Date: 2016-07-24T17:11:07+00:00

Actual source code: dmplexsnes.c
petsc-3.7.3 2016-07-24
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      1: #include <petsc/private/dmpleximpl.h>   /*I "petscdmplex.h" I*/
      2: #include <petsc/private/snesimpl.h>     /*I "petscsnes.h"   I*/
      3: #include <petscds.h>
      4: #include <petsc/private/petscimpl.h>
      5: #include <petsc/private/petscfeimpl.h>

      7: /************************** Interpolation *******************************/

     11: static PetscErrorCode DMSNESConvertPlex(DM dm, DM *plex, PetscBool copy)
     12: {
     13:   PetscBool      isPlex;

     17:   PetscObjectTypeCompare((PetscObject) dm, DMPLEX, &isPlex);
     18:   if (isPlex) {
     19:     *plex = dm;
     20:     PetscObjectReference((PetscObject) dm);
     21:   } else {
     22:     PetscObjectQuery((PetscObject) dm, "dm_plex", (PetscObject *) plex);
     23:     if (!*plex) {
     24:       DMConvert(dm,DMPLEX,plex);
     25:       PetscObjectCompose((PetscObject) dm, "dm_plex", (PetscObject) *plex);
     26:       if (copy) {
     27:         PetscInt    i;
     28:         PetscObject obj;
     29:         const char *comps[3] = {"A","dmAux","dmCh"};

     31:         DMCopyDMSNES(dm, *plex);
     32:         for (i = 0; i < 3; i++) {
     33:           PetscObjectQuery((PetscObject) dm, comps[i], &obj);
     34:           PetscObjectCompose((PetscObject) *plex, comps[i], obj);
     35:         }
     36:       }
     37:     } else {
     38:       PetscObjectReference((PetscObject) *plex);
     39:     }
     40:   }
     41:   return(0);
     42: }

     46: PetscErrorCode DMInterpolationCreate(MPI_Comm comm, DMInterpolationInfo *ctx)
     47: {

     52:   PetscMalloc(sizeof(struct _DMInterpolationInfo), ctx);

     54:   (*ctx)->comm   = comm;
     55:   (*ctx)->dim    = -1;
     56:   (*ctx)->nInput = 0;
     57:   (*ctx)->points = NULL;
     58:   (*ctx)->cells  = NULL;
     59:   (*ctx)->n      = -1;
     60:   (*ctx)->coords = NULL;
     61:   return(0);
     62: }

     66: PetscErrorCode DMInterpolationSetDim(DMInterpolationInfo ctx, PetscInt dim)
     67: {
     69:   if ((dim < 1) || (dim > 3)) SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Invalid dimension for points: %d", dim);
     70:   ctx->dim = dim;
     71:   return(0);
     72: }

     76: PetscErrorCode DMInterpolationGetDim(DMInterpolationInfo ctx, PetscInt *dim)
     77: {
     80:   *dim = ctx->dim;
     81:   return(0);
     82: }

     86: PetscErrorCode DMInterpolationSetDof(DMInterpolationInfo ctx, PetscInt dof)
     87: {
     89:   if (dof < 1) SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Invalid number of components: %d", dof);
     90:   ctx->dof = dof;
     91:   return(0);
     92: }

     96: PetscErrorCode DMInterpolationGetDof(DMInterpolationInfo ctx, PetscInt *dof)
     97: {
    100:   *dof = ctx->dof;
    101:   return(0);
    102: }

    106: PetscErrorCode DMInterpolationAddPoints(DMInterpolationInfo ctx, PetscInt n, PetscReal points[])
    107: {

    111:   if (ctx->dim < 0) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The spatial dimension has not been set");
    112:   if (ctx->points)  SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "Cannot add points multiple times yet");
    113:   ctx->nInput = n;

    115:   PetscMalloc1(n*ctx->dim, &ctx->points);
    116:   PetscMemcpy(ctx->points, points, n*ctx->dim * sizeof(PetscReal));
    117:   return(0);
    118: }

    122: PetscErrorCode DMInterpolationSetUp(DMInterpolationInfo ctx, DM dm, PetscBool redundantPoints)
    123: {
    124:   MPI_Comm          comm = ctx->comm;
    125:   PetscScalar       *a;
    126:   PetscInt          p, q, i;
    127:   PetscMPIInt       rank, size;
    128:   PetscErrorCode    ierr;
    129:   Vec               pointVec;
    130:   PetscSF           cellSF;
    131:   PetscLayout       layout;
    132:   PetscReal         *globalPoints;
    133:   PetscScalar       *globalPointsScalar;
    134:   const PetscInt    *ranges;
    135:   PetscMPIInt       *counts, *displs;
    136:   const PetscSFNode *foundCells;
    137:   const PetscInt    *foundPoints;
    138:   PetscMPIInt       *foundProcs, *globalProcs;
    139:   PetscInt          n, N, numFound;

    143:   MPI_Comm_size(comm, &size);
    144:   MPI_Comm_rank(comm, &rank);
    145:   if (ctx->dim < 0) SETERRQ(comm, PETSC_ERR_ARG_WRONGSTATE, "The spatial dimension has not been set");
    146:   /* Locate points */
    147:   n = ctx->nInput;
    148:   if (!redundantPoints) {
    149:     PetscLayoutCreate(comm, &layout);
    150:     PetscLayoutSetBlockSize(layout, 1);
    151:     PetscLayoutSetLocalSize(layout, n);
    152:     PetscLayoutSetUp(layout);
    153:     PetscLayoutGetSize(layout, &N);
    154:     /* Communicate all points to all processes */
    155:     PetscMalloc3(N*ctx->dim,&globalPoints,size,&counts,size,&displs);
    156:     PetscLayoutGetRanges(layout, &ranges);
    157:     for (p = 0; p < size; ++p) {
    158:       counts[p] = (ranges[p+1] - ranges[p])*ctx->dim;
    159:       displs[p] = ranges[p]*ctx->dim;
    160:     }
    161:     MPI_Allgatherv(ctx->points, n*ctx->dim, MPIU_REAL, globalPoints, counts, displs, MPIU_REAL, comm);
    162:   } else {
    163:     N = n;
    164:     globalPoints = ctx->points;
    165:     counts = displs = NULL;
    166:     layout = NULL;
    167:   }
    168: #if 0
    169:   PetscMalloc3(N,&foundCells,N,&foundProcs,N,&globalProcs);
    170:   /* foundCells[p] = m->locatePoint(&globalPoints[p*ctx->dim]); */
    171: #else
    172: #if defined(PETSC_USE_COMPLEX)
    173:   PetscMalloc1(N,&globalPointsScalar);
    174:   for (i=0; i<N; i++) globalPointsScalar[i] = globalPoints[i];
    175: #else
    176:   globalPointsScalar = globalPoints;
    177: #endif
    178:   VecCreateSeqWithArray(PETSC_COMM_SELF, ctx->dim, N*ctx->dim, globalPointsScalar, &pointVec);
    179:   PetscMalloc2(N,&foundProcs,N,&globalProcs);
    180:   cellSF = NULL;
    181:   DMLocatePoints(dm, pointVec, &cellSF);
    182:   PetscSFGetGraph(cellSF,NULL,&numFound,&foundPoints,&foundCells);
    183: #endif
    184:   for (p = 0; p < numFound; ++p) {
    185:     if (foundCells[p].index >= 0) foundProcs[foundPoints ? foundPoints[p] : p] = rank;
    186:     else foundProcs[foundPoints ? foundPoints[p] : p] = size;
    187:   }
    188:   /* Let the lowest rank process own each point */
    189:   MPIU_Allreduce(foundProcs, globalProcs, N, MPI_INT, MPI_MIN, comm);
    190:   ctx->n = 0;
    191:   for (p = 0; p < N; ++p) {
    192:     if (globalProcs[p] == size) SETERRQ4(comm, PETSC_ERR_PLIB, "Point %d: %g %g %g not located in mesh", p, globalPoints[p*ctx->dim+0], ctx->dim > 1 ? globalPoints[p*ctx->dim+1] : 0.0, ctx->dim > 2 ? globalPoints[p*ctx->dim+2] : 0.0);
    193:     else if (globalProcs[p] == rank) ctx->n++;
    194:   }
    195:   /* Create coordinates vector and array of owned cells */
    196:   PetscMalloc1(ctx->n, &ctx->cells);
    197:   VecCreate(comm, &ctx->coords);
    198:   VecSetSizes(ctx->coords, ctx->n*ctx->dim, PETSC_DECIDE);
    199:   VecSetBlockSize(ctx->coords, ctx->dim);
    200:   VecSetType(ctx->coords,VECSTANDARD);
    201:   VecGetArray(ctx->coords, &a);
    202:   for (p = 0, q = 0, i = 0; p < N; ++p) {
    203:     if (globalProcs[p] == rank) {
    204:       PetscInt d;

    206:       for (d = 0; d < ctx->dim; ++d, ++i) a[i] = globalPoints[p*ctx->dim+d];
    207:       ctx->cells[q++] = foundCells[p].index;
    208:     }
    209:   }
    210:   VecRestoreArray(ctx->coords, &a);
    211: #if 0
    212:   PetscFree3(foundCells,foundProcs,globalProcs);
    213: #else
    214:   PetscFree2(foundProcs,globalProcs);
    215:   PetscSFDestroy(&cellSF);
    216:   VecDestroy(&pointVec);
    217: #endif
    218:   if ((void*)globalPointsScalar != (void*)globalPoints) {PetscFree(globalPointsScalar);}
    219:   if (!redundantPoints) {PetscFree3(globalPoints,counts,displs);}
    220:   PetscLayoutDestroy(&layout);
    221:   return(0);
    222: }

    226: PetscErrorCode DMInterpolationGetCoordinates(DMInterpolationInfo ctx, Vec *coordinates)
    227: {
    230:   if (!ctx->coords) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The interpolation context has not been setup.");
    231:   *coordinates = ctx->coords;
    232:   return(0);
    233: }

    237: PetscErrorCode DMInterpolationGetVector(DMInterpolationInfo ctx, Vec *v)
    238: {

    243:   if (!ctx->coords) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The interpolation context has not been setup.");
    244:   VecCreate(ctx->comm, v);
    245:   VecSetSizes(*v, ctx->n*ctx->dof, PETSC_DECIDE);
    246:   VecSetBlockSize(*v, ctx->dof);
    247:   VecSetType(*v,VECSTANDARD);
    248:   return(0);
    249: }

    253: PetscErrorCode DMInterpolationRestoreVector(DMInterpolationInfo ctx, Vec *v)
    254: {

    259:   if (!ctx->coords) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The interpolation context has not been setup.");
    260:   VecDestroy(v);
    261:   return(0);
    262: }

    266: PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Triangle_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
    267: {
    268:   PetscReal      *v0, *J, *invJ, detJ;
    269:   const PetscScalar *coords;
    270:   PetscScalar    *a;
    271:   PetscInt       p;

    275:   PetscMalloc3(ctx->dim,&v0,ctx->dim*ctx->dim,&J,ctx->dim*ctx->dim,&invJ);
    276:   VecGetArrayRead(ctx->coords, &coords);
    277:   VecGetArray(v, &a);
    278:   for (p = 0; p < ctx->n; ++p) {
    279:     PetscInt     c = ctx->cells[p];
    280:     PetscScalar *x = NULL;
    281:     PetscReal    xi[4];
    282:     PetscInt     d, f, comp;

    284:     DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ);
    285:     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ, c);
    286:     DMPlexVecGetClosure(dm, NULL, xLocal, c, NULL, &x);
    287:     for (comp = 0; comp < ctx->dof; ++comp) a[p*ctx->dof+comp] = x[0*ctx->dof+comp];

    289:     for (d = 0; d < ctx->dim; ++d) {
    290:       xi[d] = 0.0;
    291:       for (f = 0; f < ctx->dim; ++f) xi[d] += invJ[d*ctx->dim+f]*0.5*PetscRealPart(coords[p*ctx->dim+f] - v0[f]);
    292:       for (comp = 0; comp < ctx->dof; ++comp) a[p*ctx->dof+comp] += PetscRealPart(x[(d+1)*ctx->dof+comp] - x[0*ctx->dof+comp])*xi[d];
    293:     }
    294:     DMPlexVecRestoreClosure(dm, NULL, xLocal, c, NULL, &x);
    295:   }
    296:   VecRestoreArray(v, &a);
    297:   VecRestoreArrayRead(ctx->coords, &coords);
    298:   PetscFree3(v0, J, invJ);
    299:   return(0);
    300: }

    304: PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Tetrahedron_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
    305: {
    306:   PetscReal      *v0, *J, *invJ, detJ;
    307:   const PetscScalar *coords;
    308:   PetscScalar    *a;
    309:   PetscInt       p;

    313:   PetscMalloc3(ctx->dim,&v0,ctx->dim*ctx->dim,&J,ctx->dim*ctx->dim,&invJ);
    314:   VecGetArrayRead(ctx->coords, &coords);
    315:   VecGetArray(v, &a);
    316:   for (p = 0; p < ctx->n; ++p) {
    317:     PetscInt       c = ctx->cells[p];
    318:     const PetscInt order[3] = {2, 1, 3};
    319:     PetscScalar   *x = NULL;
    320:     PetscReal      xi[4];
    321:     PetscInt       d, f, comp;

    323:     DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ);
    324:     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ, c);
    325:     DMPlexVecGetClosure(dm, NULL, xLocal, c, NULL, &x);
    326:     for (comp = 0; comp < ctx->dof; ++comp) a[p*ctx->dof+comp] = x[0*ctx->dof+comp];

