xref: /petsc/src/snes/tutorials/ex28.c (revision fb3c7e2dd4f43a268b95c335e0bddf05b42b9816)

static const char help[] = "1D multiphysics prototype with analytic Jacobians to solve individual problems and a coupled problem.\n\n";

/* Solve a PDE coupled to an algebraic system in 1D
 *
 * PDE (U):
 *     -(k u_x)_x = 1 on (0,1), subject to u(0) = 0, u(1) = 1
 * Algebraic (K):
 *     exp(k-1) + k = 1/(1/(1+u) + 1/(1+u_x^2))
 *
 * The discretization places k at staggered points, and a separate DMDA is used for each "physics".
 *
 * This example is a prototype for coupling in multi-physics problems, therefore residual evaluation and assembly for
 * each problem (referred to as U and K) are written separately.  This permits the same "physics" code to be used for
 * solving each uncoupled problem as well as the coupled system.  In particular, run with -problem_type 0 to solve only
 * problem U (with K fixed), -problem_type 1 to solve only K (with U fixed), and -problem_type 2 to solve both at once.
 *
 * In all cases, a fully-assembled analytic Jacobian is available, so the systems can be solved with a direct solve or
 * any other standard method.  Additionally, by running with
 *
 *   -pack_dm_mat_type nest
 *
 * The same code assembles a coupled matrix where each block is stored separately, which allows the use of PCFieldSplit
 * without copying values to extract submatrices.
 */

#include <petscsnes.h>
#include <petscdm.h>
#include <petscdmda.h>
#include <petscdmcomposite.h>

typedef struct _UserCtx *User;
struct _UserCtx {
  PetscInt ptype;
  DM       pack;
  Vec      Uloc, Kloc;
};

static PetscErrorCode FormFunctionLocal_U(User user, DMDALocalInfo *info, const PetscScalar u[], const PetscScalar k[], PetscScalar f[])
{
  PetscReal hx = 1. / info->mx;
  PetscInt  i;

  PetscFunctionBeginUser;
  for (i = info->xs; i < info->xs + info->xm; i++) {
    if (i == 0) f[i] = 1. / hx * u[i];
    else if (i == info->mx - 1) f[i] = 1. / hx * (u[i] - 1.0);
    else f[i] = hx * ((k[i - 1] * (u[i] - u[i - 1]) - k[i] * (u[i + 1] - u[i])) / (hx * hx) - 1.0);
  }
  PetscFunctionReturn(0);
}

static PetscErrorCode FormFunctionLocal_K(User user, DMDALocalInfo *info, const PetscScalar u[], const PetscScalar k[], PetscScalar f[])
{
  PetscReal hx = 1. / info->mx;
  PetscInt  i;

  PetscFunctionBeginUser;
  for (i = info->xs; i < info->xs + info->xm; i++) {
    const PetscScalar ubar = 0.5 * (u[i + 1] + u[i]), gradu = (u[i + 1] - u[i]) / hx, g = 1. + gradu * gradu, w = 1. / (1. + ubar) + 1. / g;
    f[i] = hx * (PetscExpScalar(k[i] - 1.0) + k[i] - 1. / w);
  }
  PetscFunctionReturn(0);
}

static PetscErrorCode FormFunction_All(SNES snes, Vec X, Vec F, void *ctx)
{
  User          user = (User)ctx;
  DM            dau, dak;
  DMDALocalInfo infou, infok;
  PetscScalar  *u, *k;
  PetscScalar  *fu, *fk;
  Vec           Uloc, Kloc, Fu, Fk;

