xref: /libCEED/examples/petsc/src/swarmutils.c (revision b6972d7456611f84b0e462eb1490bcb662442e6a)

#include "../include/swarmutils.h"
#include "../qfunctions/swarm/swarmmass.h"

// ------------------------------------------------------------------------------------------------
// Context utilities
// ------------------------------------------------------------------------------------------------
PetscErrorCode DMSwarmCeedContextCreate(DM dm_swarm, const char *ceed_resource, DMSwarmCeedContext *ctx) {
  DM                  dm_mesh, dm_coord;
  CeedElemRestriction elem_restr_u_mesh, elem_restr_x_mesh, elem_restr_x_points, elem_restr_u_points, elem_restr_q_data_points;
  CeedBasis           basis_u, basis_x;
  CeedVector          x_ref_points, q_data_points;
  CeedInt             num_comp;

  PetscFunctionBeginUser;
  PetscCall(PetscNew(ctx));
  PetscCall(DMSwarmGetCellDM(dm_swarm, &dm_mesh));
  PetscCall(DMGetCoordinateDM(dm_mesh, &dm_coord));

  CeedInit(ceed_resource, &(*ctx)->ceed);
  // Background mesh objects
  {
    BPData bp_data = {.q_mode = CEED_GAUSS};

    PetscCall(CreateBasisFromPlex((*ctx)->ceed, dm_mesh, NULL, 0, 0, 0, bp_data, &basis_u));
    PetscCall(CreateBasisFromPlex((*ctx)->ceed, dm_coord, NULL, 0, 0, 0, bp_data, &basis_x));
    PetscCall(CreateRestrictionFromPlex((*ctx)->ceed, dm_mesh, 0, NULL, 0, &elem_restr_u_mesh));
    PetscCall(CreateRestrictionFromPlex((*ctx)->ceed, dm_coord, 0, NULL, 0, &elem_restr_x_mesh));

    // -- Mesh vectors
    CeedElemRestrictionCreateVector(elem_restr_u_mesh, &(*ctx)->u_mesh, NULL);
    CeedElemRestrictionCreateVector(elem_restr_u_mesh, &(*ctx)->v_mesh, NULL);
  }
  // Swarm objects
  {
    PetscInt        dim;
    const PetscInt *cell_points;
    IS              is_points;
    Vec             X_ref;
    CeedInt         num_elem;

    PetscCall(DMSwarmCreateReferenceCoordinates(dm_swarm, &is_points, &X_ref));
    PetscCall(DMGetDimension(dm_mesh, &dim));
    CeedElemRestrictionGetNumElements(elem_restr_u_mesh, &num_elem);
    CeedElemRestrictionGetNumComponents(elem_restr_u_mesh, &num_comp);

    PetscCall(ISGetIndices(is_points, &cell_points));
    PetscInt num_points = cell_points[num_elem + 1] - num_elem - 2;
    CeedInt  offsets[num_elem + 1 + num_points];

    for (PetscInt i = 0; i < num_elem + 1; i++) offsets[i] = cell_points[i + 1] - 1;
    for (PetscInt i = num_elem + 1; i < num_points + num_elem + 1; i++) offsets[i] = cell_points[i + 1];
    PetscCall(ISRestoreIndices(is_points, &cell_points));

    // -- Points restrictions
    CeedElemRestrictionCreateAtPoints((*ctx)->ceed, num_elem, num_points, num_comp, num_points * num_comp, CEED_MEM_HOST, CEED_COPY_VALUES, offsets,
                                      &elem_restr_u_points);
    CeedElemRestrictionCreateAtPoints((*ctx)->ceed, num_elem, num_points, dim, num_points * dim, CEED_MEM_HOST, CEED_COPY_VALUES, offsets,
                                      &elem_restr_x_points);
    CeedElemRestrictionCreateAtPoints((*ctx)->ceed, num_elem, num_points, 1, num_points, CEED_MEM_HOST, CEED_COPY_VALUES, offsets,
                                      &elem_restr_q_data_points);