    328:     for (d = 0; d < ctx->dim; ++d) {
    329:       xi[d] = 0.0;
    330:       for (f = 0; f < ctx->dim; ++f) xi[d] += invJ[d*ctx->dim+f]*0.5*PetscRealPart(coords[p*ctx->dim+f] - v0[f]);
    331:       for (comp = 0; comp < ctx->dof; ++comp) a[p*ctx->dof+comp] += PetscRealPart(x[order[d]*ctx->dof+comp] - x[0*ctx->dof+comp])*xi[d];
    332:     }
    333:     DMPlexVecRestoreClosure(dm, NULL, xLocal, c, NULL, &x);
    334:   }
    335:   VecRestoreArray(v, &a);
    336:   VecRestoreArrayRead(ctx->coords, &coords);
    337:   PetscFree3(v0, J, invJ);
    338:   return(0);
    339: }

    343: PETSC_STATIC_INLINE PetscErrorCode QuadMap_Private(SNES snes, Vec Xref, Vec Xreal, void *ctx)
    344: {
    345:   const PetscScalar *vertices = (const PetscScalar*) ctx;
    346:   const PetscScalar x0        = vertices[0];
    347:   const PetscScalar y0        = vertices[1];
    348:   const PetscScalar x1        = vertices[2];
    349:   const PetscScalar y1        = vertices[3];
    350:   const PetscScalar x2        = vertices[4];
    351:   const PetscScalar y2        = vertices[5];
    352:   const PetscScalar x3        = vertices[6];
    353:   const PetscScalar y3        = vertices[7];
    354:   const PetscScalar f_1       = x1 - x0;
    355:   const PetscScalar g_1       = y1 - y0;
    356:   const PetscScalar f_3       = x3 - x0;
    357:   const PetscScalar g_3       = y3 - y0;
    358:   const PetscScalar f_01      = x2 - x1 - x3 + x0;
    359:   const PetscScalar g_01      = y2 - y1 - y3 + y0;
    360:   const PetscScalar *ref;
    361:   PetscScalar       *real;
    362:   PetscErrorCode    ierr;

    365:   VecGetArrayRead(Xref,  &ref);
    366:   VecGetArray(Xreal, &real);
    367:   {
    368:     const PetscScalar p0 = ref[0];
    369:     const PetscScalar p1 = ref[1];

    371:     real[0] = x0 + f_1 * p0 + f_3 * p1 + f_01 * p0 * p1;
    372:     real[1] = y0 + g_1 * p0 + g_3 * p1 + g_01 * p0 * p1;
    373:   }
    374:   PetscLogFlops(28);
    375:   VecRestoreArrayRead(Xref,  &ref);
    376:   VecRestoreArray(Xreal, &real);
    377:   return(0);
    378: }

    380: #include <petsc/private/dmimpl.h>
    383: PETSC_STATIC_INLINE PetscErrorCode QuadJacobian_Private(SNES snes, Vec Xref, Mat J, Mat M, void *ctx)
    384: {
    385:   const PetscScalar *vertices = (const PetscScalar*) ctx;
    386:   const PetscScalar x0        = vertices[0];
    387:   const PetscScalar y0        = vertices[1];
    388:   const PetscScalar x1        = vertices[2];
    389:   const PetscScalar y1        = vertices[3];
    390:   const PetscScalar x2        = vertices[4];
    391:   const PetscScalar y2        = vertices[5];
    392:   const PetscScalar x3        = vertices[6];
    393:   const PetscScalar y3        = vertices[7];
    394:   const PetscScalar f_01      = x2 - x1 - x3 + x0;
    395:   const PetscScalar g_01      = y2 - y1 - y3 + y0;
    396:   const PetscScalar *ref;
    397:   PetscErrorCode    ierr;

    400:   VecGetArrayRead(Xref,  &ref);
    401:   {
    402:     const PetscScalar x       = ref[0];
    403:     const PetscScalar y       = ref[1];
    404:     const PetscInt    rows[2] = {0, 1};
    405:     PetscScalar       values[4];

    407:     values[0] = (x1 - x0 + f_01*y) * 0.5; values[1] = (x3 - x0 + f_01*x) * 0.5;
    408:     values[2] = (y1 - y0 + g_01*y) * 0.5; values[3] = (y3 - y0 + g_01*x) * 0.5;
    409:     MatSetValues(J, 2, rows, 2, rows, values, INSERT_VALUES);
    410:   }
    411:   PetscLogFlops(30);
    412:   VecRestoreArrayRead(Xref,  &ref);
    413:   MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY);
    414:   MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY);
    415:   return(0);
    416: }

    420: PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Quad_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
    421: {
    422:   DM             dmCoord;
    423:   SNES           snes;
    424:   KSP            ksp;
    425:   PC             pc;
    426:   Vec            coordsLocal, r, ref, real;
    427:   Mat            J;
    428:   const PetscScalar *coords;
    429:   PetscScalar    *a;
    430:   PetscInt       p;

    434:   DMGetCoordinatesLocal(dm, &coordsLocal);
    435:   DMGetCoordinateDM(dm, &dmCoord);
    436:   SNESCreate(PETSC_COMM_SELF, &snes);
    437:   SNESSetOptionsPrefix(snes, "quad_interp_");
    438:   VecCreate(PETSC_COMM_SELF, &r);
    439:   VecSetSizes(r, 2, 2);
    440:   VecSetType(r,dm->vectype);
    441:   VecDuplicate(r, &ref);
    442:   VecDuplicate(r, &real);
    443:   MatCreate(PETSC_COMM_SELF, &J);
    444:   MatSetSizes(J, 2, 2, 2, 2);
    445:   MatSetType(J, MATSEQDENSE);
    446:   MatSetUp(J);
    447:   SNESSetFunction(snes, r, QuadMap_Private, NULL);
    448:   SNESSetJacobian(snes, J, J, QuadJacobian_Private, NULL);
    449:   SNESGetKSP(snes, &ksp);
    450:   KSPGetPC(ksp, &pc);
    451:   PCSetType(pc, PCLU);
    452:   SNESSetFromOptions(snes);

    454:   VecGetArrayRead(ctx->coords, &coords);
    455:   VecGetArray(v, &a);
    456:   for (p = 0; p < ctx->n; ++p) {
    457:     PetscScalar *x = NULL, *vertices = NULL;
    458:     PetscScalar *xi;
    459:     PetscReal    xir[2];
    460:     PetscInt     c = ctx->cells[p], comp, coordSize, xSize;

    462:     /* Can make this do all points at once */
    463:     DMPlexVecGetClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);
    464:     if (4*2 != coordSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %d should be %d", coordSize, 4*2);
    465:     DMPlexVecGetClosure(dm, NULL, xLocal, c, &xSize, &x);
    466:     if (4*ctx->dof != xSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %d should be %d", xSize, 4*ctx->dof);
    467:     SNESSetFunction(snes, NULL, NULL, (void*) vertices);
    468:     SNESSetJacobian(snes, NULL, NULL, NULL, (void*) vertices);
    469:     VecGetArray(real, &xi);
    470:     xi[0]  = coords[p*ctx->dim+0];
    471:     xi[1]  = coords[p*ctx->dim+1];
    472:     VecRestoreArray(real, &xi);
    473:     SNESSolve(snes, real, ref);
    474:     VecGetArray(ref, &xi);
    475:     xir[0] = PetscRealPart(xi[0]);
    476:     xir[1] = PetscRealPart(xi[1]);
    477:     for (comp = 0; comp < ctx->dof; ++comp) a[p*ctx->dof+comp] = x[0*ctx->dof+comp]*(1 - xir[0])*(1 - xir[1]) + x[1*ctx->dof+comp]*xir[0]*(1 - xir[1]) + x[2*ctx->dof+comp]*xir[0]*xir[1] + x[3*ctx->dof+comp]*(1 - xir[0])*xir[1];

    479:     VecRestoreArray(ref, &xi);
    480:     DMPlexVecRestoreClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);
    481:     DMPlexVecRestoreClosure(dm, NULL, xLocal, c, &xSize, &x);
    482:   }
    483:   VecRestoreArray(v, &a);
    484:   VecRestoreArrayRead(ctx->coords, &coords);

    486:   SNESDestroy(&snes);
    487:   VecDestroy(&r);
    488:   VecDestroy(&ref);
    489:   VecDestroy(&real);
    490:   MatDestroy(&J);
    491:   return(0);
    492: }

    496: PETSC_STATIC_INLINE PetscErrorCode HexMap_Private(SNES snes, Vec Xref, Vec Xreal, void *ctx)
    497: {
    498:   const PetscScalar *vertices = (const PetscScalar*) ctx;
    499:   const PetscScalar x0        = vertices[0];
    500:   const PetscScalar y0        = vertices[1];
    501:   const PetscScalar z0        = vertices[2];
    502:   const PetscScalar x1        = vertices[9];
    503:   const PetscScalar y1        = vertices[10];
    504:   const PetscScalar z1        = vertices[11];
    505:   const PetscScalar x2        = vertices[6];
    506:   const PetscScalar y2        = vertices[7];
    507:   const PetscScalar z2        = vertices[8];
    508:   const PetscScalar x3        = vertices[3];
    509:   const PetscScalar y3        = vertices[4];
    510:   const PetscScalar z3        = vertices[5];
    511:   const PetscScalar x4        = vertices[12];
    512:   const PetscScalar y4        = vertices[13];
    513:   const PetscScalar z4        = vertices[14];
    514:   const PetscScalar x5        = vertices[15];
    515:   const PetscScalar y5        = vertices[16];
    516:   const PetscScalar z5        = vertices[17];
    517:   const PetscScalar x6        = vertices[18];
    518:   const PetscScalar y6        = vertices[19];
    519:   const PetscScalar z6        = vertices[20];
    520:   const PetscScalar x7        = vertices[21];
    521:   const PetscScalar y7        = vertices[22];
    522:   const PetscScalar z7        = vertices[23];
    523:   const PetscScalar f_1       = x1 - x0;
    524:   const PetscScalar g_1       = y1 - y0;
    525:   const PetscScalar h_1       = z1 - z0;
    526:   const PetscScalar f_3       = x3 - x0;
    527:   const PetscScalar g_3       = y3 - y0;
    528:   const PetscScalar h_3       = z3 - z0;
    529:   const PetscScalar f_4       = x4 - x0;
    530:   const PetscScalar g_4       = y4 - y0;
    531:   const PetscScalar h_4       = z4 - z0;
    532:   const PetscScalar f_01      = x2 - x1 - x3 + x0;
    533:   const PetscScalar g_01      = y2 - y1 - y3 + y0;
    534:   const PetscScalar h_01      = z2 - z1 - z3 + z0;
    535:   const PetscScalar f_12      = x7 - x3 - x4 + x0;
    536:   const PetscScalar g_12      = y7 - y3 - y4 + y0;
    537:   const PetscScalar h_12      = z7 - z3 - z4 + z0;
    538:   const PetscScalar f_02      = x5 - x1 - x4 + x0;
    539:   const PetscScalar g_02      = y5 - y1 - y4 + y0;
    540:   const PetscScalar h_02      = z5 - z1 - z4 + z0;
    541:   const PetscScalar f_012     = x6 - x0 + x1 - x2 + x3 + x4 - x5 - x7;
    542:   const PetscScalar g_012     = y6 - y0 + y1 - y2 + y3 + y4 - y5 - y7;
    543:   const PetscScalar h_012     = z6 - z0 + z1 - z2 + z3 + z4 - z5 - z7;
    544:   const PetscScalar *ref;
    545:   PetscScalar       *real;
    546:   PetscErrorCode    ierr;

    549:   VecGetArrayRead(Xref,  &ref);
    550:   VecGetArray(Xreal, &real);
    551:   {
    552:     const PetscScalar p0 = ref[0];
    553:     const PetscScalar p1 = ref[1];
    554:     const PetscScalar p2 = ref[2];

    556:     real[0] = x0 + f_1*p0 + f_3*p1 + f_4*p2 + f_01*p0*p1 + f_12*p1*p2 + f_02*p0*p2 + f_012*p0*p1*p2;
    557:     real[1] = y0 + g_1*p0 + g_3*p1 + g_4*p2 + g_01*p0*p1 + g_01*p0*p1 + g_12*p1*p2 + g_02*p0*p2 + g_012*p0*p1*p2;
    558:     real[2] = z0 + h_1*p0 + h_3*p1 + h_4*p2 + h_01*p0*p1 + h_01*p0*p1 + h_12*p1*p2 + h_02*p0*p2 + h_012*p0*p1*p2;
    559:   }
    560:   PetscLogFlops(114);
    561:   VecRestoreArrayRead(Xref,  &ref);
    562:   VecRestoreArray(Xreal, &real);
    563:   return(0);
    564: }