  PetscFunctionBeginUser;
  PetscCall(DMCompositeGetEntries(user->pack, &dau, &dak));
  PetscCall(DMDAGetLocalInfo(dau, &infou));
  PetscCall(DMDAGetLocalInfo(dak, &infok));
  PetscCall(DMCompositeGetLocalVectors(user->pack, &Uloc, &Kloc));
  switch (user->ptype) {
  case 0:
    PetscCall(DMGlobalToLocalBegin(dau, X, INSERT_VALUES, Uloc));
    PetscCall(DMGlobalToLocalEnd(dau, X, INSERT_VALUES, Uloc));
    PetscCall(DMDAVecGetArray(dau, Uloc, &u));
    PetscCall(DMDAVecGetArray(dak, user->Kloc, &k));
    PetscCall(DMDAVecGetArray(dau, F, &fu));
    PetscCall(FormFunctionLocal_U(user, &infou, u, k, fu));
    PetscCall(DMDAVecRestoreArray(dau, F, &fu));
    PetscCall(DMDAVecRestoreArray(dau, Uloc, &u));
    PetscCall(DMDAVecRestoreArray(dak, user->Kloc, &k));
    break;
  case 1:
    PetscCall(DMGlobalToLocalBegin(dak, X, INSERT_VALUES, Kloc));
    PetscCall(DMGlobalToLocalEnd(dak, X, INSERT_VALUES, Kloc));
    PetscCall(DMDAVecGetArray(dau, user->Uloc, &u));
    PetscCall(DMDAVecGetArray(dak, Kloc, &k));
    PetscCall(DMDAVecGetArray(dak, F, &fk));
    PetscCall(FormFunctionLocal_K(user, &infok, u, k, fk));
    PetscCall(DMDAVecRestoreArray(dak, F, &fk));
    PetscCall(DMDAVecRestoreArray(dau, user->Uloc, &u));
    PetscCall(DMDAVecRestoreArray(dak, Kloc, &k));
    break;
  case 2:
    PetscCall(DMCompositeScatter(user->pack, X, Uloc, Kloc));
    PetscCall(DMDAVecGetArray(dau, Uloc, &u));
    PetscCall(DMDAVecGetArray(dak, Kloc, &k));
    PetscCall(DMCompositeGetAccess(user->pack, F, &Fu, &Fk));
    PetscCall(DMDAVecGetArray(dau, Fu, &fu));
    PetscCall(DMDAVecGetArray(dak, Fk, &fk));
    PetscCall(FormFunctionLocal_U(user, &infou, u, k, fu));
    PetscCall(FormFunctionLocal_K(user, &infok, u, k, fk));
    PetscCall(DMDAVecRestoreArray(dau, Fu, &fu));
    PetscCall(DMDAVecRestoreArray(dak, Fk, &fk));
    PetscCall(DMCompositeRestoreAccess(user->pack, F, &Fu, &Fk));
    PetscCall(DMDAVecRestoreArray(dau, Uloc, &u));
    PetscCall(DMDAVecRestoreArray(dak, Kloc, &k));
    break;
  }
  PetscCall(DMCompositeRestoreLocalVectors(user->pack, &Uloc, &Kloc));
  PetscFunctionReturn(0);
}

static PetscErrorCode FormJacobianLocal_U(User user, DMDALocalInfo *info, const PetscScalar u[], const PetscScalar k[], Mat Buu)
{
  PetscReal hx = 1. / info->mx;
  PetscInt  i;

  PetscFunctionBeginUser;
  for (i = info->xs; i < info->xs + info->xm; i++) {
    PetscInt    row = i - info->gxs, cols[] = {row - 1, row, row + 1};
    PetscScalar val = 1. / hx;
    if (i == 0) {
      PetscCall(MatSetValuesLocal(Buu, 1, &row, 1, &row, &val, INSERT_VALUES));
    } else if (i == info->mx - 1) {
      PetscCall(MatSetValuesLocal(Buu, 1, &row, 1, &row, &val, INSERT_VALUES));
    } else {
      PetscScalar vals[] = {-k[i - 1] / hx, (k[i - 1] + k[i]) / hx, -k[i] / hx};
      PetscCall(MatSetValuesLocal(Buu, 1, &row, 3, cols, vals, INSERT_VALUES));
    }
  }
  PetscFunctionReturn(0);
}

static PetscErrorCode FormJacobianLocal_K(User user, DMDALocalInfo *info, const PetscScalar u[], const PetscScalar k[], Mat Bkk)
{
  PetscReal hx = 1. / info->mx;
  PetscInt  i;