    // -- Points vectors
    CeedElemRestrictionCreateVector(elem_restr_u_points, &(*ctx)->u_points, NULL);
    CeedElemRestrictionCreateVector(elem_restr_q_data_points, &q_data_points, NULL);

    // -- Ref coordinates
    {
      PetscMemType       X_mem_type;
      const PetscScalar *x;

      CeedVectorCreate((*ctx)->ceed, num_points * dim, &x_ref_points);

      PetscCall(VecGetArrayReadAndMemType(X_ref, (const PetscScalar **)&x, &X_mem_type));
      CeedVectorSetArray(x_ref_points, MemTypeP2C(X_mem_type), CEED_COPY_VALUES, (CeedScalar *)x);
      PetscCall(VecRestoreArrayReadAndMemType(X_ref, (const PetscScalar **)&x));
    }

    // Create Q data
    {
      CeedQFunction qf_setup;
      CeedOperator  op_setup;
      CeedVector    x_coord;

      {
        Vec                X_loc;
        CeedInt            len;
        const PetscScalar *x;

        PetscCall(DMGetCoordinatesLocal(dm_mesh, &X_loc));
        PetscCall(VecGetLocalSize(X_loc, &len));
        CeedVectorCreate((*ctx)->ceed, len, &x_coord);

        PetscCall(VecGetArrayRead(X_loc, &x));
        CeedVectorSetArray(x_coord, CEED_MEM_HOST, CEED_COPY_VALUES, (CeedScalar *)x);
        PetscCall(VecRestoreArrayRead(X_loc, &x));
      }

      // Setup geometric scaling
      CeedQFunctionCreateInterior((*ctx)->ceed, 1, SetupMass, SetupMass_loc, &qf_setup);
      CeedQFunctionAddInput(qf_setup, "x", dim * dim, CEED_EVAL_GRAD);
      CeedQFunctionAddInput(qf_setup, "weight", 1, CEED_EVAL_WEIGHT);
      CeedQFunctionAddOutput(qf_setup, "rho", 1, CEED_EVAL_NONE);

      CeedOperatorCreateAtPoints((*ctx)->ceed, qf_setup, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE, &op_setup);
      CeedOperatorSetField(op_setup, "x", elem_restr_x_mesh, basis_x, CEED_VECTOR_ACTIVE);
      CeedOperatorSetField(op_setup, "weight", CEED_ELEMRESTRICTION_NONE, basis_x, CEED_VECTOR_NONE);
      CeedOperatorSetField(op_setup, "rho", elem_restr_q_data_points, CEED_BASIS_NONE, CEED_VECTOR_ACTIVE);
      CeedOperatorAtPointsSetPoints(op_setup, elem_restr_x_points, x_ref_points);

      CeedOperatorApply(op_setup, x_coord, q_data_points, CEED_REQUEST_IMMEDIATE);

      // Cleanup
      CeedVectorDestroy(&x_coord);
      CeedQFunctionDestroy(&qf_setup);
      CeedOperatorDestroy(&op_setup);
    }

    // -- Cleanup
    PetscCall(ISDestroy(&is_points));
    PetscCall(VecDestroy(&X_ref));
  }

  PetscCall(DMSetApplicationContext(dm_mesh, (void *)(*ctx)));

  // Create operators
  // Mesh to points interpolation operator
  {
    CeedQFunction qf_mesh_to_points;

    // -- Create operator
    CeedQFunctionCreateIdentity((*ctx)->ceed, num_comp, CEED_EVAL_INTERP, CEED_EVAL_NONE, &qf_mesh_to_points);

    CeedOperatorCreateAtPoints((*ctx)->ceed, qf_mesh_to_points, NULL, NULL, &(*ctx)->op_mesh_to_points);
    CeedOperatorSetField((*ctx)->op_mesh_to_points, "input", elem_restr_u_mesh, basis_u, CEED_VECTOR_ACTIVE);
    CeedOperatorSetField((*ctx)->op_mesh_to_points, "output", elem_restr_u_points, CEED_BASIS_NONE, CEED_VECTOR_ACTIVE);
    CeedOperatorAtPointsSetPoints((*ctx)->op_mesh_to_points, elem_restr_x_points, x_ref_points);

