xref: /petsc/src/dm/impls/swarm/swarmpic_plex.c (revision ba38deedd2838b0f18e3744cb0bafd6392690fde)

#include <petscdm.h>
#include <petscdmplex.h>
#include <petscdmswarm.h>
#include "../src/dm/impls/swarm/data_bucket.h"

PetscErrorCode private_DMSwarmSetPointCoordinatesCellwise_PLEX(DM, DM, PetscInt, PetscReal *xi);

static PetscErrorCode private_PetscFECreateDefault_scalar_pk1(DM dm, PetscInt dim, PetscBool isSimplex, PetscInt qorder, PetscFE *fem)
{
  const PetscInt  Nc = 1;
  PetscQuadrature q, fq;
  DM              K;
  PetscSpace      P;
  PetscDualSpace  Q;
  PetscInt        order, quadPointsPerEdge;
  PetscBool       tensor = isSimplex ? PETSC_FALSE : PETSC_TRUE;

  PetscFunctionBegin;
  /* Create space */
  PetscCall(PetscSpaceCreate(PetscObjectComm((PetscObject)dm), &P));
  /* PetscCall(PetscObjectSetOptionsPrefix((PetscObject) P, prefix)); */
  PetscCall(PetscSpacePolynomialSetTensor(P, tensor));
  /* PetscCall(PetscSpaceSetFromOptions(P)); */
  PetscCall(PetscSpaceSetType(P, PETSCSPACEPOLYNOMIAL));
  PetscCall(PetscSpaceSetDegree(P, 1, PETSC_DETERMINE));
  PetscCall(PetscSpaceSetNumComponents(P, Nc));
  PetscCall(PetscSpaceSetNumVariables(P, dim));
  PetscCall(PetscSpaceSetUp(P));
  PetscCall(PetscSpaceGetDegree(P, &order, NULL));
  PetscCall(PetscSpacePolynomialGetTensor(P, &tensor));
  /* Create dual space */
  PetscCall(PetscDualSpaceCreate(PetscObjectComm((PetscObject)dm), &Q));
  PetscCall(PetscDualSpaceSetType(Q, PETSCDUALSPACELAGRANGE));
  /* PetscCall(PetscObjectSetOptionsPrefix((PetscObject) Q, prefix)); */
  PetscCall(DMPlexCreateReferenceCell(PETSC_COMM_SELF, DMPolytopeTypeSimpleShape(dim, isSimplex), &K));
  PetscCall(PetscDualSpaceSetDM(Q, K));
  PetscCall(DMDestroy(&K));
  PetscCall(PetscDualSpaceSetNumComponents(Q, Nc));
  PetscCall(PetscDualSpaceSetOrder(Q, order));
  PetscCall(PetscDualSpaceLagrangeSetTensor(Q, tensor));
  /* PetscCall(PetscDualSpaceSetFromOptions(Q)); */
  PetscCall(PetscDualSpaceSetType(Q, PETSCDUALSPACELAGRANGE));
  PetscCall(PetscDualSpaceSetUp(Q));
  /* Create element */
  PetscCall(PetscFECreate(PetscObjectComm((PetscObject)dm), fem));
  /* PetscCall(PetscObjectSetOptionsPrefix((PetscObject) *fem, prefix)); */
  /* PetscCall(PetscFESetFromOptions(*fem)); */
  PetscCall(PetscFESetType(*fem, PETSCFEBASIC));
  PetscCall(PetscFESetBasisSpace(*fem, P));
  PetscCall(PetscFESetDualSpace(*fem, Q));
  PetscCall(PetscFESetNumComponents(*fem, Nc));
  PetscCall(PetscFESetUp(*fem));
  PetscCall(PetscSpaceDestroy(&P));
  PetscCall(PetscDualSpaceDestroy(&Q));
  /* Create quadrature (with specified order if given) */
  qorder            = qorder >= 0 ? qorder : order;
  quadPointsPerEdge = PetscMax(qorder + 1, 1);
  if (isSimplex) {
    PetscCall(PetscDTStroudConicalQuadrature(dim, 1, quadPointsPerEdge, -1.0, 1.0, &q));
    PetscCall(PetscDTStroudConicalQuadrature(dim - 1, 1, quadPointsPerEdge, -1.0, 1.0, &fq));
  } else {
    PetscCall(PetscDTGaussTensorQuadrature(dim, 1, quadPointsPerEdge, -1.0, 1.0, &q));
    PetscCall(PetscDTGaussTensorQuadrature(dim - 1, 1, quadPointsPerEdge, -1.0, 1.0, &fq));
  }
  PetscCall(PetscFESetQuadrature(*fem, q));
  PetscCall(PetscFESetFaceQuadrature(*fem, fq));
  PetscCall(PetscQuadratureDestroy(&q));
  PetscCall(PetscQuadratureDestroy(&fq));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode private_DMSwarmInsertPointsUsingCellDM_PLEX_SubDivide(DM dm, DM dmc, PetscInt nsub)
{
  PetscInt         dim, nfaces, nbasis;
  PetscInt         q, npoints_q, e, nel, pcnt, ps, pe, d, k, r;
  PetscTabulation  T;
  Vec              coorlocal;
  PetscSection     coordSection;
  PetscScalar     *elcoor = NULL;
  PetscReal       *swarm_coor;
  PetscInt        *swarm_cellid;
  const PetscReal *xiq;
  PetscQuadrature  quadrature;
  PetscFE          fe, feRef;
  PetscBool        is_simplex;

