  PetscCall(PetscStrallocpy(b->name, (char **)&((*bNew)->name)));
  PetscCall(PetscStrallocpy(b->lname, (char **)&((*bNew)->lname)));
  (*bNew)->type  = b->type;
  (*bNew)->label = b->label;
  (*bNew)->Nv    = b->Nv;
  PetscCall(PetscMalloc1(b->Nv, &(*bNew)->values));
  PetscCall(PetscArraycpy((*bNew)->values, b->values, b->Nv));
  (*bNew)->field = b->field;
  (*bNew)->Nc    = b->Nc;
  PetscCall(PetscMalloc1(b->Nc, &(*bNew)->comps));
  PetscCall(PetscArraycpy((*bNew)->comps, b->comps, b->Nc));
  (*bNew)->func   = b->func;
  (*bNew)->func_t = b->func_t;
  (*bNew)->ctx    = b->ctx;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSCopyBoundary - Copy all boundary condition objects to the new problem

  Not Collective

  Input Parameters:
+ ds        - The source `PetscDS` object
. numFields - The number of selected fields, or `PETSC_DEFAULT` for all fields
- fields    - The selected fields, or NULL for all fields

  Output Parameter:
. newds     - The target `PetscDS`, now with a copy of the boundary conditions

  Level: intermediate

.seealso: `PetscDS`, `DMBoundary`, `PetscDSCopyEquations()`, `PetscDSSetResidual()`, `PetscDSSetJacobian()`, `PetscDSSetRiemannSolver()`, `PetscDSSetBdResidual()`, `PetscDSSetBdJacobian()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSCopyBoundary(PetscDS ds, PetscInt numFields, const PetscInt fields[], PetscDS newds)
{
  DSBoundary b, *lastnext;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  PetscValidHeaderSpecific(newds, PETSCDS_CLASSID, 4);
  if (ds == newds) PetscFunctionReturn(PETSC_SUCCESS);
  PetscCall(PetscDSDestroyBoundary(newds));
  lastnext = &(newds->boundary);
  for (b = ds->boundary; b; b = b->next) {
    DSBoundary bNew;
    PetscInt   fieldNew = -1;

    if (numFields > 0 && fields) {
      PetscInt f;

      for (f = 0; f < numFields; ++f)
        if (b->field == fields[f]) break;
      if (f == numFields) continue;
      fieldNew = f;
    }
    PetscCall(DSBoundaryDuplicate_Internal(b, &bNew));
    bNew->field = fieldNew < 0 ? b->field : fieldNew;
    *lastnext   = bNew;
    lastnext    = &(bNew->next);
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSDestroyBoundary - Remove all `DMBoundary` objects from the `PetscDS`

  Not Collective

  Input Parameter:
. ds - The `PetscDS` object

  Level: intermediate

.seealso: `PetscDS`, `DMBoundary`, `PetscDSCopyBoundary()`, `PetscDSCopyEquations()`
@*/
PetscErrorCode PetscDSDestroyBoundary(PetscDS ds)
{
  DSBoundary next = ds->boundary;

  PetscFunctionBegin;
  while (next) {
    DSBoundary b = next;

    next = b->next;
    PetscCall(PetscWeakFormDestroy(&b->wf));
    PetscCall(PetscFree(b->name));
    PetscCall(PetscFree(b->lname));
    PetscCall(PetscFree(b->values));
    PetscCall(PetscFree(b->comps));
    PetscCall(PetscFree(b));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSSelectDiscretizations - Copy discretizations to the new problem with different field layout

  Not Collective

  Input Parameters:
+ prob - The `PetscDS` object
. numFields - Number of new fields
- fields - Old field number for each new field