    // -- Cleanup
    CeedQFunctionDestroy(&qf_mesh_to_points);
  }

  // RHS operator
  {
    CeedQFunction        qf_pts_to_mesh;
    CeedQFunctionContext qf_ctx;

    // -- Mass QFunction
    CeedQFunctionCreateInterior((*ctx)->ceed, 1, Mass, Mass_loc, &qf_pts_to_mesh);
    CeedQFunctionAddInput(qf_pts_to_mesh, "q data", 1, CEED_EVAL_NONE);
    CeedQFunctionAddInput(qf_pts_to_mesh, "u", num_comp, CEED_EVAL_NONE);
    CeedQFunctionAddOutput(qf_pts_to_mesh, "v", num_comp, CEED_EVAL_INTERP);

    // -- QFunction context
    CeedQFunctionContextCreate((*ctx)->ceed, &qf_ctx);
    CeedQFunctionContextSetData(qf_ctx, CEED_MEM_HOST, CEED_COPY_VALUES, sizeof(num_comp), &num_comp);
    CeedQFunctionSetContext(qf_pts_to_mesh, qf_ctx);

    // -- Mass Operator
    CeedOperatorCreateAtPoints((*ctx)->ceed, qf_pts_to_mesh, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE, &(*ctx)->op_points_to_mesh);
    CeedOperatorSetField((*ctx)->op_points_to_mesh, "q data", elem_restr_q_data_points, CEED_BASIS_NONE, q_data_points);
    CeedOperatorSetField((*ctx)->op_points_to_mesh, "u", elem_restr_u_points, CEED_BASIS_NONE, CEED_VECTOR_ACTIVE);
    CeedOperatorSetField((*ctx)->op_points_to_mesh, "v", elem_restr_u_mesh, basis_u, CEED_VECTOR_ACTIVE);
    CeedOperatorAtPointsSetPoints((*ctx)->op_points_to_mesh, elem_restr_x_points, x_ref_points);

    // -- Cleanup
    CeedQFunctionContextDestroy(&qf_ctx);
    CeedQFunctionDestroy(&qf_pts_to_mesh);
  }

  // Mass operator
  {
    CeedQFunction        qf_mass;
    CeedQFunctionContext ctx_mass;

    // -- Mass QFunction
    CeedQFunctionCreateInterior((*ctx)->ceed, 1, Mass, Mass_loc, &qf_mass);
    CeedQFunctionAddInput(qf_mass, "q data", 1, CEED_EVAL_NONE);
    CeedQFunctionAddInput(qf_mass, "u", num_comp, CEED_EVAL_INTERP);
    CeedQFunctionAddOutput(qf_mass, "v", num_comp, CEED_EVAL_INTERP);

    // -- QFunction context
    CeedQFunctionContextCreate((*ctx)->ceed, &ctx_mass);
    CeedQFunctionContextSetData(ctx_mass, CEED_MEM_HOST, CEED_COPY_VALUES, sizeof(num_comp), &num_comp);
    CeedQFunctionSetContext(qf_mass, ctx_mass);

    // -- Mass Operator
    CeedOperatorCreateAtPoints((*ctx)->ceed, qf_mass, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE, &(*ctx)->op_mass);
    CeedOperatorSetField((*ctx)->op_mass, "q data", elem_restr_q_data_points, CEED_BASIS_NONE, q_data_points);
    CeedOperatorSetField((*ctx)->op_mass, "u", elem_restr_u_mesh, basis_u, CEED_VECTOR_ACTIVE);
    CeedOperatorSetField((*ctx)->op_mass, "v", elem_restr_u_mesh, basis_u, CEED_VECTOR_ACTIVE);
    CeedOperatorAtPointsSetPoints((*ctx)->op_mass, elem_restr_x_points, x_ref_points);

    // -- Cleanup
    CeedQFunctionContextDestroy(&ctx_mass);
    CeedQFunctionDestroy(&qf_mass);
  }