  PetscFunctionBegin;
  PetscCall(DMGetDimension(dmc, &dim));
  is_simplex = PETSC_FALSE;
  PetscCall(DMPlexGetHeightStratum(dmc, 0, &ps, &pe));
  PetscCall(DMPlexGetConeSize(dmc, ps, &nfaces));
  if (nfaces == (dim + 1)) is_simplex = PETSC_TRUE;

  PetscCall(private_PetscFECreateDefault_scalar_pk1(dmc, dim, is_simplex, 0, &fe));

  for (r = 0; r < nsub; r++) {
    PetscCall(PetscFERefine(fe, &feRef));
    PetscCall(PetscFECopyQuadrature(feRef, fe));
    PetscCall(PetscFEDestroy(&feRef));
  }

  PetscCall(PetscFEGetQuadrature(fe, &quadrature));
  PetscCall(PetscQuadratureGetData(quadrature, NULL, NULL, &npoints_q, &xiq, NULL));
  PetscCall(PetscFEGetDimension(fe, &nbasis));
  PetscCall(PetscFEGetCellTabulation(fe, 1, &T));

  /* 0->cell, 1->edge, 2->vert */
  PetscCall(DMPlexGetHeightStratum(dmc, 0, &ps, &pe));
  nel = pe - ps;

  PetscCall(DMSwarmSetLocalSizes(dm, npoints_q * nel, -1));
  PetscCall(DMSwarmGetField(dm, DMSwarmPICField_coor, NULL, NULL, (void **)&swarm_coor));
  PetscCall(DMSwarmGetField(dm, DMSwarmPICField_cellid, NULL, NULL, (void **)&swarm_cellid));

  PetscCall(DMGetCoordinatesLocal(dmc, &coorlocal));
  PetscCall(DMGetCoordinateSection(dmc, &coordSection));

  pcnt = 0;
  for (e = 0; e < nel; e++) {
    PetscCall(DMPlexVecGetClosure(dmc, coordSection, coorlocal, ps + e, NULL, &elcoor));

    for (q = 0; q < npoints_q; q++) {
      for (d = 0; d < dim; d++) {
        swarm_coor[dim * pcnt + d] = 0.0;
        for (k = 0; k < nbasis; k++) swarm_coor[dim * pcnt + d] += T->T[0][q * nbasis + k] * PetscRealPart(elcoor[dim * k + d]);
      }
      swarm_cellid[pcnt] = e;
      pcnt++;
    }
    PetscCall(DMPlexVecRestoreClosure(dmc, coordSection, coorlocal, ps + e, NULL, &elcoor));
  }
  PetscCall(DMSwarmRestoreField(dm, DMSwarmPICField_cellid, NULL, NULL, (void **)&swarm_cellid));
  PetscCall(DMSwarmRestoreField(dm, DMSwarmPICField_coor, NULL, NULL, (void **)&swarm_coor));