  Output Parameter:
. newprob - The `PetscDS` copy

  Level: intermediate

.seealso: `PetscDS`, `PetscDSSelectEquations()`, `PetscDSCopyBoundary()`, `PetscDSSetResidual()`, `PetscDSSetJacobian()`, `PetscDSSetRiemannSolver()`, `PetscDSSetBdResidual()`, `PetscDSSetBdJacobian()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSSelectDiscretizations(PetscDS prob, PetscInt numFields, const PetscInt fields[], PetscDS newprob)
{
  PetscInt Nf, Nfn, fn;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  if (fields) PetscValidIntPointer(fields, 3);
  PetscValidHeaderSpecific(newprob, PETSCDS_CLASSID, 4);
  PetscCall(PetscDSGetNumFields(prob, &Nf));
  PetscCall(PetscDSGetNumFields(newprob, &Nfn));
  numFields = numFields < 0 ? Nf : numFields;
  for (fn = 0; fn < numFields; ++fn) {
    const PetscInt f = fields ? fields[fn] : fn;
    PetscObject    disc;

    if (f >= Nf) continue;
    PetscCall(PetscDSGetDiscretization(prob, f, &disc));
    PetscCall(PetscDSSetDiscretization(newprob, fn, disc));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSSelectEquations - Copy pointwise function pointers to the new problem with different field layout

  Not Collective

  Input Parameters:
+ prob - The `PetscDS` object
. numFields - Number of new fields
- fields - Old field number for each new field

  Output Parameter:
. newprob - The `PetscDS` copy

  Level: intermediate

.seealso: `PetscDS`, `PetscDSSelectDiscretizations()`, `PetscDSCopyBoundary()`, `PetscDSSetResidual()`, `PetscDSSetJacobian()`, `PetscDSSetRiemannSolver()`, `PetscDSSetBdResidual()`, `PetscDSSetBdJacobian()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSSelectEquations(PetscDS prob, PetscInt numFields, const PetscInt fields[], PetscDS newprob)
{
  PetscInt Nf, Nfn, fn, gn;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  if (fields) PetscValidIntPointer(fields, 3);
  PetscValidHeaderSpecific(newprob, PETSCDS_CLASSID, 4);
  PetscCall(PetscDSGetNumFields(prob, &Nf));
  PetscCall(PetscDSGetNumFields(newprob, &Nfn));
  PetscCheck(numFields <= Nfn, PetscObjectComm((PetscObject)prob), PETSC_ERR_ARG_SIZ, "Number of fields %" PetscInt_FMT " to transfer must not be greater then the total number of fields %" PetscInt_FMT, numFields, Nfn);
  for (fn = 0; fn < numFields; ++fn) {
    const PetscInt   f = fields ? fields[fn] : fn;
    PetscPointFunc   obj;
    PetscPointFunc   f0, f1;
    PetscBdPointFunc f0Bd, f1Bd;
    PetscRiemannFunc r;

    if (f >= Nf) continue;
    PetscCall(PetscDSGetObjective(prob, f, &obj));
    PetscCall(PetscDSGetResidual(prob, f, &f0, &f1));
    PetscCall(PetscDSGetBdResidual(prob, f, &f0Bd, &f1Bd));
    PetscCall(PetscDSGetRiemannSolver(prob, f, &r));
    PetscCall(PetscDSSetObjective(newprob, fn, obj));
    PetscCall(PetscDSSetResidual(newprob, fn, f0, f1));
    PetscCall(PetscDSSetBdResidual(newprob, fn, f0Bd, f1Bd));
    PetscCall(PetscDSSetRiemannSolver(newprob, fn, r));
    for (gn = 0; gn < numFields; ++gn) {
      const PetscInt  g = fields ? fields[gn] : gn;
      PetscPointJac   g0, g1, g2, g3;
      PetscPointJac   g0p, g1p, g2p, g3p;
      PetscBdPointJac g0Bd, g1Bd, g2Bd, g3Bd;