  PetscFunctionBeginUser;
  for (i = info->xs; i < info->xs + info->xm; i++) {
    PetscInt    row    = i - info->gxs;
    PetscScalar vals[] = {hx * (PetscExpScalar(k[i] - 1.) + (PetscScalar)1.)};
    PetscCall(MatSetValuesLocal(Bkk, 1, &row, 1, &row, vals, INSERT_VALUES));
  }
  PetscFunctionReturn(0);
}

static PetscErrorCode FormJacobianLocal_UK(User user, DMDALocalInfo *info, DMDALocalInfo *infok, const PetscScalar u[], const PetscScalar k[], Mat Buk)
{
  PetscReal   hx = 1. / info->mx;
  PetscInt    i;
  PetscInt    row, cols[2];
  PetscScalar vals[2];

  PetscFunctionBeginUser;
  if (!Buk) PetscFunctionReturn(0); /* Not assembling this block */
  for (i = info->xs; i < info->xs + info->xm; i++) {
    if (i == 0 || i == info->mx - 1) continue;
    row     = i - info->gxs;
    cols[0] = i - 1 - infok->gxs;
    vals[0] = (u[i] - u[i - 1]) / hx;
    cols[1] = i - infok->gxs;
    vals[1] = (u[i] - u[i + 1]) / hx;
    PetscCall(MatSetValuesLocal(Buk, 1, &row, 2, cols, vals, INSERT_VALUES));
  }
  PetscFunctionReturn(0);
}

static PetscErrorCode FormJacobianLocal_KU(User user, DMDALocalInfo *info, DMDALocalInfo *infok, const PetscScalar u[], const PetscScalar k[], Mat Bku)
{
  PetscInt  i;
  PetscReal hx = 1. / (info->mx - 1);

  PetscFunctionBeginUser;
  if (!Bku) PetscFunctionReturn(0); /* Not assembling this block */
  for (i = infok->xs; i < infok->xs + infok->xm; i++) {
    PetscInt    row = i - infok->gxs, cols[2];
    PetscScalar vals[2];
    const PetscScalar ubar = 0.5 * (u[i] + u[i + 1]), ubar_L = 0.5, ubar_R = 0.5, gradu = (u[i + 1] - u[i]) / hx, gradu_L = -1. / hx, gradu_R = 1. / hx, g = 1. + PetscSqr(gradu), g_gradu = 2. * gradu, w = 1. / (1. + ubar) + 1. / g, w_ubar = -1. / PetscSqr(1. + ubar), w_gradu = -g_gradu / PetscSqr(g), iw = 1. / w, iw_ubar = -w_ubar * PetscSqr(iw), iw_gradu = -w_gradu * PetscSqr(iw);
    cols[0] = i - info->gxs;
    vals[0] = -hx * (iw_ubar * ubar_L + iw_gradu * gradu_L);
    cols[1] = i + 1 - info->gxs;
    vals[1] = -hx * (iw_ubar * ubar_R + iw_gradu * gradu_R);
    PetscCall(MatSetValuesLocal(Bku, 1, &row, 2, cols, vals, INSERT_VALUES));
  }
  PetscFunctionReturn(0);
}

static PetscErrorCode FormJacobian_All(SNES snes, Vec X, Mat J, Mat B, void *ctx)
{
  User          user = (User)ctx;
  DM            dau, dak;
  DMDALocalInfo infou, infok;
  PetscScalar  *u, *k;
  Vec           Uloc, Kloc;