  PetscCall(PetscFEDestroy(&fe));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode private_DMSwarmInsertPointsUsingCellDM_PLEX2D_Regular(DM dm, DM dmc, PetscInt npoints)
{
  PetscInt     dim;
  PetscInt     ii, jj, q, npoints_q, e, nel, npe, pcnt, ps, pe, d, k, nfaces;
  PetscReal   *xi, ds, ds2;
  PetscReal  **basis;
  Vec          coorlocal;
  PetscSection coordSection;
  PetscScalar *elcoor = NULL;
  PetscReal   *swarm_coor;
  PetscInt    *swarm_cellid;
  PetscBool    is_simplex;

  PetscFunctionBegin;
  PetscCall(DMGetDimension(dmc, &dim));
  PetscCheck(dim == 2, PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Only 2D is supported");
  is_simplex = PETSC_FALSE;
  PetscCall(DMPlexGetHeightStratum(dmc, 0, &ps, &pe));
  PetscCall(DMPlexGetConeSize(dmc, ps, &nfaces));
  if (nfaces == (dim + 1)) is_simplex = PETSC_TRUE;
  PetscCheck(is_simplex, PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Only the simplex is supported");

  PetscCall(PetscMalloc1(dim * npoints * npoints, &xi));
  pcnt = 0;
  ds   = 1.0 / ((PetscReal)(npoints - 1));
  ds2  = 1.0 / ((PetscReal)(npoints));
  for (jj = 0; jj < npoints; jj++) {
    for (ii = 0; ii < npoints - jj; ii++) {
      xi[dim * pcnt + 0] = ii * ds;
      xi[dim * pcnt + 1] = jj * ds;

      xi[dim * pcnt + 0] *= (1.0 - 1.2 * ds2);
      xi[dim * pcnt + 1] *= (1.0 - 1.2 * ds2);

      xi[dim * pcnt + 0] += 0.35 * ds2;
      xi[dim * pcnt + 1] += 0.35 * ds2;
      pcnt++;
    }
  }
  npoints_q = pcnt;

  npe = 3; /* nodes per element (triangle) */
  PetscCall(PetscMalloc1(npoints_q, &basis));
  for (q = 0; q < npoints_q; q++) {
    PetscCall(PetscMalloc1(npe, &basis[q]));

    basis[q][0] = 1.0 - xi[dim * q + 0] - xi[dim * q + 1];
    basis[q][1] = xi[dim * q + 0];
    basis[q][2] = xi[dim * q + 1];
  }

  /* 0->cell, 1->edge, 2->vert */
  PetscCall(DMPlexGetHeightStratum(dmc, 0, &ps, &pe));
  nel = pe - ps;

  PetscCall(DMSwarmSetLocalSizes(dm, npoints_q * nel, -1));
  PetscCall(DMSwarmGetField(dm, DMSwarmPICField_coor, NULL, NULL, (void **)&swarm_coor));
  PetscCall(DMSwarmGetField(dm, DMSwarmPICField_cellid, NULL, NULL, (void **)&swarm_cellid));

  PetscCall(DMGetCoordinatesLocal(dmc, &coorlocal));
  PetscCall(DMGetCoordinateSection(dmc, &coordSection));

  pcnt = 0;
  for (e = 0; e < nel; e++) {
    PetscCall(DMPlexVecGetClosure(dmc, coordSection, coorlocal, e, NULL, &elcoor));

    for (q = 0; q < npoints_q; q++) {
      for (d = 0; d < dim; d++) {
        swarm_coor[dim * pcnt + d] = 0.0;
        for (k = 0; k < npe; k++) swarm_coor[dim * pcnt + d] += basis[q][k] * PetscRealPart(elcoor[dim * k + d]);
      }
      swarm_cellid[pcnt] = e;
      pcnt++;
    }
    PetscCall(DMPlexVecRestoreClosure(dmc, coordSection, coorlocal, e, NULL, &elcoor));
  }
  PetscCall(DMSwarmRestoreField(dm, DMSwarmPICField_cellid, NULL, NULL, (void **)&swarm_cellid));
  PetscCall(DMSwarmRestoreField(dm, DMSwarmPICField_coor, NULL, NULL, (void **)&swarm_coor));

  PetscCall(PetscFree(xi));
  for (q = 0; q < npoints_q; q++) PetscCall(PetscFree(basis[q]));
  PetscCall(PetscFree(basis));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode private_DMSwarmInsertPointsUsingCellDM_PLEX(DM dm, DM celldm, DMSwarmPICLayoutType layout, PetscInt layout_param)
{
  PetscInt dim;