      if (g >= Nf) continue;
      PetscCall(PetscDSGetJacobian(prob, f, g, &g0, &g1, &g2, &g3));
      PetscCall(PetscDSGetJacobianPreconditioner(prob, f, g, &g0p, &g1p, &g2p, &g3p));
      PetscCall(PetscDSGetBdJacobian(prob, f, g, &g0Bd, &g1Bd, &g2Bd, &g3Bd));
      PetscCall(PetscDSSetJacobian(newprob, fn, gn, g0, g1, g2, g3));
      PetscCall(PetscDSSetJacobianPreconditioner(newprob, fn, gn, g0p, g1p, g2p, g3p));
      PetscCall(PetscDSSetBdJacobian(newprob, fn, gn, g0Bd, g1Bd, g2Bd, g3Bd));
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSCopyEquations - Copy all pointwise function pointers to another `PetscDS`

  Not Collective

  Input Parameter:
. prob - The `PetscDS` object

  Output Parameter:
. newprob - The `PetscDS` copy

  Level: intermediate

.seealso: `PetscDS`, `PetscDSCopyBoundary()`, `PetscDSSetResidual()`, `PetscDSSetJacobian()`, `PetscDSSetRiemannSolver()`, `PetscDSSetBdResidual()`, `PetscDSSetBdJacobian()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSCopyEquations(PetscDS prob, PetscDS newprob)
{
  PetscWeakForm wf, newwf;
  PetscInt      Nf, Ng;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  PetscValidHeaderSpecific(newprob, PETSCDS_CLASSID, 2);
  PetscCall(PetscDSGetNumFields(prob, &Nf));
  PetscCall(PetscDSGetNumFields(newprob, &Ng));
  PetscCheck(Nf == Ng, PetscObjectComm((PetscObject)prob), PETSC_ERR_ARG_SIZ, "Number of fields must match %" PetscInt_FMT " != %" PetscInt_FMT, Nf, Ng);
  PetscCall(PetscDSGetWeakForm(prob, &wf));
  PetscCall(PetscDSGetWeakForm(newprob, &newwf));
  PetscCall(PetscWeakFormCopy(wf, newwf));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSCopyConstants - Copy all constants to another `PetscDS`

  Not Collective

  Input Parameter:
. prob - The `PetscDS` object

  Output Parameter:
. newprob - The `PetscDS` copy

  Level: intermediate

.seealso: `PetscDS`, `PetscDSCopyBoundary()`, `PetscDSCopyEquations()`, `PetscDSSetResidual()`, `PetscDSSetJacobian()`, `PetscDSSetRiemannSolver()`, `PetscDSSetBdResidual()`, `PetscDSSetBdJacobian()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSCopyConstants(PetscDS prob, PetscDS newprob)
{
  PetscInt           Nc;
  const PetscScalar *constants;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  PetscValidHeaderSpecific(newprob, PETSCDS_CLASSID, 2);
  PetscCall(PetscDSGetConstants(prob, &Nc, &constants));
  PetscCall(PetscDSSetConstants(newprob, Nc, (PetscScalar *)constants));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscDSCopyExactSolutions - Copy all exact solutions to another `PetscDS`