  PetscFunctionBeginUser;
  PetscCall(DMCompositeGetEntries(user->pack, &dau, &dak));
  PetscCall(DMDAGetLocalInfo(dau, &infou));
  PetscCall(DMDAGetLocalInfo(dak, &infok));
  PetscCall(DMCompositeGetLocalVectors(user->pack, &Uloc, &Kloc));
  switch (user->ptype) {
  case 0:
    PetscCall(DMGlobalToLocalBegin(dau, X, INSERT_VALUES, Uloc));
    PetscCall(DMGlobalToLocalEnd(dau, X, INSERT_VALUES, Uloc));
    PetscCall(DMDAVecGetArray(dau, Uloc, &u));
    PetscCall(DMDAVecGetArray(dak, user->Kloc, &k));
    PetscCall(FormJacobianLocal_U(user, &infou, u, k, B));
    PetscCall(DMDAVecRestoreArray(dau, Uloc, &u));
    PetscCall(DMDAVecRestoreArray(dak, user->Kloc, &k));
    break;
  case 1:
    PetscCall(DMGlobalToLocalBegin(dak, X, INSERT_VALUES, Kloc));
    PetscCall(DMGlobalToLocalEnd(dak, X, INSERT_VALUES, Kloc));
    PetscCall(DMDAVecGetArray(dau, user->Uloc, &u));
    PetscCall(DMDAVecGetArray(dak, Kloc, &k));
    PetscCall(FormJacobianLocal_K(user, &infok, u, k, B));
    PetscCall(DMDAVecRestoreArray(dau, user->Uloc, &u));
    PetscCall(DMDAVecRestoreArray(dak, Kloc, &k));
    break;
  case 2: {
    Mat       Buu, Buk, Bku, Bkk;
    PetscBool nest;
    IS       *is;
    PetscCall(DMCompositeScatter(user->pack, X, Uloc, Kloc));
    PetscCall(DMDAVecGetArray(dau, Uloc, &u));
    PetscCall(DMDAVecGetArray(dak, Kloc, &k));
    PetscCall(DMCompositeGetLocalISs(user->pack, &is));
    PetscCall(MatGetLocalSubMatrix(B, is[0], is[0], &Buu));
    PetscCall(MatGetLocalSubMatrix(B, is[0], is[1], &Buk));
    PetscCall(MatGetLocalSubMatrix(B, is[1], is[0], &Bku));
    PetscCall(MatGetLocalSubMatrix(B, is[1], is[1], &Bkk));
    PetscCall(FormJacobianLocal_U(user, &infou, u, k, Buu));
    PetscCall(PetscObjectTypeCompare((PetscObject)B, MATNEST, &nest));
    if (!nest) {
      /*
         DMCreateMatrix_Composite()  for a nested matrix does not generate off-block matrices that one can call MatSetValuesLocal() on, it just creates dummy
         matrices with no entries; there cannot insert values into them. Commit b6480e041dd2293a65f96222772d68cdb4ed6306
         changed Mat_Nest() from returning NULL pointers for these submatrices to dummy matrices because PCFIELDSPLIT could not
         handle the returned null matrices.
      */
      PetscCall(FormJacobianLocal_UK(user, &infou, &infok, u, k, Buk));
      PetscCall(FormJacobianLocal_KU(user, &infou, &infok, u, k, Bku));
    }
    PetscCall(FormJacobianLocal_K(user, &infok, u, k, Bkk));
    PetscCall(MatRestoreLocalSubMatrix(B, is[0], is[0], &Buu));
    PetscCall(MatRestoreLocalSubMatrix(B, is[0], is[1], &Buk));
    PetscCall(MatRestoreLocalSubMatrix(B, is[1], is[0], &Bku));
    PetscCall(MatRestoreLocalSubMatrix(B, is[1], is[1], &Bkk));
    PetscCall(DMDAVecRestoreArray(dau, Uloc, &u));
    PetscCall(DMDAVecRestoreArray(dak, Kloc, &k));

    PetscCall(ISDestroy(&is[0]));
    PetscCall(ISDestroy(&is[1]));
    PetscCall(PetscFree(is));
  } break;
  }
  PetscCall(DMCompositeRestoreLocalVectors(user->pack, &Uloc, &Kloc));
  PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
  if (J != B) {
    PetscCall(MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY));
    PetscCall(MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY));
  }
  PetscFunctionReturn(0);
}

static PetscErrorCode FormInitial_Coupled(User user, Vec X)
{
  DM            dau, dak;
  DMDALocalInfo infou, infok;
  Vec           Xu, Xk;
  PetscScalar  *u, *k, hx;
  PetscInt      i;