    568: PETSC_STATIC_INLINE PetscErrorCode HexJacobian_Private(SNES snes, Vec Xref, Mat J, Mat M, void *ctx)
    569: {
    570:   const PetscScalar *vertices = (const PetscScalar*) ctx;
    571:   const PetscScalar x0        = vertices[0];
    572:   const PetscScalar y0        = vertices[1];
    573:   const PetscScalar z0        = vertices[2];
    574:   const PetscScalar x1        = vertices[9];
    575:   const PetscScalar y1        = vertices[10];
    576:   const PetscScalar z1        = vertices[11];
    577:   const PetscScalar x2        = vertices[6];
    578:   const PetscScalar y2        = vertices[7];
    579:   const PetscScalar z2        = vertices[8];
    580:   const PetscScalar x3        = vertices[3];
    581:   const PetscScalar y3        = vertices[4];
    582:   const PetscScalar z3        = vertices[5];
    583:   const PetscScalar x4        = vertices[12];
    584:   const PetscScalar y4        = vertices[13];
    585:   const PetscScalar z4        = vertices[14];
    586:   const PetscScalar x5        = vertices[15];
    587:   const PetscScalar y5        = vertices[16];
    588:   const PetscScalar z5        = vertices[17];
    589:   const PetscScalar x6        = vertices[18];
    590:   const PetscScalar y6        = vertices[19];
    591:   const PetscScalar z6        = vertices[20];
    592:   const PetscScalar x7        = vertices[21];
    593:   const PetscScalar y7        = vertices[22];
    594:   const PetscScalar z7        = vertices[23];
    595:   const PetscScalar f_xy      = x2 - x1 - x3 + x0;
    596:   const PetscScalar g_xy      = y2 - y1 - y3 + y0;
    597:   const PetscScalar h_xy      = z2 - z1 - z3 + z0;
    598:   const PetscScalar f_yz      = x7 - x3 - x4 + x0;
    599:   const PetscScalar g_yz      = y7 - y3 - y4 + y0;
    600:   const PetscScalar h_yz      = z7 - z3 - z4 + z0;
    601:   const PetscScalar f_xz      = x5 - x1 - x4 + x0;
    602:   const PetscScalar g_xz      = y5 - y1 - y4 + y0;
    603:   const PetscScalar h_xz      = z5 - z1 - z4 + z0;
    604:   const PetscScalar f_xyz     = x6 - x0 + x1 - x2 + x3 + x4 - x5 - x7;
    605:   const PetscScalar g_xyz     = y6 - y0 + y1 - y2 + y3 + y4 - y5 - y7;
    606:   const PetscScalar h_xyz     = z6 - z0 + z1 - z2 + z3 + z4 - z5 - z7;
    607:   const PetscScalar *ref;
    608:   PetscErrorCode    ierr;

    611:   VecGetArrayRead(Xref,  &ref);
    612:   {
    613:     const PetscScalar x       = ref[0];
    614:     const PetscScalar y       = ref[1];
    615:     const PetscScalar z       = ref[2];
    616:     const PetscInt    rows[3] = {0, 1, 2};
    617:     PetscScalar       values[9];

    619:     values[0] = (x1 - x0 + f_xy*y + f_xz*z + f_xyz*y*z) / 2.0;
    620:     values[1] = (x3 - x0 + f_xy*x + f_yz*z + f_xyz*x*z) / 2.0;
    621:     values[2] = (x4 - x0 + f_yz*y + f_xz*x + f_xyz*x*y) / 2.0;
    622:     values[3] = (y1 - y0 + g_xy*y + g_xz*z + g_xyz*y*z) / 2.0;
    623:     values[4] = (y3 - y0 + g_xy*x + g_yz*z + g_xyz*x*z) / 2.0;
    624:     values[5] = (y4 - y0 + g_yz*y + g_xz*x + g_xyz*x*y) / 2.0;
    625:     values[6] = (z1 - z0 + h_xy*y + h_xz*z + h_xyz*y*z) / 2.0;
    626:     values[7] = (z3 - z0 + h_xy*x + h_yz*z + h_xyz*x*z) / 2.0;
    627:     values[8] = (z4 - z0 + h_yz*y + h_xz*x + h_xyz*x*y) / 2.0;

    629:     MatSetValues(J, 3, rows, 3, rows, values, INSERT_VALUES);
    630:   }
    631:   PetscLogFlops(152);
    632:   VecRestoreArrayRead(Xref,  &ref);
    633:   MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY);
    634:   MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY);
    635:   return(0);
    636: }

    640: PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Hex_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
    641: {
    642:   DM             dmCoord;
    643:   SNES           snes;
    644:   KSP            ksp;
    645:   PC             pc;
    646:   Vec            coordsLocal, r, ref, real;
    647:   Mat            J;
    648:   const PetscScalar *coords;
    649:   PetscScalar    *a;
    650:   PetscInt       p;

    654:   DMGetCoordinatesLocal(dm, &coordsLocal);
    655:   DMGetCoordinateDM(dm, &dmCoord);
    656:   SNESCreate(PETSC_COMM_SELF, &snes);
    657:   SNESSetOptionsPrefix(snes, "hex_interp_");
    658:   VecCreate(PETSC_COMM_SELF, &r);
    659:   VecSetSizes(r, 3, 3);
    660:   VecSetType(r,dm->vectype);
    661:   VecDuplicate(r, &ref);
    662:   VecDuplicate(r, &real);
    663:   MatCreate(PETSC_COMM_SELF, &J);
    664:   MatSetSizes(J, 3, 3, 3, 3);
    665:   MatSetType(J, MATSEQDENSE);
    666:   MatSetUp(J);
    667:   SNESSetFunction(snes, r, HexMap_Private, NULL);
    668:   SNESSetJacobian(snes, J, J, HexJacobian_Private, NULL);
    669:   SNESGetKSP(snes, &ksp);
    670:   KSPGetPC(ksp, &pc);
    671:   PCSetType(pc, PCLU);
    672:   SNESSetFromOptions(snes);

    674:   VecGetArrayRead(ctx->coords, &coords);
    675:   VecGetArray(v, &a);
    676:   for (p = 0; p < ctx->n; ++p) {
    677:     PetscScalar *x = NULL, *vertices = NULL;
    678:     PetscScalar *xi;
    679:     PetscReal    xir[3];
    680:     PetscInt     c = ctx->cells[p], comp, coordSize, xSize;

    682:     /* Can make this do all points at once */
    683:     DMPlexVecGetClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);
    684:     if (8*3 != coordSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %d should be %d", coordSize, 8*3);
    685:     DMPlexVecGetClosure(dm, NULL, xLocal, c, &xSize, &x);
    686:     if (8*ctx->dof != xSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %d should be %d", xSize, 8*ctx->dof);
    687:     SNESSetFunction(snes, NULL, NULL, (void*) vertices);
    688:     SNESSetJacobian(snes, NULL, NULL, NULL, (void*) vertices);
    689:     VecGetArray(real, &xi);
    690:     xi[0]  = coords[p*ctx->dim+0];
    691:     xi[1]  = coords[p*ctx->dim+1];
    692:     xi[2]  = coords[p*ctx->dim+2];
    693:     VecRestoreArray(real, &xi);
    694:     SNESSolve(snes, real, ref);
    695:     VecGetArray(ref, &xi);
    696:     xir[0] = PetscRealPart(xi[0]);
    697:     xir[1] = PetscRealPart(xi[1]);
    698:     xir[2] = PetscRealPart(xi[2]);
    699:     for (comp = 0; comp < ctx->dof; ++comp) {
    700:       a[p*ctx->dof+comp] =
    701:         x[0*ctx->dof+comp]*(1-xir[0])*(1-xir[1])*(1-xir[2]) +
    702:         x[3*ctx->dof+comp]*    xir[0]*(1-xir[1])*(1-xir[2]) +
    703:         x[2*ctx->dof+comp]*    xir[0]*    xir[1]*(1-xir[2]) +
    704:         x[1*ctx->dof+comp]*(1-xir[0])*    xir[1]*(1-xir[2]) +
    705:         x[4*ctx->dof+comp]*(1-xir[0])*(1-xir[1])*   xir[2] +
    706:         x[5*ctx->dof+comp]*    xir[0]*(1-xir[1])*   xir[2] +
    707:         x[6*ctx->dof+comp]*    xir[0]*    xir[1]*   xir[2] +
    708:         x[7*ctx->dof+comp]*(1-xir[0])*    xir[1]*   xir[2];
    709:     }
    710:     VecRestoreArray(ref, &xi);
    711:     DMPlexVecRestoreClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);
    712:     DMPlexVecRestoreClosure(dm, NULL, xLocal, c, &xSize, &x);
    713:   }
    714:   VecRestoreArray(v, &a);
    715:   VecRestoreArrayRead(ctx->coords, &coords);

    717:   SNESDestroy(&snes);
    718:   VecDestroy(&r);
    719:   VecDestroy(&ref);
    720:   VecDestroy(&real);
    721:   MatDestroy(&J);
    722:   return(0);
    723: }

    727: /*
    728:   Input Parameters:
    729: + ctx - The DMInterpolationInfo context
    730: . dm  - The DM
    731: - x   - The local vector containing the field to be interpolated

    733:   Output Parameters:
    734: . v   - The vector containing the interpolated values
    735: */
    736: PetscErrorCode DMInterpolationEvaluate(DMInterpolationInfo ctx, DM dm, Vec x, Vec v)
    737: {
    738:   PetscInt       dim, coneSize, n;

    745:   VecGetLocalSize(v, &n);
    746:   if (n != ctx->n*ctx->dof) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid input vector size %d should be %d", n, ctx->n*ctx->dof);
    747:   if (n) {
    748:     DMGetDimension(dm, &dim);
    749:     DMPlexGetConeSize(dm, ctx->cells[0], &coneSize);
    750:     if (dim == 2) {
    751:       if (coneSize == 3) {
    752:         DMInterpolate_Triangle_Private(ctx, dm, x, v);
    753:       } else if (coneSize == 4) {
    754:         DMInterpolate_Quad_Private(ctx, dm, x, v);
    755:       } else SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Unsupported dimension %d for point interpolation", dim);
    756:     } else if (dim == 3) {
    757:       if (coneSize == 4) {
    758:         DMInterpolate_Tetrahedron_Private(ctx, dm, x, v);
    759:       } else {
    760:         DMInterpolate_Hex_Private(ctx, dm, x, v);
    761:       }
    762:     } else SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Unsupported dimension %d for point interpolation", dim);
    763:   }
    764:   return(0);
    765: }

    769: PetscErrorCode DMInterpolationDestroy(DMInterpolationInfo *ctx)
    770: {

    775:   VecDestroy(&(*ctx)->coords);
    776:   PetscFree((*ctx)->points);
    777:   PetscFree((*ctx)->cells);
    778:   PetscFree(*ctx);
    779:   *ctx = NULL;
    780:   return(0);
    781: }

    785: /*@C
    786:   SNESMonitorFields - Monitors the residual for each field separately

    788:   Collective on SNES

    790:   Input Parameters:
    791: + snes   - the SNES context
    792: . its    - iteration number
    793: . fgnorm - 2-norm of residual
    794: - vf  - PetscViewerAndFormat of type ASCII

    796:   Notes:
    797:   This routine prints the residual norm at each iteration.

    799:   Level: intermediate

    801: .keywords: SNES, nonlinear, default, monitor, norm
    802: .seealso: SNESMonitorSet(), SNESMonitorDefault()
    803: @*/
    804: PetscErrorCode SNESMonitorFields(SNES snes, PetscInt its, PetscReal fgnorm, PetscViewerAndFormat *vf)
    805: {
    806:   PetscViewer        viewer = vf->viewer;
    807:   Vec                res;
    808:   DM                 dm;
    809:   PetscSection       s;
    810:   const PetscScalar *r;
    811:   PetscReal         *lnorms, *norms;
    812:   PetscInt           numFields, f, pStart, pEnd, p;
    813:   PetscErrorCode     ierr;

    817:   SNESGetFunction(snes, &res, 0, 0);
    818:   SNESGetDM(snes, &dm);
    819:   DMGetDefaultSection(dm, &s);
    820:   PetscSectionGetNumFields(s, &numFields);
    821:   PetscSectionGetChart(s, &pStart, &pEnd);
    822:   PetscCalloc2(numFields, &lnorms, numFields, &norms);
    823:   VecGetArrayRead(res, &r);
    824:   for (p = pStart; p < pEnd; ++p) {
    825:     for (f = 0; f < numFields; ++f) {
    826:       PetscInt fdof, foff, d;

    828:       PetscSectionGetFieldDof(s, p, f, &fdof);
    829:       PetscSectionGetFieldOffset(s, p, f, &foff);
    830:       for (d = 0; d < fdof; ++d) lnorms[f] += PetscRealPart(PetscSqr(r[foff+d]));
    831:     }
    832:   }
    833:   VecRestoreArrayRead(res, &r);
    834:   MPIU_Allreduce(lnorms, norms, numFields, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject) dm));
    835:   PetscViewerPushFormat(viewer,vf->format);
    836:   PetscViewerASCIIAddTab(viewer, ((PetscObject) snes)->tablevel);
    837:   PetscViewerASCIIPrintf(viewer, "%3D SNES Function norm %14.12e [", its, (double) fgnorm);
    838:   for (f = 0; f < numFields; ++f) {
    839:     if (f > 0) {PetscViewerASCIIPrintf(viewer, ", ");}
    840:     PetscViewerASCIIPrintf(viewer, "%14.12e", (double) PetscSqrtReal(norms[f]));
    841:   }
    842:   PetscViewerASCIIPrintf(viewer, "]\n");
    843:   PetscViewerASCIISubtractTab(viewer, ((PetscObject) snes)->tablevel);
    844:   PetscViewerPopFormat(viewer);
    845:   PetscFree2(lnorms, norms);
    846:   return(0);
    847: }

    849: /********************* Residual Computation **************************/

    853: /*@
    854:   DMPlexSNESGetGeometryFEM - Return precomputed geometric data

    856:   Input Parameter:
    857: . dm - The DM

    859:   Output Parameters:
    860: . cellgeom - The values precomputed from cell geometry