  Not Collective

  Input Parameter:
. ds - The `PetscDS` object

  Output Parameter:
. newds - The `PetscDS` copy

  Level: intermediate

.seealso: `PetscDS`, `PetscDSCopyBoundary()`, `PetscDSCopyEquations()`, `PetscDSSetResidual()`, `PetscDSSetJacobian()`, `PetscDSSetRiemannSolver()`, `PetscDSSetBdResidual()`, `PetscDSSetBdJacobian()`, `PetscDSCreate()`
@*/
PetscErrorCode PetscDSCopyExactSolutions(PetscDS ds, PetscDS newds)
{
  PetscSimplePointFunc sol;
  void                *ctx;
  PetscInt             Nf, f;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  PetscValidHeaderSpecific(newds, PETSCDS_CLASSID, 2);
  PetscCall(PetscDSGetNumFields(ds, &Nf));
  for (f = 0; f < Nf; ++f) {
    PetscCall(PetscDSGetExactSolution(ds, f, &sol, &ctx));
    PetscCall(PetscDSSetExactSolution(newds, f, sol, ctx));
    PetscCall(PetscDSGetExactSolutionTimeDerivative(ds, f, &sol, &ctx));
    PetscCall(PetscDSSetExactSolutionTimeDerivative(newds, f, sol, ctx));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode PetscDSCopy(PetscDS ds, DM dmNew, PetscDS dsNew)
{
  DSBoundary b;
  PetscInt   cdim, Nf, f, d;
  PetscBool  isCohesive;
  void      *ctx;

  PetscFunctionBegin;
  PetscCall(PetscDSCopyConstants(ds, dsNew));
  PetscCall(PetscDSCopyExactSolutions(ds, dsNew));
  PetscCall(PetscDSSelectDiscretizations(ds, PETSC_DETERMINE, NULL, dsNew));
  PetscCall(PetscDSCopyEquations(ds, dsNew));
  PetscCall(PetscDSGetNumFields(ds, &Nf));
  for (f = 0; f < Nf; ++f) {
    PetscCall(PetscDSGetContext(ds, f, &ctx));
    PetscCall(PetscDSSetContext(dsNew, f, ctx));
    PetscCall(PetscDSGetCohesive(ds, f, &isCohesive));
    PetscCall(PetscDSSetCohesive(dsNew, f, isCohesive));
    PetscCall(PetscDSGetJetDegree(ds, f, &d));
    PetscCall(PetscDSSetJetDegree(dsNew, f, d));
  }
  if (Nf) {
    PetscCall(PetscDSGetCoordinateDimension(ds, &cdim));
    PetscCall(PetscDSSetCoordinateDimension(dsNew, cdim));
  }
  PetscCall(PetscDSCopyBoundary(ds, PETSC_DETERMINE, NULL, dsNew));
  for (b = dsNew->boundary; b; b = b->next) {
    PetscCall(DMGetLabel(dmNew, b->lname, &b->label));
    /* Do not check if label exists here, since p4est calls this for the reference tree which does not have the labels */
    //PetscCheck(b->label,PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Label %s missing in new DM", name);
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode PetscDSGetHeightSubspace(PetscDS prob, PetscInt height, PetscDS *subprob)
{
  PetscInt dim, Nf, f;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(prob, PETSCDS_CLASSID, 1);
  PetscValidPointer(subprob, 3);
  if (height == 0) {
    *subprob = prob;
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  PetscCall(PetscDSGetNumFields(prob, &Nf));
  PetscCall(PetscDSGetSpatialDimension(prob, &dim));
  PetscCheck(height <= dim, PetscObjectComm((PetscObject)prob), PETSC_ERR_ARG_OUTOFRANGE, "DS can only handle height in [0, %" PetscInt_FMT "], not %" PetscInt_FMT, dim, height);
  if (!prob->subprobs) PetscCall(PetscCalloc1(dim, &prob->subprobs));
  if (!prob->subprobs[height - 1]) {
    PetscInt cdim;

    PetscCall(PetscDSCreate(PetscObjectComm((PetscObject)prob), &prob->subprobs[height - 1]));
    PetscCall(PetscDSGetCoordinateDimension(prob, &cdim));
    PetscCall(PetscDSSetCoordinateDimension(prob->subprobs[height - 1], cdim));
    for (f = 0; f < Nf; ++f) {
      PetscFE      subfe;
      PetscObject  obj;
      PetscClassId id;