  PetscFunctionBegin;
  PetscCall(DMGetDimension(celldm, &dim));
  switch (layout) {
  case DMSWARMPIC_LAYOUT_REGULAR:
    PetscCheck(dim != 3, PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "No 3D support for REGULAR+PLEX");
    PetscCall(private_DMSwarmInsertPointsUsingCellDM_PLEX2D_Regular(dm, celldm, layout_param));
    break;
  case DMSWARMPIC_LAYOUT_GAUSS: {
    PetscInt         npoints, npoints1, ps, pe, nfaces;
    const PetscReal *xi;
    PetscBool        is_simplex;
    PetscQuadrature  quadrature;

    is_simplex = PETSC_FALSE;
    PetscCall(DMPlexGetHeightStratum(celldm, 0, &ps, &pe));
    PetscCall(DMPlexGetConeSize(celldm, ps, &nfaces));
    if (nfaces == (dim + 1)) is_simplex = PETSC_TRUE;

    npoints1 = layout_param;
    if (is_simplex) {
      PetscCall(PetscDTStroudConicalQuadrature(dim, 1, npoints1, -1.0, 1.0, &quadrature));
    } else {
      PetscCall(PetscDTGaussTensorQuadrature(dim, 1, npoints1, -1.0, 1.0, &quadrature));
    }
    PetscCall(PetscQuadratureGetData(quadrature, NULL, NULL, &npoints, &xi, NULL));
    PetscCall(private_DMSwarmSetPointCoordinatesCellwise_PLEX(dm, celldm, npoints, (PetscReal *)xi));
    PetscCall(PetscQuadratureDestroy(&quadrature));
  } break;
  case DMSWARMPIC_LAYOUT_SUBDIVISION:
    PetscCall(private_DMSwarmInsertPointsUsingCellDM_PLEX_SubDivide(dm, celldm, layout_param));
    break;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
typedef struct {
  PetscReal x,y;
} Point2d;

static PetscErrorCode signp2d(Point2d p1, Point2d p2, Point2d p3,PetscReal *s)
{
  PetscFunctionBegin;
  *s = (p1.x - p3.x) * (p2.y - p3.y) - (p2.x - p3.x) * (p1.y - p3.y);
  PetscFunctionReturn(PETSC_SUCCESS);
}
*/
/*
static PetscErrorCode PointInTriangle(Point2d pt, Point2d v1, Point2d v2, Point2d v3,PetscBool *v)
{
  PetscReal s1,s2,s3;
  PetscBool b1, b2, b3;

  PetscFunctionBegin;
  signp2d(pt, v1, v2,&s1); b1 = s1 < 0.0f;
  signp2d(pt, v2, v3,&s2); b2 = s2 < 0.0f;
  signp2d(pt, v3, v1,&s3); b3 = s3 < 0.0f;

  *v = ((b1 == b2) && (b2 == b3));
  PetscFunctionReturn(PETSC_SUCCESS);
}
*/
/*
static PetscErrorCode _ComputeLocalCoordinateAffine2d(PetscReal xp[],PetscReal coords[],PetscReal xip[],PetscReal *dJ)
{
  PetscReal x1,y1,x2,y2,x3,y3;
  PetscReal c,b[2],A[2][2],inv[2][2],detJ,od;

  PetscFunctionBegin;
  x1 = coords[2*0+0];
  x2 = coords[2*1+0];
  x3 = coords[2*2+0];

  y1 = coords[2*0+1];
  y2 = coords[2*1+1];
  y3 = coords[2*2+1];

  c = x1 - 0.5*x1 - 0.5*x1 + 0.5*x2 + 0.5*x3;
  b[0] = xp[0] - c;
  c = y1 - 0.5*y1 - 0.5*y1 + 0.5*y2 + 0.5*y3;
  b[1] = xp[1] - c;