  // Cleanup
  CeedElemRestrictionDestroy(&elem_restr_u_mesh);
  CeedElemRestrictionDestroy(&elem_restr_x_mesh);
  CeedElemRestrictionDestroy(&elem_restr_u_points);
  CeedElemRestrictionDestroy(&elem_restr_x_points);
  CeedElemRestrictionDestroy(&elem_restr_q_data_points);
  CeedBasisDestroy(&basis_u);
  CeedBasisDestroy(&basis_x);
  CeedVectorDestroy(&x_ref_points);
  CeedVectorDestroy(&q_data_points);

  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode DMSwarmCeedContextDestroy(DMSwarmCeedContext *ctx) {
  PetscFunctionBeginUser;
  CeedDestroy(&(*ctx)->ceed);
  CeedVectorDestroy(&(*ctx)->u_mesh);
  CeedVectorDestroy(&(*ctx)->v_mesh);
  CeedVectorDestroy(&(*ctx)->u_points);
  CeedOperatorDestroy(&(*ctx)->op_mesh_to_points);
  CeedOperatorDestroy(&(*ctx)->op_points_to_mesh);
  CeedOperatorDestroy(&(*ctx)->op_mass);
  PetscCall(PetscFree(*ctx));
  PetscFunctionReturn(PETSC_SUCCESS);
}

// ------------------------------------------------------------------------------------------------
// PETSc-libCEED memory space utilities
// ------------------------------------------------------------------------------------------------
PetscErrorCode DMSwarmPICFieldP2C(DM dm_swarm, const char *field, CeedVector x_ceed) {
  PetscScalar *x;

  PetscFunctionBeginUser;
  PetscCall(DMSwarmGetField(dm_swarm, field, NULL, NULL, (void **)&x));
  CeedVectorSetArray(x_ceed, CEED_MEM_HOST, CEED_USE_POINTER, (CeedScalar *)x);
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode DMSwarmPICFieldC2P(DM dm_swarm, const char *field, CeedVector x_ceed) {
  PetscScalar *x;

  PetscFunctionBeginUser;
  CeedVectorTakeArray(x_ceed, CEED_MEM_HOST, (CeedScalar **)&x);
  PetscCall(DMSwarmRestoreField(dm_swarm, field, NULL, NULL, (void **)&x));
  PetscFunctionReturn(PETSC_SUCCESS);
}

// ------------------------------------------------------------------------------------------------
// Swarm point location utility
// ------------------------------------------------------------------------------------------------
PetscErrorCode DMSwarmInitalizePointLocations(DM dm_swarm, PointSwarmType point_swarm_type, PetscInt num_points, PetscInt num_points_per_cell) {
  PetscFunctionBeginUser;

  switch (point_swarm_type) {
    case SWARM_GAUSS:
    case SWARM_UNIFORM: {
      // -- Set gauss or uniform point locations in each cell
      PetscInt    num_points_per_cell_1d = round(cbrt(num_points_per_cell * 1.0)), dim = 3;
      PetscScalar point_coords[num_points_per_cell * 3];
      CeedScalar  points_1d[num_points_per_cell_1d], weights_1d[num_points_per_cell_1d];

      if (point_swarm_type == SWARM_GAUSS) {
        PetscCall(CeedGaussQuadrature(num_points_per_cell_1d, points_1d, weights_1d));
      } else {
        for (PetscInt i = 0; i < num_points_per_cell_1d; i++) points_1d[i] = 2.0 * (PetscReal)(i + 1) / (PetscReal)(num_points_per_cell_1d + 1) - 1;
      }
      for (PetscInt i = 0; i < num_points_per_cell_1d; i++) {
        for (PetscInt j = 0; j < num_points_per_cell_1d; j++) {
          for (PetscInt k = 0; k < num_points_per_cell_1d; k++) {
            PetscInt p = (i * num_points_per_cell_1d + j) * num_points_per_cell_1d + k;

            point_coords[p * dim + 0] = points_1d[i];
            point_coords[p * dim + 1] = points_1d[j];
            point_coords[p * dim + 2] = points_1d[k];
          }
        }
      }
      PetscCall(DMSwarmSetPointCoordinatesCellwise(dm_swarm, num_points_per_cell_1d * num_points_per_cell_1d * num_points_per_cell_1d, point_coords));
    } break;
    case SWARM_CELL_RANDOM: {
      // -- Set points randomly in each cell
      PetscInt     dim = 3, num_cells_total = 1, num_cells[] = {1, 1, 1};
      PetscScalar *point_coords;
      PetscRandom  rng;