  PetscFunctionBeginUser;
  PetscCall(DMCompositeGetEntries(user->pack, &dau, &dak));
  PetscCall(DMCompositeGetAccess(user->pack, X, &Xu, &Xk));
  PetscCall(DMDAVecGetArray(dau, Xu, &u));
  PetscCall(DMDAVecGetArray(dak, Xk, &k));
  PetscCall(DMDAGetLocalInfo(dau, &infou));
  PetscCall(DMDAGetLocalInfo(dak, &infok));
  hx = 1. / (infok.mx);
  for (i = infou.xs; i < infou.xs + infou.xm; i++) u[i] = (PetscScalar)i * hx * (1. - (PetscScalar)i * hx);
  for (i = infok.xs; i < infok.xs + infok.xm; i++) k[i] = 1.0 + 0.5 * PetscSinScalar(2 * PETSC_PI * i * hx);
  PetscCall(DMDAVecRestoreArray(dau, Xu, &u));
  PetscCall(DMDAVecRestoreArray(dak, Xk, &k));
  PetscCall(DMCompositeRestoreAccess(user->pack, X, &Xu, &Xk));
  PetscCall(DMCompositeScatter(user->pack, X, user->Uloc, user->Kloc));
  PetscFunctionReturn(0);
}

int main(int argc, char *argv[])
{
  DM              dau, dak, pack;
  const PetscInt *lxu;
  PetscInt       *lxk, m, sizes;
  User            user;
  SNES            snes;
  Vec             X, F, Xu, Xk, Fu, Fk;
  Mat             B;
  IS             *isg;
  PetscBool       pass_dm;

  PetscFunctionBeginUser;
  PetscCall(PetscInitialize(&argc, &argv, 0, help));
  PetscCall(DMDACreate1d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, 10, 1, 1, NULL, &dau));
  PetscCall(DMSetOptionsPrefix(dau, "u_"));
  PetscCall(DMSetFromOptions(dau));
  PetscCall(DMSetUp(dau));
  PetscCall(DMDAGetOwnershipRanges(dau, &lxu, 0, 0));
  PetscCall(DMDAGetInfo(dau, 0, &m, 0, 0, &sizes, 0, 0, 0, 0, 0, 0, 0, 0));
  PetscCall(PetscMalloc1(sizes, &lxk));
  PetscCall(PetscArraycpy(lxk, lxu, sizes));
  lxk[0]--;
  PetscCall(DMDACreate1d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, m - 1, 1, 1, lxk, &dak));
  PetscCall(DMSetOptionsPrefix(dak, "k_"));
  PetscCall(DMSetFromOptions(dak));
  PetscCall(DMSetUp(dak));
  PetscCall(PetscFree(lxk));

  PetscCall(DMCompositeCreate(PETSC_COMM_WORLD, &pack));
  PetscCall(DMSetOptionsPrefix(pack, "pack_"));
  PetscCall(DMCompositeAddDM(pack, dau));
  PetscCall(DMCompositeAddDM(pack, dak));
  PetscCall(DMDASetFieldName(dau, 0, "u"));
  PetscCall(DMDASetFieldName(dak, 0, "k"));
  PetscCall(DMSetFromOptions(pack));

  PetscCall(DMCreateGlobalVector(pack, &X));
  PetscCall(VecDuplicate(X, &F));

  PetscCall(PetscNew(&user));

  user->pack = pack;

  PetscCall(DMCompositeGetGlobalISs(pack, &isg));
  PetscCall(DMCompositeGetLocalVectors(pack, &user->Uloc, &user->Kloc));
  PetscCall(DMCompositeScatter(pack, X, user->Uloc, user->Kloc));

  PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Coupled problem options", "SNES");
  {
    user->ptype = 0;
    pass_dm     = PETSC_TRUE;

    PetscCall(PetscOptionsInt("-problem_type", "0: solve for u only, 1: solve for k only, 2: solve for both", 0, user->ptype, &user->ptype, NULL));
    PetscCall(PetscOptionsBool("-pass_dm", "Pass the packed DM to SNES to use when determining splits and forward into splits", 0, pass_dm, &pass_dm, NULL));
  }
  PetscOptionsEnd();