  A[0][0] = -0.5*x1 + 0.5*x2;   A[0][1] = -0.5*x1 + 0.5*x3;
  A[1][0] = -0.5*y1 + 0.5*y2;   A[1][1] = -0.5*y1 + 0.5*y3;

  detJ = A[0][0]*A[1][1] - A[0][1]*A[1][0];
  *dJ = PetscAbsReal(detJ);
  od = 1.0/detJ;

  inv[0][0] =  A[1][1] * od;
  inv[0][1] = -A[0][1] * od;
  inv[1][0] = -A[1][0] * od;
  inv[1][1] =  A[0][0] * od;

  xip[0] = inv[0][0]*b[0] + inv[0][1]*b[1];
  xip[1] = inv[1][0]*b[0] + inv[1][1]*b[1];
  PetscFunctionReturn(PETSC_SUCCESS);
}
*/

static PetscErrorCode ComputeLocalCoordinateAffine2d(PetscReal xp[], PetscScalar coords[], PetscReal xip[], PetscReal *dJ)
{
  PetscReal x1, y1, x2, y2, x3, y3;
  PetscReal b[2], A[2][2], inv[2][2], detJ, od;

  PetscFunctionBegin;
  x1 = PetscRealPart(coords[2 * 0 + 0]);
  x2 = PetscRealPart(coords[2 * 1 + 0]);
  x3 = PetscRealPart(coords[2 * 2 + 0]);

  y1 = PetscRealPart(coords[2 * 0 + 1]);
  y2 = PetscRealPart(coords[2 * 1 + 1]);
  y3 = PetscRealPart(coords[2 * 2 + 1]);

  b[0] = xp[0] - x1;
  b[1] = xp[1] - y1;

  A[0][0] = x2 - x1;
  A[0][1] = x3 - x1;
  A[1][0] = y2 - y1;
  A[1][1] = y3 - y1;

  detJ = A[0][0] * A[1][1] - A[0][1] * A[1][0];
  *dJ  = PetscAbsReal(detJ);
  od   = 1.0 / detJ;

  inv[0][0] = A[1][1] * od;
  inv[0][1] = -A[0][1] * od;
  inv[1][0] = -A[1][0] * od;
  inv[1][1] = A[0][0] * od;

  xip[0] = inv[0][0] * b[0] + inv[0][1] * b[1];
  xip[1] = inv[1][0] * b[0] + inv[1][1] * b[1];
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode DMSwarmProjectField_ApproxP1_PLEX_2D(DM swarm, PetscReal *swarm_field, DM dm, Vec v_field)
{
  const PetscReal PLEX_C_EPS = 1.0e-8;
  Vec             v_field_l, denom_l, coor_l, denom;
  PetscInt        k, p, e, npoints;
  PetscInt       *mpfield_cell;
  PetscReal      *mpfield_coor;
  PetscReal       xi_p[2];
  PetscScalar     Ni[3];
  PetscSection    coordSection;
  PetscScalar    *elcoor = NULL;

  PetscFunctionBegin;
  PetscCall(VecZeroEntries(v_field));

  PetscCall(DMGetLocalVector(dm, &v_field_l));
  PetscCall(DMGetGlobalVector(dm, &denom));
  PetscCall(DMGetLocalVector(dm, &denom_l));
  PetscCall(VecZeroEntries(v_field_l));
  PetscCall(VecZeroEntries(denom));
  PetscCall(VecZeroEntries(denom_l));

  PetscCall(DMGetCoordinatesLocal(dm, &coor_l));
  PetscCall(DMGetCoordinateSection(dm, &coordSection));

  PetscCall(DMSwarmGetLocalSize(swarm, &npoints));
  PetscCall(DMSwarmGetField(swarm, DMSwarmPICField_coor, NULL, NULL, (void **)&mpfield_coor));
  PetscCall(DMSwarmGetField(swarm, DMSwarmPICField_cellid, NULL, NULL, (void **)&mpfield_cell));

  for (p = 0; p < npoints; p++) {
    PetscReal  *coor_p, dJ;
    PetscScalar elfield[3];
    PetscBool   point_located;

    e      = mpfield_cell[p];
    coor_p = &mpfield_coor[2 * p];

    PetscCall(DMPlexVecGetClosure(dm, coordSection, coor_l, e, NULL, &elcoor));