      PetscOptionsBegin(PetscObjectComm((PetscObject)dm_swarm), NULL, "libCEED example using PETSc with DMSwarm", NULL);

      PetscCall(PetscOptionsInt("-dm_plex_dim", "Background mesh dimension", NULL, dim, &dim, NULL));
      PetscCall(PetscOptionsIntArray("-dm_plex_box_faces", "Number of cells", NULL, num_cells, &dim, NULL));

      PetscOptionsEnd();

      PetscCall(PetscRandomCreate(PetscObjectComm((PetscObject)dm_swarm), &rng));

      num_cells_total = num_cells[0] * num_cells[1] * num_cells[2];
      PetscCall(DMSwarmGetField(dm_swarm, DMSwarmPICField_coor, NULL, NULL, (void **)&point_coords));
      for (PetscInt c = 0; c < num_cells_total; c++) {
        PetscInt cell_index[3] = {c % num_cells[0], (c / num_cells[0]) % num_cells[1], (c / num_cells[0] / num_cells[1]) % num_cells[2]};

        for (PetscInt p = 0; p < num_points_per_cell; p++) {
          PetscInt    point_index = c * num_points_per_cell + p;
          PetscScalar random_value;

          for (PetscInt i = 0; i < dim; i++) {
            PetscCall(PetscRandomGetValue(rng, &random_value));
            point_coords[point_index * dim + i] = -1.0 + cell_index[i] * 2.0 / (num_cells[i] + 1.0) + random_value;
          }
        }
      }
      PetscCall(DMSwarmRestoreField(dm_swarm, DMSwarmPICField_coor, NULL, NULL, (void **)&point_coords));
      PetscCall(PetscRandomDestroy(&rng));
    } break;
    case SWARM_SINUSOIDAL: {
      // -- Set points distributed per sinusoidal functions
      PetscInt     dim = 3;
      PetscScalar *point_coords;
      DM           dm_mesh;

      PetscCall(DMSwarmGetCellDM(dm_swarm, &dm_mesh));
      PetscCall(DMGetDimension(dm_mesh, &dim));

      PetscCall(DMSwarmGetField(dm_swarm, DMSwarmPICField_coor, NULL, NULL, (void **)&point_coords));
      for (PetscInt p = 0; p < num_points; p++) {
        point_coords[p * dim + 0] = -PetscCosReal((PetscReal)(p + 1) / (PetscReal)(num_points + 1) * PETSC_PI);
        if (dim > 1) point_coords[p * dim + 1] = -PetscSinReal((PetscReal)(p + 1) / (PetscReal)(num_points + 1) * PETSC_PI);
        if (dim > 2) point_coords[p * dim + 2] = PetscSinReal((PetscReal)(p + 1) / (PetscReal)(num_points + 1) * PETSC_PI);
      }
      PetscCall(DMSwarmRestoreField(dm_swarm, DMSwarmPICField_coor, NULL, NULL, (void **)&point_coords));
    } break;
  }
  PetscCall(DMSwarmMigrate(dm_swarm, PETSC_TRUE));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  DMSwarmCreateReferenceCoordinates - Compute the cell reference coordinates for local DMSwarm points.

  Collective

  Input Parameter:
. dm_swarm  - the `DMSwarm`

  Output Parameters:
+ is_points    - The IS object for indexing into points per cell
- X_points_ref - Vec holding the cell reference coordinates for local DMSwarm points

The index set contains ranges of indices for each local cell. This range contains the indices of every point in the cell.

```
total_num_cells
cell_0_start_index
cell_1_start_index
cell_2_start_index
...
cell_n_start_index
cell_n_stop_index
cell_0_point_0
cell_0_point_0
...
cell_n_point_m
```