  PetscCall(FormInitial_Coupled(user, X));

  PetscCall(SNESCreate(PETSC_COMM_WORLD, &snes));
  switch (user->ptype) {
  case 0:
    PetscCall(DMCompositeGetAccess(pack, X, &Xu, 0));
    PetscCall(DMCompositeGetAccess(pack, F, &Fu, 0));
    PetscCall(DMCreateMatrix(dau, &B));
    PetscCall(SNESSetFunction(snes, Fu, FormFunction_All, user));
    PetscCall(SNESSetJacobian(snes, B, B, FormJacobian_All, user));
    PetscCall(SNESSetFromOptions(snes));
    PetscCall(SNESSetDM(snes, dau));
    PetscCall(SNESSolve(snes, NULL, Xu));
    PetscCall(DMCompositeRestoreAccess(pack, X, &Xu, 0));
    PetscCall(DMCompositeRestoreAccess(pack, F, &Fu, 0));
    break;
  case 1:
    PetscCall(DMCompositeGetAccess(pack, X, 0, &Xk));
    PetscCall(DMCompositeGetAccess(pack, F, 0, &Fk));
    PetscCall(DMCreateMatrix(dak, &B));
    PetscCall(SNESSetFunction(snes, Fk, FormFunction_All, user));
    PetscCall(SNESSetJacobian(snes, B, B, FormJacobian_All, user));
    PetscCall(SNESSetFromOptions(snes));
    PetscCall(SNESSetDM(snes, dak));
    PetscCall(SNESSolve(snes, NULL, Xk));
    PetscCall(DMCompositeRestoreAccess(pack, X, 0, &Xk));
    PetscCall(DMCompositeRestoreAccess(pack, F, 0, &Fk));
    break;
  case 2:
    PetscCall(DMCreateMatrix(pack, &B));
    /* This example does not correctly allocate off-diagonal blocks. These options allows new nonzeros (slow). */
    PetscCall(MatSetOption(B, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_FALSE));
    PetscCall(MatSetOption(B, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_FALSE));
    PetscCall(SNESSetFunction(snes, F, FormFunction_All, user));
    PetscCall(SNESSetJacobian(snes, B, B, FormJacobian_All, user));
    PetscCall(SNESSetFromOptions(snes));
    if (!pass_dm) { /* Manually provide index sets and names for the splits */
      KSP ksp;
      PC  pc;
      PetscCall(SNESGetKSP(snes, &ksp));
      PetscCall(KSPGetPC(ksp, &pc));
      PetscCall(PCFieldSplitSetIS(pc, "u", isg[0]));
      PetscCall(PCFieldSplitSetIS(pc, "k", isg[1]));
    } else {
      /* The same names come from the options prefix for dau and dak. This option can support geometric multigrid inside
       * of splits, but it requires using a DM (perhaps your own implementation). */
      PetscCall(SNESSetDM(snes, pack));
    }
    PetscCall(SNESSolve(snes, NULL, X));
    break;
  }
  PetscCall(VecViewFromOptions(X, NULL, "-view_sol"));

  if (0) {
    PetscInt  col      = 0;
    PetscBool mult_dup = PETSC_FALSE, view_dup = PETSC_FALSE;
    Mat       D;
    Vec       Y;

    PetscCall(PetscOptionsGetInt(NULL, 0, "-col", &col, 0));
    PetscCall(PetscOptionsGetBool(NULL, 0, "-mult_dup", &mult_dup, 0));
    PetscCall(PetscOptionsGetBool(NULL, 0, "-view_dup", &view_dup, 0));

    PetscCall(VecDuplicate(X, &Y));
    /* PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY)); */
    /* PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY)); */
    PetscCall(MatConvert(B, MATAIJ, MAT_INITIAL_MATRIX, &D));
    PetscCall(VecZeroEntries(X));
    PetscCall(VecSetValue(X, col, 1.0, INSERT_VALUES));
    PetscCall(VecAssemblyBegin(X));
    PetscCall(VecAssemblyEnd(X));
    PetscCall(MatMult(mult_dup ? D : B, X, Y));
    PetscCall(MatView(view_dup ? D : B, PETSC_VIEWER_STDOUT_WORLD));
    /* PetscCall(VecView(X,PETSC_VIEWER_STDOUT_WORLD)); */
    PetscCall(VecView(Y, PETSC_VIEWER_STDOUT_WORLD));
    PetscCall(MatDestroy(&D));
    PetscCall(VecDestroy(&Y));
  }