    /*
    while (!point_located && (failed_counter < 25)) {
      PetscCall(PointInTriangle(point, coords[0], coords[1], coords[2], &point_located));
      point.x = coor_p[0];
      point.y = coor_p[1];
      point.x += 1.0e-10 * (2.0 * rand()/((double)RAND_MAX)-1.0);
      point.y += 1.0e-10 * (2.0 * rand()/((double)RAND_MAX)-1.0);
      failed_counter++;
    }

    if (!point_located) {
        PetscPrintf(PETSC_COMM_SELF,"Failed to locate point (%1.8e,%1.8e) in local mesh (cell %" PetscInt_FMT ") with triangle coords (%1.8e,%1.8e) : (%1.8e,%1.8e) : (%1.8e,%1.8e) in %" PetscInt_FMT " iterations\n",point.x,point.y,e,coords[0].x,coords[0].y,coords[1].x,coords[1].y,coords[2].x,coords[2].y,failed_counter);
    }

    PetscCheck(point_located,PETSC_COMM_SELF,PETSC_ERR_SUP,"Failed to locate point (%1.8e,%1.8e) in local mesh (cell %" PetscInt_FMT ")",point.x,point.y,e);
    else {
      PetscCall(_ComputeLocalCoordinateAffine2d(coor_p,elcoor,xi_p,&dJ));
      xi_p[0] = 0.5*(xi_p[0] + 1.0);
      xi_p[1] = 0.5*(xi_p[1] + 1.0);

      PetscPrintf(PETSC_COMM_SELF,"[p=%" PetscInt_FMT "] x(%+1.4e,%+1.4e) -> mapped to element %" PetscInt_FMT " xi(%+1.4e,%+1.4e)\n",p,point.x,point.y,e,xi_p[0],xi_p[1]);

    }
*/

    PetscCall(ComputeLocalCoordinateAffine2d(coor_p, elcoor, xi_p, &dJ));
    /*
    PetscPrintf(PETSC_COMM_SELF,"[p=%" PetscInt_FMT "] x(%+1.4e,%+1.4e) -> mapped to element %" PetscInt_FMT " xi(%+1.4e,%+1.4e)\n",p,point.x,point.y,e,xi_p[0],xi_p[1]);
    */
    /*
     point_located = PETSC_TRUE;
    if (xi_p[0] < 0.0) {
      if (xi_p[0] > -PLEX_C_EPS) {
        xi_p[0] = 0.0;
      } else {
        point_located = PETSC_FALSE;
      }
    }
    if (xi_p[1] < 0.0) {
      if (xi_p[1] > -PLEX_C_EPS) {
        xi_p[1] = 0.0;
      } else {
        point_located = PETSC_FALSE;
      }
    }
    if (xi_p[1] > (1.0-xi_p[0])) {
      if ((xi_p[1] - 1.0 + xi_p[0]) < PLEX_C_EPS) {
        xi_p[1] = 1.0 - xi_p[0];
      } else {
        point_located = PETSC_FALSE;
      }
    }
    if (!point_located) {
      PetscPrintf(PETSC_COMM_SELF,"[Error] xi,eta = %+1.8e, %+1.8e\n",xi_p[0],xi_p[1]);
      PetscPrintf(PETSC_COMM_SELF,"[Error] Failed to locate point (%1.8e,%1.8e) in local mesh (cell %" PetscInt_FMT ") with triangle coords (%1.8e,%1.8e) : (%1.8e,%1.8e) : (%1.8e,%1.8e)\n",coor_p[0],coor_p[1],e,elcoor[0],elcoor[1],elcoor[2],elcoor[3],elcoor[4],elcoor[5]);
    }
    PetscCheck(point_located,PETSC_COMM_SELF,PETSC_ERR_SUP,"Failed to locate point (%1.8e,%1.8e) in local mesh (cell %" PetscInt_FMT ")",coor_p[0],coor_p[1],e);
    */

    Ni[0] = 1.0 - xi_p[0] - xi_p[1];
    Ni[1] = xi_p[0];
    Ni[2] = xi_p[1];