    862:   Level: developer

    864: .seealso: DMPlexSNESSetFunctionLocal()
    865: @*/
    866: PetscErrorCode DMPlexSNESGetGeometryFEM(DM dm, Vec *cellgeom)
    867: {
    868:   DMSNES         dmsnes;
    869:   PetscObject    obj;

    874:   DMGetDMSNES(dm, &dmsnes);
    875:   PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_cellgeom_fem", &obj);
    876:   if (!obj) {
    877:     Vec cellgeom;

    879:     DMPlexComputeGeometryFEM(dm, &cellgeom);
    880:     PetscObjectCompose((PetscObject) dmsnes, "DMPlexSNES_cellgeom_fem", (PetscObject) cellgeom);
    881:     VecDestroy(&cellgeom);
    882:   }
    884:   return(0);
    885: }

    889: /*@
    890:   DMPlexSNESGetGeometryFVM - Return precomputed geometric data

    892:   Input Parameter:
    893: . dm - The DM

    895:   Output Parameters:
    896: + facegeom - The values precomputed from face geometry
    897: . cellgeom - The values precomputed from cell geometry
    898: - minRadius - The minimum radius over the mesh of an inscribed sphere in a cell

    900:   Level: developer

    902: .seealso: DMPlexTSSetRHSFunctionLocal()
    903: @*/
    904: PetscErrorCode DMPlexSNESGetGeometryFVM(DM dm, Vec *facegeom, Vec *cellgeom, PetscReal *minRadius)
    905: {
    906:   DMSNES         dmsnes;
    907:   PetscObject    obj;

    912:   DMGetDMSNES(dm, &dmsnes);
    913:   PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_facegeom_fvm", &obj);
    914:   if (!obj) {
    915:     Vec cellgeom, facegeom;

    917:     DMPlexComputeGeometryFVM(dm, &cellgeom, &facegeom);
    918:     PetscObjectCompose((PetscObject) dmsnes, "DMPlexSNES_facegeom_fvm", (PetscObject) facegeom);
    919:     PetscObjectCompose((PetscObject) dmsnes, "DMPlexSNES_cellgeom_fvm", (PetscObject) cellgeom);
    920:     VecDestroy(&facegeom);
    921:     VecDestroy(&cellgeom);
    922:   }
    925:   if (minRadius) {DMPlexGetMinRadius(dm, minRadius);}
    926:   return(0);
    927: }

    931: /*@
    932:   DMPlexSNESGetGradientDM - Return gradient data layout

    934:   Input Parameters:
    935: + dm - The DM
    936: - fv - The PetscFV

    938:   Output Parameter:
    939: . dmGrad - The layout for gradient values

    941:   Level: developer

    943: .seealso: DMPlexSNESGetGeometryFVM()
    944: @*/
    945: PetscErrorCode DMPlexSNESGetGradientDM(DM dm, PetscFV fv, DM *dmGrad)
    946: {
    947:   DMSNES         dmsnes;
    948:   PetscObject    obj;
    949:   PetscBool      computeGradients;

    956:   PetscFVGetComputeGradients(fv, &computeGradients);
    957:   if (!computeGradients) {*dmGrad = NULL; return(0);}
    958:   DMGetDMSNES(dm, &dmsnes);
    959:   PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_dmgrad_fvm", &obj);
    960:   if (!obj) {
    961:     DM  dmGrad;
    962:     Vec faceGeometry, cellGeometry;

    964:     DMPlexSNESGetGeometryFVM(dm, &faceGeometry, &cellGeometry, NULL);
    965:     DMPlexComputeGradientFVM(dm, fv, faceGeometry, cellGeometry, &dmGrad);
    966:     PetscObjectCompose((PetscObject) dmsnes, "DMPlexSNES_dmgrad_fvm", (PetscObject) dmGrad);
    967:     DMDestroy(&dmGrad);
    968:   }
    969:   PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_dmgrad_fvm", (PetscObject *) dmGrad);
    970:   return(0);
    971: }

    975: /*@C
    976:   DMPlexGetCellFields - Retrieve the field values values for a chunk of cells

    978:   Input Parameters:
    979: + dm     - The DM
    980: . cStart - The first cell to include
    981: . cEnd   - The first cell to exclude
    982: . locX   - A local vector with the solution fields
    983: . locX_t - A local vector with solution field time derivatives, or NULL
    984: - locA   - A local vector with auxiliary fields, or NULL

    986:   Output Parameters:
    987: + u   - The field coefficients
    988: . u_t - The fields derivative coefficients
    989: - a   - The auxiliary field coefficients

    991:   Level: developer

    993: .seealso: DMPlexGetFaceFields()
    994: @*/
    995: PetscErrorCode DMPlexGetCellFields(DM dm, PetscInt cStart, PetscInt cEnd, Vec locX, Vec locX_t, Vec locA, PetscScalar **u, PetscScalar **u_t, PetscScalar **a)
    996: {
    997:   DM             dmAux;
    998:   PetscSection   section, sectionAux;
    999:   PetscDS        prob;
    1000:   PetscInt       numCells = cEnd - cStart, totDim, totDimAux, c;

    1011:   DMGetDefaultSection(dm, &section);
    1012:   DMGetDS(dm, &prob);
    1013:   PetscDSGetTotalDimension(prob, &totDim);
    1014:   if (locA) {
    1015:     PetscDS probAux;

    1017:     VecGetDM(locA, &dmAux);
    1018:     DMGetDefaultSection(dmAux, &sectionAux);
    1019:     DMGetDS(dmAux, &probAux);
    1020:     PetscDSGetTotalDimension(probAux, &totDimAux);
    1021:   }
    1022:   DMGetWorkArray(dm, numCells*totDim, PETSC_SCALAR, u);
    1023:   if (locX_t) {DMGetWorkArray(dm, numCells*totDim, PETSC_SCALAR, u_t);} else {*u_t = NULL;}
    1024:   if (locA)   {DMGetWorkArray(dm, numCells*totDimAux, PETSC_SCALAR, a);} else {*a = NULL;}
    1025:   for (c = cStart; c < cEnd; ++c) {
    1026:     PetscScalar *x = NULL, *x_t = NULL, *ul = *u, *ul_t = *u_t, *al = *a;
    1027:     PetscInt     i;

    1029:     DMPlexVecGetClosure(dm, section, locX, c, NULL, &x);
    1030:     for (i = 0; i < totDim; ++i) ul[(c-cStart)*totDim+i] = x[i];
    1031:     DMPlexVecRestoreClosure(dm, section, locX, c, NULL, &x);
    1032:     if (locX_t) {
    1033:       DMPlexVecGetClosure(dm, section, locX_t, c, NULL, &x_t);
    1034:       for (i = 0; i < totDim; ++i) ul_t[(c-cStart)*totDim+i] = x_t[i];
    1035:       DMPlexVecRestoreClosure(dm, section, locX_t, c, NULL, &x_t);
    1036:     }
    1037:     if (locA) {
    1038:       DM dmAuxPlex;

    1040:       DMSNESConvertPlex(dmAux, &dmAuxPlex, PETSC_FALSE);
    1041:       DMPlexVecGetClosure(dmAuxPlex, sectionAux, locA, c, NULL, &x);
    1042:       for (i = 0; i < totDimAux; ++i) al[(c-cStart)*totDimAux+i] = x[i];
    1043:       DMPlexVecRestoreClosure(dmAuxPlex, sectionAux, locA, c, NULL, &x);
    1044:       DMDestroy(&dmAuxPlex);
    1045:     }
    1046:   }
    1047:   return(0);
    1048: }

    1052: /*@C
    1053:   DMPlexRestoreCellFields - Restore the field values values for a chunk of cells

    1055:   Input Parameters:
    1056: + dm     - The DM
    1057: . cStart - The first cell to include
    1058: . cEnd   - The first cell to exclude
    1059: . locX   - A local vector with the solution fields
    1060: . locX_t - A local vector with solution field time derivatives, or NULL
    1061: - locA   - A local vector with auxiliary fields, or NULL

    1063:   Output Parameters:
    1064: + u   - The field coefficients
    1065: . u_t - The fields derivative coefficients
    1066: - a   - The auxiliary field coefficients

    1068:   Level: developer

    1070: .seealso: DMPlexGetFaceFields()
    1071: @*/
    1072: PetscErrorCode DMPlexRestoreCellFields(DM dm, PetscInt cStart, PetscInt cEnd, Vec locX, Vec locX_t, Vec locA, PetscScalar **u, PetscScalar **u_t, PetscScalar **a)
    1073: {

    1077:   DMRestoreWorkArray(dm, 0, PETSC_SCALAR, u);
    1078:   if (*u_t) {DMRestoreWorkArray(dm, 0, PETSC_SCALAR, u_t);}
    1079:   if (*a)   {DMRestoreWorkArray(dm, 0, PETSC_SCALAR, a);}
    1080:   return(0);
    1081: }

    1085: /*@C
    1086:   DMPlexGetFaceFields - Retrieve the field values values for a chunk of faces

    1088:   Input Parameters:
    1089: + dm     - The DM
    1090: . fStart - The first face to include
    1091: . fEnd   - The first face to exclude
    1092: . locX   - A local vector with the solution fields
    1093: . locX_t - A local vector with solution field time derivatives, or NULL
    1094: . faceGeometry - A local vector with face geometry
    1095: . cellGeometry - A local vector with cell geometry
    1096: - locaGrad - A local vector with field gradients, or NULL

    1098:   Output Parameters:
    1099: + uL - The field values at the left side of the face
    1100: - uR - The field values at the right side of the face

    1102:   Level: developer

    1104: .seealso: DMPlexGetCellFields()
    1105: @*/
    1106: PetscErrorCode DMPlexGetFaceFields(DM dm, PetscInt fStart, PetscInt fEnd, Vec locX, Vec locX_t, Vec faceGeometry, Vec cellGeometry, Vec locGrad, PetscScalar **uL, PetscScalar **uR)
    1107: {
    1108:   DM                 dmFace, dmCell, dmGrad = NULL;
    1109:   PetscSection       section;
    1110:   PetscDS            prob;
    1111:   DMLabel            ghostLabel;
    1112:   const PetscScalar *facegeom, *cellgeom, *x, *lgrad;
    1113:   PetscBool         *isFE;
    1114:   PetscInt           dim, Nf, f, Nc, numFaces = fEnd - fStart, iface, face;
    1115:   PetscErrorCode     ierr;

    1126:   DMGetDimension(dm, &dim);
    1127:   DMGetDS(dm, &prob);
    1128:   DMGetDefaultSection(dm, &section);
    1129:   PetscDSGetNumFields(prob, &Nf);
    1130:   PetscDSGetTotalComponents(prob, &Nc);
    1131:   PetscMalloc1(Nf, &isFE);
    1132:   for (f = 0; f < Nf; ++f) {
    1133:     PetscObject  obj;
    1134:     PetscClassId id;

    1136:     DMGetField(dm, f, &obj);
    1137:     PetscObjectGetClassId(obj, &id);
    1138:     if (id == PETSCFE_CLASSID)      {isFE[f] = PETSC_TRUE;}
    1139:     else if (id == PETSCFV_CLASSID) {isFE[f] = PETSC_FALSE;}
    1140:     else                            {isFE[f] = PETSC_FALSE;}
    1141:   }
    1142:   DMGetLabel(dm, "ghost", &ghostLabel);
    1143:   VecGetArrayRead(locX, &x);
    1144:   VecGetDM(faceGeometry, &dmFace);
    1145:   VecGetArrayRead(faceGeometry, &facegeom);
    1146:   VecGetDM(cellGeometry, &dmCell);
    1147:   VecGetArrayRead(cellGeometry, &cellgeom);
    1148:   if (locGrad) {
    1149:     VecGetDM(locGrad, &dmGrad);
    1150:     VecGetArrayRead(locGrad, &lgrad);
    1151:   }
    1152:   DMGetWorkArray(dm, numFaces*Nc, PETSC_SCALAR, uL);
    1153:   DMGetWorkArray(dm, numFaces*Nc, PETSC_SCALAR, uR);
    1154:   /* Right now just eat the extra work for FE (could make a cell loop) */
    1155:   for (face = fStart, iface = 0; face < fEnd; ++face) {
    1156:     const PetscInt        *cells;
    1157:     PetscFVFaceGeom       *fg;
    1158:     PetscFVCellGeom       *cgL, *cgR;
    1159:     PetscScalar           *xL, *xR, *gL, *gR;
    1160:     PetscScalar           *uLl = *uL, *uRl = *uR;
    1161:     PetscInt               ghost, nsupp;

    1163:     DMLabelGetValue(ghostLabel, face, &ghost);
    1164:     DMPlexGetSupportSize(dm, face, &nsupp);
    1165:     if (ghost >= 0) continue;
    1166:     DMPlexPointLocalRead(dmFace, face, facegeom, &fg);
    1167:     DMPlexGetSupport(dm, face, &cells);
    1168:     DMPlexPointLocalRead(dmCell, cells[0], cellgeom, &cgL);
    1169:     DMPlexPointLocalRead(dmCell, cells[1], cellgeom, &cgR);
    1170:     for (f = 0; f < Nf; ++f) {
    1171:       PetscInt off;

    1173:       PetscDSGetComponentOffset(prob, f, &off);
    1174:       if (isFE[f]) {
    1175:         const PetscInt *cone;
    1176:         PetscInt        comp, coneSize, faceLocL, faceLocR, ldof, rdof, d;