      PetscCall(PetscDSGetDiscretization(prob, f, &obj));
      PetscCall(PetscObjectGetClassId(obj, &id));
      if (id == PETSCFE_CLASSID) PetscCall(PetscFEGetHeightSubspace((PetscFE)obj, height, &subfe));
      else SETERRQ(PetscObjectComm((PetscObject)prob), PETSC_ERR_ARG_WRONG, "Unsupported discretization type for field %" PetscInt_FMT, f);
      PetscCall(PetscDSSetDiscretization(prob->subprobs[height - 1], f, (PetscObject)subfe));
    }
  }
  *subprob = prob->subprobs[height - 1];
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode PetscDSPermuteQuadPoint(PetscDS ds, PetscInt ornt, PetscInt field, PetscInt q, PetscInt *qperm)
{
  IS              permIS;
  PetscQuadrature quad;
  DMPolytopeType  ct;
  const PetscInt *perm;
  PetscInt        Na, Nq;

  PetscFunctionBeginHot;
  PetscCall(PetscFEGetQuadrature((PetscFE)ds->disc[field], &quad));
  PetscCall(PetscQuadratureGetData(quad, NULL, NULL, &Nq, NULL, NULL));
  PetscCall(PetscQuadratureGetCellType(quad, &ct));
  PetscCheck(q >= 0 && q < Nq, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Quadrature point %" PetscInt_FMT " is not in [0, %" PetscInt_FMT ")", q, Nq);
  Na = DMPolytopeTypeGetNumArrangments(ct) / 2;
  PetscCheck(ornt >= -Na && ornt < Na, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Orientation %" PetscInt_FMT " of %s is not in [%" PetscInt_FMT ", %" PetscInt_FMT ")", ornt, DMPolytopeTypes[ct], -Na, Na);
  if (!ds->quadPerm[(PetscInt)ct]) PetscCall(PetscQuadratureComputePermutations(quad, NULL, &ds->quadPerm[(PetscInt)ct]));
  permIS = ds->quadPerm[(PetscInt)ct][ornt + Na];
  PetscCall(ISGetIndices(permIS, &perm));
  *qperm = perm[q];
  PetscCall(ISRestoreIndices(permIS, &perm));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode PetscDSGetDiscType_Internal(PetscDS ds, PetscInt f, PetscDiscType *disctype)
{
  PetscObject  obj;
  PetscClassId id;
  PetscInt     Nf;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  PetscValidPointer(disctype, 3);
  *disctype = PETSC_DISC_NONE;
  PetscCall(PetscDSGetNumFields(ds, &Nf));
  PetscCheck(f < Nf, PetscObjectComm((PetscObject)ds), PETSC_ERR_ARG_SIZ, "Field %" PetscInt_FMT " must be in [0, %" PetscInt_FMT ")", f, Nf);
  PetscCall(PetscDSGetDiscretization(ds, f, &obj));
  if (obj) {
    PetscCall(PetscObjectGetClassId(obj, &id));
    if (id == PETSCFE_CLASSID) *disctype = PETSC_DISC_FE;
    else *disctype = PETSC_DISC_FV;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PetscDSDestroy_Basic(PetscDS ds)
{
  PetscFunctionBegin;
  PetscCall(PetscFree(ds->data));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PetscDSInitialize_Basic(PetscDS ds)
{
  PetscFunctionBegin;
  ds->ops->setfromoptions = NULL;
  ds->ops->setup          = NULL;
  ds->ops->view           = NULL;
  ds->ops->destroy        = PetscDSDestroy_Basic;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*MC
  PETSCDSBASIC = "basic" - A discrete system with pointwise residual and boundary residual functions

  Level: intermediate

.seealso: `PetscDSType`, `PetscDSCreate()`, `PetscDSSetType()`
M*/

PETSC_EXTERN PetscErrorCode PetscDSCreate_Basic(PetscDS ds)
{
  PetscDS_Basic *b;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds, PETSCDS_CLASSID, 1);
  PetscCall(PetscNew(&b));
  ds->data = b;

  PetscCall(PetscDSInitialize_Basic(ds));
  PetscFunctionReturn(PETSC_SUCCESS);
}