    point_located = PETSC_TRUE;
    for (k = 0; k < 3; k++) {
      if (PetscRealPart(Ni[k]) < -PLEX_C_EPS) point_located = PETSC_FALSE;
      if (PetscRealPart(Ni[k]) > (1.0 + PLEX_C_EPS)) point_located = PETSC_FALSE;
    }
    if (!point_located) {
      PetscCall(PetscPrintf(PETSC_COMM_SELF, "[Error] xi,eta = %+1.8e, %+1.8e\n", (double)xi_p[0], (double)xi_p[1]));
      PetscCall(PetscPrintf(PETSC_COMM_SELF, "[Error] Failed to locate point (%1.8e,%1.8e) in local mesh (cell %" PetscInt_FMT ") with triangle coords (%1.8e,%1.8e) : (%1.8e,%1.8e) : (%1.8e,%1.8e)\n", (double)coor_p[0], (double)coor_p[1], e, (double)PetscRealPart(elcoor[0]), (double)PetscRealPart(elcoor[1]), (double)PetscRealPart(elcoor[2]), (double)PetscRealPart(elcoor[3]), (double)PetscRealPart(elcoor[4]), (double)PetscRealPart(elcoor[5])));
    }
    PetscCheck(point_located, PETSC_COMM_SELF, PETSC_ERR_SUP, "Failed to locate point (%1.8e,%1.8e) in local mesh (cell %" PetscInt_FMT ")", (double)coor_p[0], (double)coor_p[1], e);

    for (k = 0; k < 3; k++) {
      Ni[k]      = Ni[k] * dJ;
      elfield[k] = Ni[k] * swarm_field[p];
    }
    PetscCall(DMPlexVecRestoreClosure(dm, coordSection, coor_l, e, NULL, &elcoor));

    PetscCall(DMPlexVecSetClosure(dm, NULL, v_field_l, e, elfield, ADD_VALUES));
    PetscCall(DMPlexVecSetClosure(dm, NULL, denom_l, e, Ni, ADD_VALUES));
  }

  PetscCall(DMSwarmRestoreField(swarm, DMSwarmPICField_cellid, NULL, NULL, (void **)&mpfield_cell));
  PetscCall(DMSwarmRestoreField(swarm, DMSwarmPICField_coor, NULL, NULL, (void **)&mpfield_coor));

  PetscCall(DMLocalToGlobalBegin(dm, v_field_l, ADD_VALUES, v_field));
  PetscCall(DMLocalToGlobalEnd(dm, v_field_l, ADD_VALUES, v_field));
  PetscCall(DMLocalToGlobalBegin(dm, denom_l, ADD_VALUES, denom));
  PetscCall(DMLocalToGlobalEnd(dm, denom_l, ADD_VALUES, denom));

  PetscCall(VecPointwiseDivide(v_field, v_field, denom));

  PetscCall(DMRestoreLocalVector(dm, &v_field_l));
  PetscCall(DMRestoreLocalVector(dm, &denom_l));
  PetscCall(DMRestoreGlobalVector(dm, &denom));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode private_DMSwarmProjectFields_PLEX(DM swarm, DM celldm, PetscInt project_type, PetscInt nfields, DMSwarmDataField dfield[], Vec vecs[])
{
  PetscInt f, dim;

  PetscFunctionBegin;
  PetscCall(DMGetDimension(swarm, &dim));
  switch (dim) {
  case 2:
    for (f = 0; f < nfields; f++) {
      PetscReal *swarm_field;

      PetscCall(DMSwarmDataFieldGetEntries(dfield[f], (void **)&swarm_field));
      PetscCall(DMSwarmProjectField_ApproxP1_PLEX_2D(swarm, swarm_field, celldm, vecs[f]));
    }
    break;
  case 3:
    SETERRQ(PetscObjectComm((PetscObject)swarm), PETSC_ERR_SUP, "No support for 3D");
  default:
    break;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode private_DMSwarmSetPointCoordinatesCellwise_PLEX(DM dm, DM dmc, PetscInt npoints, PetscReal xi[])
{
  PetscBool       is_simplex, is_tensorcell;
  PetscInt        dim, nfaces, ps, pe, p, d, nbasis, pcnt, e, k, nel;
  PetscFE         fe;
  PetscQuadrature quadrature;
  PetscTabulation T;
  PetscReal      *xiq;
  Vec             coorlocal;
  PetscSection    coordSection;
  PetscScalar    *elcoor = NULL;
  PetscReal      *swarm_coor;
  PetscInt       *swarm_cellid;