    1178:         xL = xR = NULL;
    1179:         DMPlexVecGetClosure(dm, section, locX, cells[0], &ldof, (PetscScalar **) &xL);
    1180:         DMPlexVecGetClosure(dm, section, locX, cells[1], &rdof, (PetscScalar **) &xR);
    1181:         DMPlexGetCone(dm, cells[0], &cone);
    1182:         DMPlexGetConeSize(dm, cells[0], &coneSize);
    1183:         for (faceLocL = 0; faceLocL < coneSize; ++faceLocL) if (cone[faceLocL] == face) break;
    1184:         if (faceLocL == coneSize) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Could not find face %d in cone of cell %d", face, cells[0]);
    1185:         DMPlexGetCone(dm, cells[1], &cone);
    1186:         DMPlexGetConeSize(dm, cells[1], &coneSize);
    1187:         for (faceLocR = 0; faceLocR < coneSize; ++faceLocR) if (cone[faceLocR] == face) break;
    1188:         if (faceLocR == coneSize) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Could not find face %d in cone of cell %d", face, cells[1]);
    1189:         /* Check that FEM field has values in the right cell (sometimes its an FV ghost cell) */
    1190:         EvaluateFaceFields(prob, f, faceLocL, xL, &uLl[iface*Nc+off]);
    1191:         if (rdof == ldof) {EvaluateFaceFields(prob, f, faceLocR, xR, &uRl[iface*Nc+off]);}
    1192:         else              {PetscSectionGetFieldComponents(section, f, &comp); for(d = 0; d < comp; ++d) uRl[iface*Nc+off+d] = uLl[iface*Nc+off+d];}
    1193:         DMPlexVecRestoreClosure(dm, section, locX, cells[0], &ldof, (PetscScalar **) &xL);
    1194:         DMPlexVecRestoreClosure(dm, section, locX, cells[1], &rdof, (PetscScalar **) &xR);
    1195:       } else {
    1196:         PetscFV  fv;
    1197:         PetscInt numComp, c;

    1199:         PetscDSGetDiscretization(prob, f, (PetscObject *) &fv);
    1200:         PetscFVGetNumComponents(fv, &numComp);
    1201:         if (nsupp > 2) {
    1202:           for (f = 0; f < Nf; ++f) {
    1203:             PetscInt off;

    1205:             PetscDSGetComponentOffset(prob, f, &off);
    1206:             PetscFVGetNumComponents(fv, &numComp);
    1207:             for (c = 0; c < numComp; ++c) {
    1208:               uLl[iface*Nc+off+c] = 0.;
    1209:               uRl[iface*Nc+off+c] = 0.;
    1210:             }
    1211:           }
    1212:           continue;
    1213:         }
    1214:         DMPlexPointLocalFieldRead(dm, cells[0], f, x, &xL);
    1215:         DMPlexPointLocalFieldRead(dm, cells[1], f, x, &xR);
    1216:         if (dmGrad) {
    1217:           PetscReal dxL[3], dxR[3];

    1219:           DMPlexPointLocalRead(dmGrad, cells[0], lgrad, &gL);
    1220:           DMPlexPointLocalRead(dmGrad, cells[1], lgrad, &gR);
    1221:           DMPlex_WaxpyD_Internal(dim, -1, cgL->centroid, fg->centroid, dxL);
    1222:           DMPlex_WaxpyD_Internal(dim, -1, cgR->centroid, fg->centroid, dxR);
    1223:           for (c = 0; c < numComp; ++c) {
    1224:             uLl[iface*Nc+off+c] = xL[c] + DMPlex_DotD_Internal(dim, &gL[c*dim], dxL);
    1225:             uRl[iface*Nc+off+c] = xR[c] + DMPlex_DotD_Internal(dim, &gR[c*dim], dxR);
    1226:           }
    1227:         } else {
    1228:           for (c = 0; c < numComp; ++c) {
    1229:             uLl[iface*Nc+off+c] = xL[c];
    1230:             uRl[iface*Nc+off+c] = xR[c];
    1231:           }
    1232:         }
    1233:       }
    1234:     }
    1235:     ++iface;
    1236:   }
    1237:   VecRestoreArrayRead(locX, &x);
    1238:   VecRestoreArrayRead(faceGeometry, &facegeom);
    1239:   VecRestoreArrayRead(cellGeometry, &cellgeom);
    1240:   if (locGrad) {
    1241:     VecRestoreArrayRead(locGrad, &lgrad);
    1242:   }
    1243:   PetscFree(isFE);
    1244:   return(0);
    1245: }

    1249: /*@C
    1250:   DMPlexRestoreFaceFields - Restore the field values values for a chunk of faces

    1252:   Input Parameters:
    1253: + dm     - The DM
    1254: . fStart - The first face to include
    1255: . fEnd   - The first face to exclude
    1256: . locX   - A local vector with the solution fields
    1257: . locX_t - A local vector with solution field time derivatives, or NULL
    1258: . faceGeometry - A local vector with face geometry
    1259: . cellGeometry - A local vector with cell geometry
    1260: - locaGrad - A local vector with field gradients, or NULL

    1262:   Output Parameters:
    1263: + uL - The field values at the left side of the face
    1264: - uR - The field values at the right side of the face

    1266:   Level: developer

    1268: .seealso: DMPlexGetFaceFields()
    1269: @*/
    1270: PetscErrorCode DMPlexRestoreFaceFields(DM dm, PetscInt fStart, PetscInt fEnd, Vec locX, Vec locX_t, Vec faceGeometry, Vec cellGeometry, Vec locGrad, PetscScalar **uL, PetscScalar **uR)
    1271: {

    1275:   DMRestoreWorkArray(dm, 0, PETSC_SCALAR, uL);
    1276:   DMRestoreWorkArray(dm, 0, PETSC_SCALAR, uR);
    1277:   return(0);
    1278: }

    1282: /*@C
    1283:   DMPlexGetFaceGeometry - Retrieve the geometric values for a chunk of faces

    1285:   Input Parameters:
    1286: + dm     - The DM
    1287: . fStart - The first face to include
    1288: . fEnd   - The first face to exclude
    1289: . faceGeometry - A local vector with face geometry
    1290: - cellGeometry - A local vector with cell geometry

    1292:   Output Parameters:
    1293: + fgeom - The extract the face centroid and normal
    1294: - vol   - The cell volume

    1296:   Level: developer

    1298: .seealso: DMPlexGetCellFields()
    1299: @*/
    1300: PetscErrorCode DMPlexGetFaceGeometry(DM dm, PetscInt fStart, PetscInt fEnd, Vec faceGeometry, Vec cellGeometry, PetscFVFaceGeom **fgeom, PetscReal **vol)
    1301: {
    1302:   DM                 dmFace, dmCell;
    1303:   DMLabel            ghostLabel;
    1304:   const PetscScalar *facegeom, *cellgeom;
    1305:   PetscInt           dim, numFaces = fEnd - fStart, iface, face;
    1306:   PetscErrorCode     ierr;

    1314:   DMGetDimension(dm, &dim);
    1315:   DMGetLabel(dm, "ghost", &ghostLabel);
    1316:   VecGetDM(faceGeometry, &dmFace);
    1317:   VecGetArrayRead(faceGeometry, &facegeom);
    1318:   VecGetDM(cellGeometry, &dmCell);
    1319:   VecGetArrayRead(cellGeometry, &cellgeom);
    1320:   PetscMalloc1(numFaces, fgeom);
    1321:   DMGetWorkArray(dm, numFaces*2, PETSC_SCALAR, vol);
    1322:   for (face = fStart, iface = 0; face < fEnd; ++face) {
    1323:     const PetscInt        *cells;
    1324:     PetscFVFaceGeom       *fg;
    1325:     PetscFVCellGeom       *cgL, *cgR;
    1326:     PetscFVFaceGeom       *fgeoml = *fgeom;
    1327:     PetscReal             *voll   = *vol;
    1328:     PetscInt               ghost, d;

    1330:     DMLabelGetValue(ghostLabel, face, &ghost);
    1331:     if (ghost >= 0) continue;
    1332:     DMPlexPointLocalRead(dmFace, face, facegeom, &fg);
    1333:     DMPlexGetSupport(dm, face, &cells);
    1334:     DMPlexPointLocalRead(dmCell, cells[0], cellgeom, &cgL);
    1335:     DMPlexPointLocalRead(dmCell, cells[1], cellgeom, &cgR);
    1336:     for (d = 0; d < dim; ++d) {
    1337:       fgeoml[iface].centroid[d] = fg->centroid[d];
    1338:       fgeoml[iface].normal[d]   = fg->normal[d];
    1339:     }
    1340:     voll[iface*2+0] = cgL->volume;
    1341:     voll[iface*2+1] = cgR->volume;
    1342:     ++iface;
    1343:   }
    1344:   VecRestoreArrayRead(faceGeometry, &facegeom);
    1345:   VecRestoreArrayRead(cellGeometry, &cellgeom);
    1346:   return(0);
    1347: }

    1351: /*@C
    1352:   DMPlexRestoreFaceGeometry - Restore the field values values for a chunk of faces

    1354:   Input Parameters:
    1355: + dm     - The DM
    1356: . fStart - The first face to include
    1357: . fEnd   - The first face to exclude
    1358: . faceGeometry - A local vector with face geometry
    1359: - cellGeometry - A local vector with cell geometry

    1361:   Output Parameters:
    1362: + fgeom - The extract the face centroid and normal
    1363: - vol   - The cell volume

    1365:   Level: developer

    1367: .seealso: DMPlexGetFaceFields()
    1368: @*/
    1369: PetscErrorCode DMPlexRestoreFaceGeometry(DM dm, PetscInt fStart, PetscInt fEnd, Vec faceGeometry, Vec cellGeometry, PetscFVFaceGeom **fgeom, PetscReal **vol)
    1370: {

    1374:   PetscFree(*fgeom);
    1375:   DMRestoreWorkArray(dm, 0, PETSC_REAL, vol);
    1376:   return(0);
    1377: }

    1381: static PetscErrorCode DMPlexApplyLimiter_Internal (DM dm, DM dmCell, PetscLimiter lim, PetscInt dim, PetscInt totDim, PetscInt cell, PetscInt face, PetscInt fStart, PetscInt fEnd, PetscReal *cellPhi, const PetscScalar *x,
    1382:                                                    const PetscScalar *cellgeom, const PetscFVCellGeom *cg, const PetscScalar *cx, const PetscScalar *cgrad)
    1383: {
    1384:   const PetscInt        *children;
    1385:   PetscInt               numChildren;
    1386:   PetscErrorCode         ierr;

    1389:   DMPlexGetTreeChildren(dm,face,&numChildren,&children);
    1390:   if (numChildren) {
    1391:     PetscInt c;

    1393:     for (c = 0; c < numChildren; c++) {
    1394:       PetscInt childFace = children[c];

    1396:       if (childFace >= fStart && childFace < fEnd) {
    1397:         DMPlexApplyLimiter_Internal(dm,dmCell,lim,dim,totDim,cell,childFace,fStart,fEnd,cellPhi,x,cellgeom,cg,cx,cgrad);
    1398:       }
    1399:     }
    1400:   }
    1401:   else {
    1402:     PetscScalar           *ncx;
    1403:     PetscFVCellGeom       *ncg;
    1404:     const PetscInt        *fcells;
    1405:     PetscInt               ncell, d;
    1406:     PetscReal              v[3];

    1408:     DMPlexGetSupport(dm, face, &fcells);
    1409:     ncell = cell == fcells[0] ? fcells[1] : fcells[0];
    1410:     DMPlexPointLocalRead(dm, ncell, x, &ncx);
    1411:     DMPlexPointLocalRead(dmCell, ncell, cellgeom, &ncg);
    1412:     DMPlex_WaxpyD_Internal(dim, -1, cg->centroid, ncg->centroid, v);
    1413:     for (d = 0; d < totDim; ++d) {
    1414:       /* We use the symmetric slope limited form of Berger, Aftosmis, and Murman 2005 */
    1415:       PetscReal phi, flim = 0.5 * PetscRealPart(ncx[d] - cx[d]) / DMPlex_DotD_Internal(dim, &cgrad[d*dim], v);

    1417:       PetscLimiterLimit(lim, flim, &phi);
    1418:       cellPhi[d] = PetscMin(cellPhi[d], phi);
    1419:     }
    1420:   }
    1421:   return(0);
    1422: }

    1426: PetscErrorCode DMPlexReconstructGradients_Internal(DM dm, PetscInt fStart, PetscInt fEnd, Vec faceGeometry, Vec cellGeometry, Vec locX, Vec grad)
    1427: {
    1428:   DM                 dmFace, dmCell, dmGrad;
    1429:   DMLabel            ghostLabel;
    1430:   PetscDS            prob;
    1431:   PetscFV            fvm;
    1432:   PetscLimiter       lim;
    1433:   const PetscScalar *facegeom, *cellgeom, *x;
    1434:   PetscScalar       *gr;
    1435:   PetscReal         *cellPhi;
    1436:   PetscInt           dim, face, cell, totDim, cStart, cEnd, cEndInterior;
    1437:   PetscErrorCode     ierr;