  Level: beginner

.seealso: `DMSwarm`
@*/
PetscErrorCode DMSwarmCreateReferenceCoordinates(DM dm_swarm, IS *is_points, Vec *X_points_ref) {
  PetscInt           cell_start, cell_end, num_cells_local, dim, num_points_local, *cell_points, points_offset;
  PetscScalar       *coords_points_ref;
  const PetscScalar *coords_points_true;
  DM                 dm_mesh;

  PetscFunctionBeginUser;
  PetscCall(DMSwarmGetCellDM(dm_swarm, &dm_mesh));

  // Create vector to hold reference coordinates
  {
    Vec X_points_true;

    PetscCall(DMSwarmCreateLocalVectorFromField(dm_swarm, DMSwarmPICField_coor, &X_points_true));
    PetscCall(VecDuplicate(X_points_true, X_points_ref));
    PetscCall(DMSwarmDestroyLocalVectorFromField(dm_swarm, DMSwarmPICField_coor, &X_points_true));
  }

  // Allocate index set array
  PetscCall(DMPlexGetHeightStratum(dm_mesh, 0, &cell_start, &cell_end));
  num_cells_local = cell_end - cell_start;
  points_offset   = num_cells_local + 2;
  PetscCall(VecGetLocalSize(*X_points_ref, &num_points_local));
  PetscCall(DMGetDimension(dm_mesh, &dim));
  num_points_local /= dim;
  PetscCall(PetscMalloc1(num_points_local + num_cells_local + 2, &cell_points));
  cell_points[0] = num_cells_local;

  // Get reference coordinates for each swarm point wrt the elements in the background mesh
  PetscCall(DMSwarmSortGetAccess(dm_swarm));
  PetscCall(DMSwarmGetField(dm_swarm, DMSwarmPICField_coor, NULL, NULL, (void **)&coords_points_true));
  PetscCall(VecGetArray(*X_points_ref, &coords_points_ref));
  for (PetscInt cell = cell_start, num_points_processed = 0; cell < cell_end; cell++) {
    PetscInt *points_in_cell, num_points_in_cell, local_cell = cell - cell_start;
    PetscReal v[3], J[9], invJ[9], detJ, v0_ref[3] = {-1.0, -1.0, -1.0};

    PetscCall(DMSwarmSortGetPointsPerCell(dm_swarm, cell, &num_points_in_cell, &points_in_cell));
    // -- Reference coordinates for swarm points in background mesh element
    PetscCall(DMPlexComputeCellGeometryFEM(dm_mesh, cell, NULL, v, J, invJ, &detJ));
    cell_points[local_cell + 1] = num_points_processed + points_offset;
    for (PetscInt p = 0; p < num_points_in_cell; p++) {
      const CeedInt point = points_in_cell[p];

      cell_points[points_offset + (num_points_processed++)] = point;
      CoordinatesRealToRef(dim, dim, v0_ref, v, invJ, &coords_points_true[point * dim], &coords_points_ref[point * dim]);
    }

    // -- Cleanup
    PetscCall(PetscFree(points_in_cell));
  }
  cell_points[points_offset - 1] = num_points_local + points_offset;

  // Cleanup
  PetscCall(DMSwarmRestoreField(dm_swarm, DMSwarmPICField_coor, NULL, NULL, (void **)&coords_points_true));
  PetscCall(VecRestoreArray(*X_points_ref, &coords_points_ref));
  PetscCall(DMSwarmSortRestoreAccess(dm_swarm));

  // Create index set
  PetscCall(ISCreateGeneral(PETSC_COMM_SELF, num_points_local + points_offset, cell_points, PETSC_OWN_POINTER, is_points));
  PetscFunctionReturn(PETSC_SUCCESS);
}

// ------------------------------------------------------------------------------------------------
// RHS for Swarm to Mesh projection
// ------------------------------------------------------------------------------------------------
PetscErrorCode DMSwarmCreateProjectionRHS(DM dm_swarm, const char *field, Vec B_mesh) {
  PetscMemType       B_mem_type;
  DM                 dm_mesh;
  Vec                B_mesh_loc;
  DMSwarmCeedContext swarm_ceed_context;