  PetscCall(DMCompositeRestoreLocalVectors(pack, &user->Uloc, &user->Kloc));
  PetscCall(PetscFree(user));

  PetscCall(ISDestroy(&isg[0]));
  PetscCall(ISDestroy(&isg[1]));
  PetscCall(PetscFree(isg));
  PetscCall(VecDestroy(&X));
  PetscCall(VecDestroy(&F));
  PetscCall(MatDestroy(&B));
  PetscCall(DMDestroy(&dau));
  PetscCall(DMDestroy(&dak));
  PetscCall(DMDestroy(&pack));
  PetscCall(SNESDestroy(&snes));
  PetscCall(PetscFinalize());
  return 0;
}

/*TEST

   test:
      suffix: 0
      nsize: 3
      args: -u_da_grid_x 20 -snes_converged_reason -snes_monitor_short -problem_type 0

   test:
      suffix: 1
      nsize: 3
      args: -u_da_grid_x 20 -snes_converged_reason -snes_monitor_short -problem_type 1

   test:
      suffix: 2
      nsize: 3
      args: -u_da_grid_x 20 -snes_converged_reason -snes_monitor_short -problem_type 2

   testset:
      suffix: 3
      nsize: 3
      output_file: output/ex28_3.out
      args: -u_da_grid_x 20 -snes_converged_reason -snes_monitor_short -ksp_monitor_short -problem_type 2 -snes_mf_operator  -pc_type fieldsplit -pc_fieldsplit_dm_splits -pc_fieldsplit_type additive -fieldsplit_u_ksp_type gmres -fieldsplit_k_pc_type jacobi

      test:
        suffix: std
        args: -pack_dm_mat_type {{aij nest}}

      test:
        suffix: cuda
        requires: cuda
        args: -pack_dm_mat_type aijcusparse -pack_dm_vec_type cuda

      test:
        suffix: hip
        requires: hip
        args: -pack_dm_mat_type aijhipsparse -pack_dm_vec_type hip

      test:
        suffix: kok
        requires: kokkos_kernels
        args: -pack_dm_mat_type aijkokkos -pack_dm_vec_type kokkos

   test:
      suffix: 4
      nsize: 6
      args: -u_da_grid_x 257 -snes_converged_reason -snes_monitor_short -ksp_monitor_short -problem_type 2 -snes_mf_operator -pack_dm_mat_type aij -pc_type fieldsplit -pc_fieldsplit_type multiplicative -fieldsplit_u_ksp_type gmres -fieldsplit_u_ksp_pc_side right -fieldsplit_u_pc_type mg -fieldsplit_u_pc_mg_levels 4 -fieldsplit_u_mg_levels_ksp_type richardson -fieldsplit_u_mg_levels_ksp_max_it 1 -fieldsplit_u_mg_levels_pc_type sor -fieldsplit_u_pc_mg_galerkin pmat -fieldsplit_u_ksp_converged_reason -fieldsplit_k_pc_type jacobi
      requires: !single

   test:
      suffix: glvis_composite_da_1d
      args: -u_da_grid_x 20 -problem_type 0 -snes_monitor_solution glvis:

   test:
      suffix: cuda
      nsize: 1
      requires: cuda
      args: -u_da_grid_x 20 -snes_converged_reason -snes_monitor_short -problem_type 2 -pack_dm_mat_type aijcusparse -pack_dm_vec_type cuda

   test:
      suffix: viennacl
      nsize: 1
      requires: viennacl
      args: -u_da_grid_x 20 -snes_converged_reason -snes_monitor_short -problem_type 2 -pack_dm_mat_type aijviennacl -pack_dm_vec_type viennacl

TEST*/