    1440:   DMGetDimension(dm, &dim);
    1441:   DMGetDS(dm, &prob);
    1442:   PetscDSGetTotalDimension(prob, &totDim);
    1443:   DMGetLabel(dm, "ghost", &ghostLabel);
    1444:   PetscDSGetDiscretization(prob, 0, (PetscObject *) &fvm);
    1445:   PetscFVGetLimiter(fvm, &lim);
    1446:   VecGetDM(faceGeometry, &dmFace);
    1447:   VecGetArrayRead(faceGeometry, &facegeom);
    1448:   VecGetDM(cellGeometry, &dmCell);
    1449:   VecGetArrayRead(cellGeometry, &cellgeom);
    1450:   VecGetArrayRead(locX, &x);
    1451:   VecGetDM(grad, &dmGrad);
    1452:   VecZeroEntries(grad);
    1453:   VecGetArray(grad, &gr);
    1454:   /* Reconstruct gradients */
    1455:   for (face = fStart; face < fEnd; ++face) {
    1456:     const PetscInt        *cells;
    1457:     PetscFVFaceGeom       *fg;
    1458:     PetscScalar           *cx[2];
    1459:     PetscScalar           *cgrad[2];
    1460:     PetscBool              boundary;
    1461:     PetscInt               ghost, c, pd, d, numChildren, numCells;

    1463:     DMLabelGetValue(ghostLabel, face, &ghost);
    1464:     DMIsBoundaryPoint(dm, face, &boundary);
    1465:     DMPlexGetTreeChildren(dm, face, &numChildren, NULL);
    1466:     if (ghost >= 0 || boundary || numChildren) continue;
    1467:     DMPlexGetSupportSize(dm, face, &numCells);
    1468:     if (numCells != 2) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "facet %d has %d support points: expected 2",face,numCells);
    1469:     DMPlexGetSupport(dm, face, &cells);
    1470:     DMPlexPointLocalRead(dmFace, face, facegeom, &fg);
    1471:     for (c = 0; c < 2; ++c) {
    1472:       DMPlexPointLocalRead(dm, cells[c], x, &cx[c]);
    1473:       DMPlexPointGlobalRef(dmGrad, cells[c], gr, &cgrad[c]);
    1474:     }
    1475:     for (pd = 0; pd < totDim; ++pd) {
    1476:       PetscScalar delta = cx[1][pd] - cx[0][pd];

    1478:       for (d = 0; d < dim; ++d) {
    1479:         if (cgrad[0]) cgrad[0][pd*dim+d] += fg->grad[0][d] * delta;
    1480:         if (cgrad[1]) cgrad[1][pd*dim+d] -= fg->grad[1][d] * delta;
    1481:       }
    1482:     }
    1483:   }
    1484:   /* Limit interior gradients (using cell-based loop because it generalizes better to vector limiters) */
    1485:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
    1486:   DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);
    1487:   cEndInterior = cEndInterior < 0 ? cEnd : cEndInterior;
    1488:   DMGetWorkArray(dm, totDim, PETSC_REAL, &cellPhi);
    1489:   for (cell = dmGrad && lim ? cStart : cEnd; cell < cEndInterior; ++cell) {
    1490:     const PetscInt        *faces;
    1491:     PetscScalar           *cx;
    1492:     PetscFVCellGeom       *cg;
    1493:     PetscScalar           *cgrad;
    1494:     PetscInt               coneSize, f, pd, d;

    1496:     DMPlexGetConeSize(dm, cell, &coneSize);
    1497:     DMPlexGetCone(dm, cell, &faces);
    1498:     DMPlexPointLocalRead(dm, cell, x, &cx);
    1499:     DMPlexPointLocalRead(dmCell, cell, cellgeom, &cg);
    1500:     DMPlexPointGlobalRef(dmGrad, cell, gr, &cgrad);
    1501:     if (!cgrad) continue; /* Unowned overlap cell, we do not compute */
    1502:     /* Limiter will be minimum value over all neighbors */
    1503:     for (d = 0; d < totDim; ++d) cellPhi[d] = PETSC_MAX_REAL;
    1504:     for (f = 0; f < coneSize; ++f) {
    1505:       DMPlexApplyLimiter_Internal(dm,dmCell,lim,dim,totDim,cell,faces[f],fStart,fEnd,cellPhi,x,cellgeom,cg,cx,cgrad);
    1506:     }
    1507:     /* Apply limiter to gradient */
    1508:     for (pd = 0; pd < totDim; ++pd)
    1509:       /* Scalar limiter applied to each component separately */
    1510:       for (d = 0; d < dim; ++d) cgrad[pd*dim+d] *= cellPhi[pd];
    1511:   }
    1512:   DMRestoreWorkArray(dm, totDim, PETSC_REAL, &cellPhi);
    1513:   VecRestoreArrayRead(faceGeometry, &facegeom);
    1514:   VecRestoreArrayRead(cellGeometry, &cellgeom);
    1515:   VecRestoreArrayRead(locX, &x);
    1516:   VecRestoreArray(grad, &gr);
    1517:   return(0);
    1518: }

    1522: PetscErrorCode DMPlexComputeBdResidual_Internal(DM dm, Vec locX, Vec locX_t, Vec locF, void *user)
    1523: {
    1524:   DM_Plex         *mesh = (DM_Plex *) dm->data;
    1525:   PetscSection     section;
    1526:   PetscDS          prob;
    1527:   DMLabel          depth;
    1528:   PetscFECellGeom *cgeom;
    1529:   PetscScalar     *u = NULL, *u_t = NULL, *elemVec = NULL;
    1530:   PetscInt         dim, Nf, f, totDimBd, numBd, bd;
    1531:   PetscErrorCode   ierr;

    1534:   DMGetDimension(dm, &dim);
    1535:   DMGetDefaultSection(dm, &section);
    1536:   DMGetDS(dm, &prob);
    1537:   PetscDSGetNumFields(prob, &Nf);
    1538:   PetscDSGetTotalBdDimension(prob, &totDimBd);
    1539:   DMPlexGetDepthLabel(dm, &depth);
    1540:   DMGetNumBoundary(dm, &numBd);
    1541:   for (bd = 0; bd < numBd; ++bd) {
    1542:     const char     *bdLabel;
    1543:     DMLabel         label;
    1544:     IS              pointIS;
    1545:     const PetscInt *points;
    1546:     const PetscInt *values;
    1547:     PetscInt        field, numValues, v, numPoints, p, dep, numFaces;
    1548:     PetscBool       isEssential;
    1549:     PetscObject     obj;
    1550:     PetscClassId    id;

    1552:     DMGetBoundary(dm, bd, &isEssential, NULL, &bdLabel, &field, NULL, NULL, NULL, &numValues, &values, NULL);
    1553:     DMGetField(dm, field, &obj);
    1554:     PetscObjectGetClassId(obj, &id);
    1555:     if ((id != PETSCFE_CLASSID) || isEssential) continue;
    1556:     DMGetLabel(dm, bdLabel, &label);
    1557:     for (v = 0; v < numValues; ++v) {
    1558:       DMLabelGetStratumSize(label, values[v], &numPoints);
    1559:       DMLabelGetStratumIS(label, values[v], &pointIS);
    1560:       if (!pointIS) continue; /* No points with that id on this process */
    1561:       ISGetIndices(pointIS, &points);
    1562:       for (p = 0, numFaces = 0; p < numPoints; ++p) {
    1563:         DMLabelGetValue(depth, points[p], &dep);
    1564:         if (dep == dim-1) ++numFaces;
    1565:       }
    1566:       PetscMalloc3(numFaces*totDimBd,&u,numFaces,&cgeom,numFaces*totDimBd,&elemVec);
    1567:       if (locX_t) {PetscMalloc1(numFaces*totDimBd,&u_t);}
    1568:       for (p = 0, f = 0; p < numPoints; ++p) {
    1569:         const PetscInt point = points[p];
    1570:         PetscScalar   *x     = NULL;
    1571:         PetscInt       i;

    1573:         DMLabelGetValue(depth, points[p], &dep);
    1574:         if (dep != dim-1) continue;
    1575:         DMPlexComputeCellGeometryFEM(dm, point, NULL, cgeom[f].v0, cgeom[f].J, cgeom[f].invJ, &cgeom[f].detJ);
    1576:         DMPlexComputeCellGeometryFVM(dm, point, NULL, NULL, cgeom[f].n);
    1577:         if (cgeom[f].detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", cgeom[f].detJ, point);
    1578:         /* TODO: Matt, this is wrong if feBd does not match fe: i.e., if the order differs. */
    1579:         DMPlexVecGetClosure(dm, section, locX, point, NULL, &x);
    1580:         for (i = 0; i < totDimBd; ++i) u[f*totDimBd+i] = x[i];
    1581:         DMPlexVecRestoreClosure(dm, section, locX, point, NULL, &x);
    1582:         if (locX_t) {
    1583:           DMPlexVecGetClosure(dm, section, locX_t, point, NULL, &x);
    1584:           for (i = 0; i < totDimBd; ++i) u_t[f*totDimBd+i] = x[i];
    1585:           DMPlexVecRestoreClosure(dm, section, locX_t, point, NULL, &x);
    1586:         }
    1587:         ++f;
    1588:       }
    1589:       for (f = 0; f < Nf; ++f) {
    1590:         PetscFE         fe;
    1591:         PetscQuadrature q;
    1592:         PetscInt        numQuadPoints, Nb;
    1593:         /* Conforming batches */
    1594:         PetscInt        numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
    1595:         /* Remainder */
    1596:         PetscInt        Nr, offset;

    1598:         PetscDSGetBdDiscretization(prob, f, (PetscObject *) &fe);
    1599:         PetscFEGetQuadrature(fe, &q);
    1600:         PetscFEGetDimension(fe, &Nb);
    1601:         PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);
    1602:         PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);
    1603:         blockSize = Nb*numQuadPoints;
    1604:         batchSize = numBlocks * blockSize;
    1605:          PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);
    1606:         numChunks = numFaces / (numBatches*batchSize);
    1607:         Ne        = numChunks*numBatches*batchSize;
    1608:         Nr        = numFaces % (numBatches*batchSize);
    1609:         offset    = numFaces - Nr;
    1610:         PetscFEIntegrateBdResidual(fe, prob, f, Ne, cgeom, u, u_t, NULL, NULL, elemVec);
    1611:         PetscFEIntegrateBdResidual(fe, prob, f, Nr, &cgeom[offset], &u[offset*totDimBd], u_t ? &u_t[offset*totDimBd] : NULL, NULL, NULL, &elemVec[offset*totDimBd]);
    1612:       }
    1613:       for (p = 0, f = 0; p < numPoints; ++p) {
    1614:         const PetscInt point = points[p];

    1616:         DMLabelGetValue(depth, point, &dep);
    1617:         if (dep != dim-1) continue;
    1618:         if (mesh->printFEM > 1) {DMPrintCellVector(point, "BdResidual", totDimBd, &elemVec[f*totDimBd]);}
    1619:         DMPlexVecSetClosure(dm, NULL, locF, point, &elemVec[f*totDimBd], ADD_ALL_VALUES);
    1620:         ++f;
    1621:       }
    1622:       ISRestoreIndices(pointIS, &points);
    1623:       ISDestroy(&pointIS);
    1624:       PetscFree3(u,cgeom,elemVec);
    1625:       if (locX_t) {PetscFree(u_t);}
    1626:     }
    1627:   }
    1628:   return(0);
    1629: }

    1633: /*@
    1634:   DMPlexReconstructGradientsFVM - reconstruct the gradient of a vector using a finite volume method.

    1636:   Input Parameters:
    1637: + dm - the mesh
    1638: - locX - the local representation of the vector

    1640:   Output Parameter:
    1641: . grad - the global representation of the gradient

    1643:   Level: developer

    1645: .seealso: DMPlexSNESGetGradientDM()
    1646: @*/
    1647: PetscErrorCode DMPlexReconstructGradientsFVM(DM dm, Vec locX, Vec grad)
    1648: {
    1649:   PetscDS          prob;
    1650:   PetscInt         Nf, f, fStart, fEnd;
    1651:   PetscBool        useFVM = PETSC_FALSE;
    1652:   PetscFV          fvm = NULL;
    1653:   Vec              faceGeometryFVM, cellGeometryFVM;
    1654:   PetscFVCellGeom  *cgeomFVM   = NULL;
    1655:   PetscFVFaceGeom  *fgeomFVM   = NULL;
    1656:   DM               dmGrad = NULL;
    1657:   PetscErrorCode   ierr;

    1660:   DMGetDS(dm, &prob);
    1661:   PetscDSGetNumFields(prob, &Nf);
    1662:   for (f = 0; f < Nf; ++f) {
    1663:     PetscObject  obj;
    1664:     PetscClassId id;

    1666:     PetscDSGetDiscretization(prob, f, &obj);
    1667:     PetscObjectGetClassId(obj, &id);
    1668:     if (id == PETSCFV_CLASSID) {useFVM = PETSC_TRUE; fvm = (PetscFV) obj;}
    1669:   }
    1670:   if (!useFVM) SETERRQ(PetscObjectComm((PetscObject)dm),PETSC_ERR_SUP,"This dm does not have a finite volume discretization");
    1671:   DMPlexSNESGetGradientDM(dm, fvm, &dmGrad);
    1672:   if (!dmGrad) SETERRQ(PetscObjectComm((PetscObject)dm),PETSC_ERR_SUP,"This dm's finite volume discretization does not reconstruct gradients");
    1673:   DMPlexSNESGetGeometryFVM(dm, &faceGeometryFVM, &cellGeometryFVM, NULL);
    1674:   VecGetArrayRead(faceGeometryFVM, (const PetscScalar **) &fgeomFVM);
    1675:   VecGetArrayRead(cellGeometryFVM, (const PetscScalar **) &cgeomFVM);
    1676:   DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);
    1677:   DMPlexReconstructGradients_Internal(dm, fStart, fEnd, faceGeometryFVM, cellGeometryFVM, locX, grad);
    1678:   return(0);
    1679: }