  PetscFunctionBeginUser;
  // Get mesh DM
  PetscCall(DMSwarmGetCellDM(dm_swarm, &dm_mesh));
  PetscCall(DMGetApplicationContext(dm_mesh, (void *)&swarm_ceed_context));

  // Get mesh values
  PetscCall(DMGetLocalVector(dm_mesh, &B_mesh_loc));
  PetscCall(VecZeroEntries(B_mesh_loc));
  PetscCall(VecP2C(B_mesh_loc, &B_mem_type, swarm_ceed_context->v_mesh));

  // Get swarm access
  PetscCall(DMSwarmSortGetAccess(dm_swarm));
  PetscCall(DMSwarmPICFieldP2C(dm_swarm, field, swarm_ceed_context->u_points));

  // Interpolate field from swarm points to mesh
  CeedOperatorApply(swarm_ceed_context->op_points_to_mesh, swarm_ceed_context->u_points, swarm_ceed_context->v_mesh, CEED_REQUEST_IMMEDIATE);

  // Restore PETSc Vecs and Local to Global
  PetscCall(VecC2P(swarm_ceed_context->v_mesh, B_mem_type, B_mesh_loc));
  PetscCall(VecZeroEntries(B_mesh));
  PetscCall(DMLocalToGlobal(dm_mesh, B_mesh_loc, ADD_VALUES, B_mesh));

  // Cleanup
  PetscCall(DMSwarmPICFieldC2P(dm_swarm, field, swarm_ceed_context->u_points));
  PetscCall(DMSwarmSortRestoreAccess(dm_swarm));
  PetscCall(DMRestoreLocalVector(dm_mesh, &B_mesh_loc));
  PetscFunctionReturn(PETSC_SUCCESS);
}

// ------------------------------------------------------------------------------------------------
// Swarm "mass matrix"
// ------------------------------------------------------------------------------------------------
PetscErrorCode MatMult_SwarmMass(Mat A, Vec U_mesh, Vec V_mesh) {
  PetscMemType       U_mem_type, V_mem_type;
  DM                 dm_mesh;
  Vec                U_mesh_loc, V_mesh_loc;
  DMSwarmCeedContext swarm_ceed_context;

  PetscFunctionBeginUser;
  // Get mesh DM
  PetscCall(MatGetDM(A, &dm_mesh));
  PetscCall(DMGetApplicationContext(dm_mesh, (void *)&swarm_ceed_context));

  // Global to Local and get PETSc Vec access
  PetscCall(DMGetLocalVector(dm_mesh, &U_mesh_loc));
  PetscCall(VecZeroEntries(U_mesh_loc));
  PetscCall(DMGlobalToLocal(dm_mesh, U_mesh, INSERT_VALUES, U_mesh_loc));
  PetscCall(VecReadP2C(U_mesh_loc, &U_mem_type, swarm_ceed_context->u_mesh));
  PetscCall(DMGetLocalVector(dm_mesh, &V_mesh_loc));
  PetscCall(VecZeroEntries(V_mesh_loc));
  PetscCall(VecP2C(V_mesh_loc, &V_mem_type, swarm_ceed_context->v_mesh));

  // Apply swarm mass operator
  CeedOperatorApply(swarm_ceed_context->op_mass, swarm_ceed_context->u_mesh, swarm_ceed_context->v_mesh, CEED_REQUEST_IMMEDIATE);

  // Restore PETSc Vecs and Local to Global
  PetscCall(VecReadC2P(swarm_ceed_context->u_mesh, U_mem_type, U_mesh_loc));
  PetscCall(VecC2P(swarm_ceed_context->v_mesh, V_mem_type, V_mesh_loc));
  PetscCall(VecZeroEntries(V_mesh));
  PetscCall(DMLocalToGlobal(dm_mesh, V_mesh_loc, ADD_VALUES, V_mesh));

  // Cleanup
  PetscCall(DMRestoreLocalVector(dm_mesh, &U_mesh_loc));
  PetscCall(DMRestoreLocalVector(dm_mesh, &V_mesh_loc));
  PetscFunctionReturn(PETSC_SUCCESS);
}