  PetscFunctionBegin;
  PetscCall(DMGetDimension(dmc, &dim));

  is_simplex    = PETSC_FALSE;
  is_tensorcell = PETSC_FALSE;
  PetscCall(DMPlexGetHeightStratum(dmc, 0, &ps, &pe));
  PetscCall(DMPlexGetConeSize(dmc, ps, &nfaces));

  if (nfaces == (dim + 1)) is_simplex = PETSC_TRUE;

  switch (dim) {
  case 2:
    if (nfaces == 4) is_tensorcell = PETSC_TRUE;
    break;
  case 3:
    if (nfaces == 6) is_tensorcell = PETSC_TRUE;
    break;
  default:
    SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Only support for 2D, 3D");
  }

  /* check points provided fail inside the reference cell */
  if (is_simplex) {
    for (p = 0; p < npoints; p++) {
      PetscReal sum;
      for (d = 0; d < dim; d++) PetscCheck(xi[dim * p + d] >= -1.0, PetscObjectComm((PetscObject)dm), PETSC_ERR_USER, "Points do not fail inside the simplex domain");
      sum = 0.0;
      for (d = 0; d < dim; d++) sum += xi[dim * p + d];
      PetscCheck(sum <= 0.0, PetscObjectComm((PetscObject)dm), PETSC_ERR_USER, "Points do not fail inside the simplex domain");
    }
  } else if (is_tensorcell) {
    for (p = 0; p < npoints; p++) {
      for (d = 0; d < dim; d++) PetscCheck(PetscAbsReal(xi[dim * p + d]) <= 1.0, PetscObjectComm((PetscObject)dm), PETSC_ERR_USER, "Points do not fail inside the tensor domain [-1,1]^d");
    }
  } else SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Only support for d-simplex and d-tensorcell");

  PetscCall(PetscQuadratureCreate(PetscObjectComm((PetscObject)dm), &quadrature));
  PetscCall(PetscMalloc1(npoints * dim, &xiq));
  PetscCall(PetscArraycpy(xiq, xi, npoints * dim));
  PetscCall(PetscQuadratureSetData(quadrature, dim, 1, npoints, (const PetscReal *)xiq, NULL));
  PetscCall(private_PetscFECreateDefault_scalar_pk1(dmc, dim, is_simplex, 0, &fe));
  PetscCall(PetscFESetQuadrature(fe, quadrature));
  PetscCall(PetscFEGetDimension(fe, &nbasis));
  PetscCall(PetscFEGetCellTabulation(fe, 1, &T));

  /* for each cell, interpolate coordaintes and insert the interpolated points coordinates into swarm */
  /* 0->cell, 1->edge, 2->vert */
  PetscCall(DMPlexGetHeightStratum(dmc, 0, &ps, &pe));
  nel = pe - ps;

  PetscCall(DMSwarmSetLocalSizes(dm, npoints * nel, -1));
  PetscCall(DMSwarmGetField(dm, DMSwarmPICField_coor, NULL, NULL, (void **)&swarm_coor));
  PetscCall(DMSwarmGetField(dm, DMSwarmPICField_cellid, NULL, NULL, (void **)&swarm_cellid));

  PetscCall(DMGetCoordinatesLocal(dmc, &coorlocal));
  PetscCall(DMGetCoordinateSection(dmc, &coordSection));

  pcnt = 0;
  for (e = 0; e < nel; e++) {
    PetscCall(DMPlexVecGetClosure(dmc, coordSection, coorlocal, ps + e, NULL, &elcoor));

    for (p = 0; p < npoints; p++) {
      for (d = 0; d < dim; d++) {
        swarm_coor[dim * pcnt + d] = 0.0;
        for (k = 0; k < nbasis; k++) swarm_coor[dim * pcnt + d] += T->T[0][p * nbasis + k] * PetscRealPart(elcoor[dim * k + d]);
      }
      swarm_cellid[pcnt] = e;
      pcnt++;
    }
    PetscCall(DMPlexVecRestoreClosure(dmc, coordSection, coorlocal, ps + e, NULL, &elcoor));
  }
  PetscCall(DMSwarmRestoreField(dm, DMSwarmPICField_cellid, NULL, NULL, (void **)&swarm_cellid));
  PetscCall(DMSwarmRestoreField(dm, DMSwarmPICField_coor, NULL, NULL, (void **)&swarm_coor));

  PetscCall(PetscQuadratureDestroy(&quadrature));
  PetscCall(PetscFEDestroy(&fe));
  PetscFunctionReturn(PETSC_SUCCESS);
}