    1683: PetscErrorCode DMPlexComputeResidual_Internal(DM dm, PetscInt cStart, PetscInt cEnd, PetscReal time, Vec locX, Vec locX_t, Vec locF, void *user)
    1684: {
    1685:   DM_Plex          *mesh       = (DM_Plex *) dm->data;
    1686:   const char       *name       = "Residual";
    1687:   DM                dmAux      = NULL;
    1688:   DM                dmGrad     = NULL;
    1689:   DMLabel           ghostLabel = NULL;
    1690:   PetscDS           prob       = NULL;
    1691:   PetscDS           probAux    = NULL;
    1692:   PetscSection      section    = NULL;
    1693:   PetscBool         useFEM     = PETSC_FALSE;
    1694:   PetscBool         useFVM     = PETSC_FALSE;
    1695:   PetscBool         isImplicit = (locX_t || time == PETSC_MIN_REAL) ? PETSC_TRUE : PETSC_FALSE;
    1696:   PetscFV           fvm        = NULL;
    1697:   PetscFECellGeom  *cgeomFEM   = NULL;
    1698:   PetscScalar      *cgeomScal;
    1699:   PetscFVCellGeom  *cgeomFVM   = NULL;
    1700:   PetscFVFaceGeom  *fgeomFVM   = NULL;
    1701:   Vec               locA, cellGeometryFEM = NULL, cellGeometryFVM = NULL, faceGeometryFVM = NULL, grad, locGrad = NULL;
    1702:   PetscScalar      *u, *u_t, *a, *uL, *uR;
    1703:   PetscInt          Nf, f, totDim, totDimAux, numChunks, cellChunkSize, faceChunkSize, chunk, fStart, fEnd;
    1704:   PetscErrorCode    ierr;

    1707:   PetscLogEventBegin(DMPLEX_ResidualFEM,dm,0,0,0);
    1708:   /* TODO The places where we have to use isFE are probably the member functions for the PetscDisc class */
    1709:   /* TODO The FVM geometry is over-manipulated. Make the precalc functions return exactly what we need */
    1710:   /* FEM+FVM */
    1711:   /* 1: Get sizes from dm and dmAux */
    1712:   DMGetDefaultSection(dm, &section);
    1713:   DMGetLabel(dm, "ghost", &ghostLabel);
    1714:   DMGetDS(dm, &prob);
    1715:   PetscDSGetNumFields(prob, &Nf);
    1716:   PetscDSGetTotalDimension(prob, &totDim);
    1717:   PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &locA);
    1718:   if (locA) {
    1719:     VecGetDM(locA, &dmAux);
    1720:     DMGetDS(dmAux, &probAux);
    1721:     PetscDSGetTotalDimension(probAux, &totDimAux);
    1722:   }
    1723:   /* 2: Get geometric data */
    1724:   for (f = 0; f < Nf; ++f) {
    1725:     PetscObject  obj;
    1726:     PetscClassId id;
    1727:     PetscBool    fimp;

    1729:     PetscDSGetImplicit(prob, f, &fimp);
    1730:     if (isImplicit != fimp) continue;
    1731:     PetscDSGetDiscretization(prob, f, &obj);
    1732:     PetscObjectGetClassId(obj, &id);
    1733:     if (id == PETSCFE_CLASSID) {useFEM = PETSC_TRUE;}
    1734:     if (id == PETSCFV_CLASSID) {useFVM = PETSC_TRUE; fvm = (PetscFV) obj;}
    1735:   }
    1736:   if (useFEM) {
    1737:     DMPlexSNESGetGeometryFEM(dm, &cellGeometryFEM);
    1738:     VecGetArray(cellGeometryFEM, &cgeomScal);
    1739:     if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
    1740:       DM dmCell;
    1741:       PetscInt c;

    1743:       VecGetDM(cellGeometryFEM,&dmCell);
    1744:       PetscMalloc1(cEnd-cStart,&cgeomFEM);
    1745:       for (c = 0; c < cEnd - cStart; c++) {
    1746:         PetscScalar *thisgeom;

    1748:         DMPlexPointLocalRef(dmCell, c + cStart, cgeomScal, &thisgeom);
    1749:         cgeomFEM[c] = *((PetscFECellGeom *) thisgeom);
    1750:       }
    1751:     }
    1752:     else {
    1753:       cgeomFEM = (PetscFECellGeom *) cgeomScal;
    1754:     }
    1755:   }
    1756:   if (useFVM) {
    1757:     DMPlexSNESGetGeometryFVM(dm, &faceGeometryFVM, &cellGeometryFVM, NULL);
    1758:     VecGetArrayRead(faceGeometryFVM, (const PetscScalar **) &fgeomFVM);
    1759:     VecGetArrayRead(cellGeometryFVM, (const PetscScalar **) &cgeomFVM);
    1760:     /* Reconstruct and limit cell gradients */
    1761:     DMPlexSNESGetGradientDM(dm, fvm, &dmGrad);
    1762:     if (dmGrad) {
    1763:       DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);
    1764:       DMGetGlobalVector(dmGrad, &grad);
    1765:       DMPlexReconstructGradients_Internal(dm, fStart, fEnd, faceGeometryFVM, cellGeometryFVM, locX, grad);
    1766:       /* Communicate gradient values */
    1767:       DMGetLocalVector(dmGrad, &locGrad);
    1768:       DMGlobalToLocalBegin(dmGrad, grad, INSERT_VALUES, locGrad);
    1769:       DMGlobalToLocalEnd(dmGrad, grad, INSERT_VALUES, locGrad);
    1770:       DMRestoreGlobalVector(dmGrad, &grad);
    1771:     }
    1772:     /* Handle non-essential (e.g. outflow) boundary values */
    1773:     DMPlexInsertBoundaryValues(dm, PETSC_FALSE, locX, time, faceGeometryFVM, cellGeometryFVM, locGrad);
    1774:   }
    1775:   /* Loop over chunks */
    1776:   DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);
    1777:   numChunks     = 1;
    1778:   cellChunkSize = (cEnd - cStart)/numChunks;
    1779:   faceChunkSize = (fEnd - fStart)/numChunks;
    1780:   for (chunk = 0; chunk < numChunks; ++chunk) {
    1781:     PetscScalar     *elemVec, *fluxL, *fluxR;
    1782:     PetscReal       *vol;
    1783:     PetscFVFaceGeom *fgeom;
    1784:     PetscInt         cS = cStart+chunk*cellChunkSize, cE = PetscMin(cS+cellChunkSize, cEnd), numCells = cE - cS, cell;
    1785:     PetscInt         fS = fStart+chunk*faceChunkSize, fE = PetscMin(fS+faceChunkSize, fEnd), numFaces = fE - fS, face;

    1787:     /* Extract field coefficients */
    1788:     if (useFEM) {
    1789:       DMPlexGetCellFields(dm, cS, cE, locX, locX_t, locA, &u, &u_t, &a);
    1790:       DMGetWorkArray(dm, numCells*totDim, PETSC_SCALAR, &elemVec);
    1791:       PetscMemzero(elemVec, numCells*totDim * sizeof(PetscScalar));
    1792:     }
    1793:     if (useFVM) {
    1794:       DMPlexGetFaceFields(dm, fS, fE, locX, locX_t, faceGeometryFVM, cellGeometryFVM, locGrad, &uL, &uR);
    1795:       DMPlexGetFaceGeometry(dm, fS, fE, faceGeometryFVM, cellGeometryFVM, &fgeom, &vol);
    1796:       DMGetWorkArray(dm, numFaces*totDim, PETSC_SCALAR, &fluxL);
    1797:       DMGetWorkArray(dm, numFaces*totDim, PETSC_SCALAR, &fluxR);
    1798:       PetscMemzero(fluxL, numFaces*totDim * sizeof(PetscScalar));
    1799:       PetscMemzero(fluxR, numFaces*totDim * sizeof(PetscScalar));
    1800:     }
    1801:     /* TODO We will interlace both our field coefficients (u, u_t, uL, uR, etc.) and our output (elemVec, fL, fR). I think this works */
    1802:     /* Loop over fields */
    1803:     for (f = 0; f < Nf; ++f) {
    1804:       PetscObject  obj;
    1805:       PetscClassId id;
    1806:       PetscBool    fimp;
    1807:       PetscInt     numChunks, numBatches, batchSize, numBlocks, blockSize, Ne, Nr, offset;

    1809:       PetscDSGetImplicit(prob, f, &fimp);
    1810:       if (isImplicit != fimp) continue;
    1811:       PetscDSGetDiscretization(prob, f, &obj);
    1812:       PetscObjectGetClassId(obj, &id);
    1813:       if (id == PETSCFE_CLASSID) {
    1814:         PetscFE         fe = (PetscFE) obj;
    1815:         PetscQuadrature q;
    1816:         PetscInt        Nq, Nb;

    1818:         PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);

    1820:         PetscFEGetQuadrature(fe, &q);
    1821:         PetscQuadratureGetData(q, NULL, &Nq, NULL, NULL);
    1822:         PetscFEGetDimension(fe, &Nb);
    1823:         blockSize = Nb*Nq;
    1824:         batchSize = numBlocks * blockSize;
    1825:          PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);
    1826:         numChunks = numCells / (numBatches*batchSize);
    1827:         Ne        = numChunks*numBatches*batchSize;
    1828:         Nr        = numCells % (numBatches*batchSize);
    1829:         offset    = numCells - Nr;
    1830:         /* Integrate FE residual to get elemVec (need fields at quadrature points) */
    1831:         /*   For FV, I think we use a P0 basis and the cell coefficients (for subdivided cells, we can tweak the basis tabulation to be the indicator function) */
    1832:         PetscFEIntegrateResidual(fe, prob, f, Ne, cgeomFEM, u, u_t, probAux, a, elemVec);
    1833:         PetscFEIntegrateResidual(fe, prob, f, Nr, &cgeomFEM[offset], &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], &elemVec[offset*totDim]);
    1834:       } else if (id == PETSCFV_CLASSID) {
    1835:         PetscFV fv = (PetscFV) obj;

    1837:         Ne = numFaces;
    1838:         /* Riemann solve over faces (need fields at face centroids) */
    1839:         /*   We need to evaluate FE fields at those coordinates */
    1840:         PetscFVIntegrateRHSFunction(fv, prob, f, Ne, fgeom, vol, uL, uR, fluxL, fluxR);
    1841:       } else SETERRQ1(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", f);
    1842:     }
    1843:     if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
    1844:       PetscFree(cgeomFEM);
    1845:     }
    1846:     else {
    1847:       cgeomFEM = NULL;
    1848:     }
    1849:     if (cellGeometryFEM) {VecRestoreArray(cellGeometryFEM, &cgeomScal);}
    1850:     /* Loop over domain */
    1851:     if (useFEM) {
    1852:       /* Add elemVec to locX */
    1853:       for (cell = cS; cell < cE; ++cell) {
    1854:         if (mesh->printFEM > 1) {DMPrintCellVector(cell, name, totDim, &elemVec[cell*totDim]);}
    1855:         DMPlexVecSetClosure(dm, section, locF, cell, &elemVec[cell*totDim], ADD_ALL_VALUES);
    1856:       }
    1857:     }
    1858:     if (useFVM) {
    1859:       PetscScalar *fa;
    1860:       PetscInt     iface;

    1862:       VecGetArray(locF, &fa);
    1863:       for (f = 0; f < Nf; ++f) {
    1864:         PetscFV      fv;
    1865:         PetscObject  obj;
    1866:         PetscClassId id;
    1867:         PetscInt     foff, pdim;

    1869:         PetscDSGetDiscretization(prob, f, &obj);
    1870:         PetscDSGetFieldOffset(prob, f, &foff);
    1871:         PetscObjectGetClassId(obj, &id);
    1872:         if (id != PETSCFV_CLASSID) continue;
    1873:         fv   = (PetscFV) obj;
    1874:         PetscFVGetNumComponents(fv, &pdim);
    1875:         /* Accumulate fluxes to cells */
    1876:         for (face = fS, iface = 0; face < fE; ++face) {
    1877:           const PetscInt *cells;
    1878:           PetscScalar    *fL, *fR;
    1879:           PetscInt        ghost, d, nsupp;

    1881:           DMLabelGetValue(ghostLabel, face, &ghost);
    1882:           DMPlexGetSupportSize(dm, face, &nsupp);
    1883:           if (ghost >= 0) continue;
    1884:           if (nsupp > 2) { /* noop */
    1885:             ++iface;
    1886:             continue;
    1887:           }
    1888:           DMPlexGetSupport(dm, face, &cells);
    1889:           DMPlexPointGlobalFieldRef(dm, cells[0], f, fa, &fL);
    1890:           DMPlexPointGlobalFieldRef(dm, cells[1], f, fa, &fR);
    1891:           for (d = 0; d < pdim; ++d) {
    1892:             if (fL) fL[d] -= fluxL[iface*totDim+foff+d];
    1893:             if (fR) fR[d] += fluxR[iface*totDim+foff+d];
    1894:           }
    1895:           ++iface;
    1896:         }
    1897:       }
    1898:       VecRestoreArray(locF, &fa);
    1899:     }
    1900:     /* Handle time derivative */
    1901:     if (locX_t) {
    1902:       PetscScalar *x_t, *fa;