// ------------------------------------------------------------------------------------------------
// Swarm to mesh projection
// ------------------------------------------------------------------------------------------------
PetscErrorCode DMSwarmProjectFromSwarmToCells(DM dm_swarm, const char *field, Vec U_mesh) {
  PetscBool          test_mode;
  Vec                B_mesh;
  Mat                M;
  KSP                ksp;
  DM                 dm_mesh;
  DMSwarmCeedContext swarm_ceed_context;
  MPI_Comm           comm;

  PetscFunctionBeginUser;

  PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Swarm-to-Mesh Projection Options", NULL);
  PetscCall(PetscOptionsBool("-test", "Testing mode (do not print unless error is large)", NULL, test_mode, &test_mode, NULL));
  PetscOptionsEnd();

  comm = PetscObjectComm((PetscObject)dm_swarm);
  PetscCall(DMSwarmGetCellDM(dm_swarm, &dm_mesh));
  PetscCall(DMGetApplicationContext(dm_mesh, (void *)&swarm_ceed_context));
  PetscCall(VecDuplicate(U_mesh, &B_mesh));

  // Setup "mass matrix"
  {
    PetscInt l_size, g_size;

    PetscCall(VecGetLocalSize(U_mesh, &l_size));
    PetscCall(VecGetSize(U_mesh, &g_size));
    PetscCall(MatCreateShell(comm, l_size, l_size, g_size, g_size, swarm_ceed_context, &M));
    PetscCall(MatSetDM(M, dm_mesh));
    PetscCall(MatShellSetOperation(M, MATOP_MULT, (void (*)(void))MatMult_SwarmMass));
  }

  // Setup KSP
  {
    PC pc;

    PetscCall(KSPCreate(comm, &ksp));
    PetscCall(KSPGetPC(ksp, &pc));
    PetscCall(PCSetType(pc, PCJACOBI));
    PetscCall(PCJacobiSetType(pc, PC_JACOBI_ROWSUM));
    PetscCall(KSPSetType(ksp, KSPCG));
    PetscCall(KSPSetNormType(ksp, KSP_NORM_NATURAL));
    PetscCall(KSPSetTolerances(ksp, 1e-10, PETSC_DEFAULT, PETSC_DEFAULT, PETSC_DEFAULT));
    PetscCall(KSPSetOperators(ksp, M, M));
    PetscCall(KSPSetFromOptions(ksp));
    PetscCall(PetscObjectSetName((PetscObject)ksp, "Swarm-to-Mesh Projection"));
    PetscCall(KSPViewFromOptions(ksp, NULL, "-ksp_projection_view"));
  }

  // Setup RHS
  PetscCall(DMSwarmCreateProjectionRHS(dm_swarm, field, B_mesh));

  // Solve
  PetscCall(VecZeroEntries(U_mesh));
  PetscCall(KSPSolve(ksp, B_mesh, U_mesh));

  // KSP summary
  {
    KSPType            ksp_type;
    KSPConvergedReason reason;
    PetscReal          rnorm;
    PetscInt           its;
    PetscCall(KSPGetType(ksp, &ksp_type));
    PetscCall(KSPGetConvergedReason(ksp, &reason));
    PetscCall(KSPGetIterationNumber(ksp, &its));
    PetscCall(KSPGetResidualNorm(ksp, &rnorm));

    if (!test_mode || reason < 0 || rnorm > 1e-8) {
      PetscCall(PetscPrintf(comm,
                            "Swarm-to-Mesh Projection KSP Solve:\n"
                            "  KSP type: %s\n"
                            "  KSP convergence: %s\n"
                            "  Total KSP iterations: %" PetscInt_FMT "\n"
                            "  Final rnorm: %e\n",
                            ksp_type, KSPConvergedReasons[reason], its, (double)rnorm));
    }
  }

  // Optional viewing
  PetscCall(KSPViewFromOptions(ksp, NULL, "-ksp_view"));

  // Cleanup
  PetscCall(VecDestroy(&B_mesh));
  PetscCall(MatDestroy(&M));
  PetscCall(KSPDestroy(&ksp));

  PetscFunctionReturn(PETSC_SUCCESS);
}