    1904:       VecGetArray(locF, &fa);
    1905:       VecGetArray(locX_t, &x_t);
    1906:       for (f = 0; f < Nf; ++f) {
    1907:         PetscFV      fv;
    1908:         PetscObject  obj;
    1909:         PetscClassId id;
    1910:         PetscInt     pdim, d;

    1912:         PetscDSGetDiscretization(prob, f, &obj);
    1913:         PetscObjectGetClassId(obj, &id);
    1914:         if (id != PETSCFV_CLASSID) continue;
    1915:         fv   = (PetscFV) obj;
    1916:         PetscFVGetNumComponents(fv, &pdim);
    1917:         for (cell = cS; cell < cE; ++cell) {
    1918:           PetscScalar *u_t, *r;

    1920:           DMPlexPointLocalFieldRead(dm, cell, f, x_t, &u_t);
    1921:           DMPlexPointLocalFieldRef(dm, cell, f, fa, &r);
    1922:           for (d = 0; d < pdim; ++d) r[d] += u_t[d];
    1923:         }
    1924:       }
    1925:       VecRestoreArray(locX_t, &x_t);
    1926:       VecRestoreArray(locF, &fa);
    1927:     }
    1928:     if (useFEM) {
    1929:       DMPlexRestoreCellFields(dm, cS, cE, locX, locX_t, locA, &u, &u_t, &a);
    1930:       DMRestoreWorkArray(dm, numCells*totDim, PETSC_SCALAR, &elemVec);
    1931:     }
    1932:     if (useFVM) {
    1933:       DMPlexRestoreFaceFields(dm, fS, fE, locX, locX_t, faceGeometryFVM, cellGeometryFVM, locGrad, &uL, &uR);
    1934:       DMPlexRestoreFaceGeometry(dm, fS, fE, faceGeometryFVM, cellGeometryFVM, &fgeom, &vol);
    1935:       DMRestoreWorkArray(dm, numFaces*totDim, PETSC_SCALAR, &fluxL);
    1936:       DMRestoreWorkArray(dm, numFaces*totDim, PETSC_SCALAR, &fluxR);
    1937:       if (dmGrad) {DMRestoreLocalVector(dmGrad, &locGrad);}
    1938:     }
    1939:   }

    1941:   if (useFEM) {DMPlexComputeBdResidual_Internal(dm, locX, locX_t, locF, user);}

    1943:   /* FEM */
    1944:   /* 1: Get sizes from dm and dmAux */
    1945:   /* 2: Get geometric data */
    1946:   /* 3: Handle boundary values */
    1947:   /* 4: Loop over domain */
    1948:   /*   Extract coefficients */
    1949:   /* Loop over fields */
    1950:   /*   Set tiling for FE*/
    1951:   /*   Integrate FE residual to get elemVec */
    1952:   /*     Loop over subdomain */
    1953:   /*       Loop over quad points */
    1954:   /*         Transform coords to real space */
    1955:   /*         Evaluate field and aux fields at point */
    1956:   /*         Evaluate residual at point */
    1957:   /*         Transform residual to real space */
    1958:   /*       Add residual to elemVec */
    1959:   /* Loop over domain */
    1960:   /*   Add elemVec to locX */

    1962:   /* FVM */
    1963:   /* Get geometric data */
    1964:   /* If using gradients */
    1965:   /*   Compute gradient data */
    1966:   /*   Loop over domain faces */
    1967:   /*     Count computational faces */
    1968:   /*     Reconstruct cell gradient */
    1969:   /*   Loop over domain cells */
    1970:   /*     Limit cell gradients */
    1971:   /* Handle boundary values */
    1972:   /* Loop over domain faces */
    1973:   /*   Read out field, centroid, normal, volume for each side of face */
    1974:   /* Riemann solve over faces */
    1975:   /* Loop over domain faces */
    1976:   /*   Accumulate fluxes to cells */
    1977:   /* TODO Change printFEM to printDisc here */
    1978:   if (mesh->printFEM) {
    1979:     Vec         locFbc;
    1980:     PetscInt    pStart, pEnd, p, maxDof;
    1981:     PetscScalar *zeroes;

    1983:     VecDuplicate(locF,&locFbc);
    1984:     VecCopy(locF,locFbc);
    1985:     PetscSectionGetChart(section,&pStart,&pEnd);
    1986:     PetscSectionGetMaxDof(section,&maxDof);
    1987:     PetscCalloc1(maxDof,&zeroes);
    1988:     for (p = pStart; p < pEnd; p++) {
    1989:       VecSetValuesSection(locFbc,section,p,zeroes,INSERT_BC_VALUES);
    1990:     }
    1991:     PetscFree(zeroes);
    1992:     DMPrintLocalVec(dm, name, mesh->printTol, locFbc);
    1993:     VecDestroy(&locFbc);
    1994:   }
    1995:   PetscLogEventEnd(DMPLEX_ResidualFEM,dm,0,0,0);
    1996:   return(0);
    1997: }

    2001: static PetscErrorCode DMPlexComputeResidualFEM_Check_Internal(DM dm, Vec X, Vec X_t, Vec F, void *user)
    2002: {
    2003:   DM                dmCh, dmAux;
    2004:   Vec               A, cellgeom;
    2005:   PetscDS           prob, probCh, probAux = NULL;
    2006:   PetscQuadrature   q;
    2007:   PetscSection      section, sectionAux;
    2008:   PetscFECellGeom  *cgeom = NULL;
    2009:   PetscScalar      *cgeomScal;
    2010:   PetscScalar      *elemVec, *elemVecCh, *u, *u_t, *a = NULL;
    2011:   PetscInt          dim, Nf, f, numCells, cStart, cEnd, c;
    2012:   PetscInt          totDim, totDimAux, diffCell = 0;
    2013:   PetscErrorCode    ierr;

    2016:   DMGetDimension(dm, &dim);
    2017:   DMGetDefaultSection(dm, &section);
    2018:   DMGetDS(dm, &prob);
    2019:   PetscDSGetTotalDimension(prob, &totDim);
    2020:   PetscSectionGetNumFields(section, &Nf);
    2021:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
    2022:   numCells = cEnd - cStart;
    2023:   PetscObjectQuery((PetscObject) dm, "dmCh", (PetscObject *) &dmCh);
    2024:   DMGetDS(dmCh, &probCh);
    2025:   PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);
    2026:   PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);
    2027:   if (dmAux) {
    2028:     DMGetDefaultSection(dmAux, &sectionAux);
    2029:     DMGetDS(dmAux, &probAux);
    2030:     PetscDSGetTotalDimension(probAux, &totDimAux);
    2031:   }
    2032:   VecSet(F, 0.0);
    2033:   PetscMalloc3(numCells*totDim,&u,X_t ? numCells*totDim : 0,&u_t,numCells*totDim,&elemVec);
    2034:   PetscMalloc1(numCells*totDim,&elemVecCh);
    2035:   if (dmAux) {PetscMalloc1(numCells*totDimAux, &a);}
    2036:   DMPlexSNESGetGeometryFEM(dm, &cellgeom);
    2037:   VecGetArray(cellgeom, &cgeomScal);
    2038:   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
    2039:     DM dmCell;

    2041:     VecGetDM(cellgeom,&dmCell);
    2042:     PetscMalloc1(cEnd-cStart,&cgeom);
    2043:     for (c = 0; c < cEnd - cStart; c++) {
    2044:       PetscScalar *thisgeom;

    2046:       DMPlexPointLocalRef(dmCell, c + cStart, cgeomScal, &thisgeom);
    2047:       cgeom[c] = *((PetscFECellGeom *) thisgeom);
    2048:     }
    2049:   }
    2050:   else {
    2051:     cgeom = (PetscFECellGeom *) cgeomScal;
    2052:   }
    2053:   for (c = cStart; c < cEnd; ++c) {
    2054:     PetscScalar *x = NULL, *x_t = NULL;
    2055:     PetscInt     i;

    2057:     DMPlexVecGetClosure(dm, section, X, c, NULL, &x);
    2058:     for (i = 0; i < totDim; ++i) u[c*totDim+i] = x[i];
    2059:     DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);
    2060:     if (X_t) {
    2061:       DMPlexVecGetClosure(dm, section, X_t, c, NULL, &x_t);
    2062:       for (i = 0; i < totDim; ++i) u_t[c*totDim+i] = x_t[i];
    2063:       DMPlexVecRestoreClosure(dm, section, X_t, c, NULL, &x_t);
    2064:     }
    2065:     if (dmAux) {
    2066:       DM dmAuxPlex;

    2068:       DMSNESConvertPlex(dmAux,&dmAuxPlex, PETSC_FALSE);
    2069:       DMPlexVecGetClosure(dmAuxPlex, sectionAux, A, c, NULL, &x);
    2070:       for (i = 0; i < totDimAux; ++i) a[c*totDimAux+i] = x[i];
    2071:       DMPlexVecRestoreClosure(dmAuxPlex, sectionAux, A, c, NULL, &x);
    2072:       DMDestroy(&dmAuxPlex);
    2073:     }
    2074:   }
    2075:   for (f = 0; f < Nf; ++f) {
    2076:     PetscFE  fe, feCh;
    2077:     PetscInt numQuadPoints, Nb;
    2078:     /* Conforming batches */
    2079:     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
    2080:     /* Remainder */
    2081:     PetscInt Nr, offset;

    2083:     PetscDSGetDiscretization(prob, f, (PetscObject *) &fe);
    2084:     PetscDSGetDiscretization(probCh, f, (PetscObject *) &feCh);
    2085:     PetscFEGetQuadrature(fe, &q);
    2086:     PetscFEGetDimension(fe, &Nb);
    2087:     PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);
    2088:     PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);
    2089:     blockSize = Nb*numQuadPoints;
    2090:     batchSize = numBlocks * blockSize;
    2091:      PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);
    2092:     numChunks = numCells / (numBatches*batchSize);
    2093:     Ne        = numChunks*numBatches*batchSize;
    2094:     Nr        = numCells % (numBatches*batchSize);
    2095:     offset    = numCells - Nr;
    2096:     PetscFEIntegrateResidual(fe, prob, f, Ne, cgeom, u, u_t, probAux, a, elemVec);
    2097:     PetscFEIntegrateResidual(feCh, prob, f, Ne, cgeom, u, u_t, probAux, a, elemVecCh);
    2098:     PetscFEIntegrateResidual(fe, prob, f, Nr, &cgeom[offset], &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], &elemVec[offset*totDim]);
    2099:     PetscFEIntegrateResidual(feCh, prob, f, Nr, &cgeom[offset], &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], &elemVecCh[offset*totDim]);
    2100:   }
    2101:   for (c = cStart; c < cEnd; ++c) {
    2102:     PetscBool diff = PETSC_FALSE;
    2103:     PetscInt  d;

    2105:     for (d = 0; d < totDim; ++d) if (PetscAbsScalar(elemVec[c*totDim+d] - elemVecCh[c*totDim+d]) > 1.0e-7) {diff = PETSC_TRUE;break;}
    2106:     if (diff) {
    2107:       PetscPrintf(PetscObjectComm((PetscObject) dm), "Different cell %d\n", c);
    2108:       DMPrintCellVector(c, "Residual", totDim, &elemVec[c*totDim]);
    2109:       DMPrintCellVector(c, "Check Residual", totDim, &elemVecCh[c*totDim]);
    2110:       ++diffCell;
    2111:     }
    2112:     if (diffCell > 9) break;
    2113:     DMPlexVecSetClosure(dm, section, F, c, &elemVec[c*totDim], ADD_ALL_VALUES);
    2114:   }
    2115:   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
    2116:     PetscFree(cgeom);
    2117:   }
    2118:   else {
    2119:     cgeom = NULL;
    2120:   }
    2121:   VecRestoreArray(cellgeom, &cgeomScal);
    2122:   PetscFree3(u,u_t,elemVec);
    2123:   PetscFree(elemVecCh);
    2124:   if (dmAux) {PetscFree(a);}
    2125:   return(0);
    2126: }

    2130: /*@
    2131:   DMPlexSNESComputeResidualFEM - Form the local residual F from the local input X using pointwise functions specified by the user

    2133:   Input Parameters:
    2134: + dm - The mesh
    2135: . X  - Local solution
    2136: - user - The user context

    2138:   Output Parameter:
    2139: . F  - Local output vector

    2141:   Level: developer

    2143: .seealso: DMPlexComputeJacobianActionFEM()
    2144: @*/
    2145: PetscErrorCode DMPlexSNESComputeResidualFEM(DM dm, Vec X, Vec F, void *user)
    2146: {
    2147:   PetscObject    check;
    2148:   PetscInt       cStart, cEnd, cEndInterior;
    2149:   DM             plex;

    2153:   DMSNESConvertPlex(dm,&plex,PETSC_TRUE);
    2154:   DMPlexGetHeightStratum(plex, 0, &cStart, &cEnd);
    2155:   DMPlexGetHybridBounds(plex, &cEndInterior, NULL, NULL, NULL);
    2156:   cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
    2157:   /* The dmCh is used to check two mathematically equivalent discretizations for computational equivalence */
    2158:   PetscObjectQuery((PetscObject) plex, "dmCh", &check);
    2159:   if (check) {DMPlexComputeResidualFEM_Check_Internal(plex, X, NULL, F, user);}
    2160:   else       {DMPlexComputeResidual_Internal(plex, cStart, cEnd, PETSC_MIN_REAL, X, NULL, F, user);}
    2161:   DMDestroy(&plex);
    2162:   return(0);
    2163: }

    2167: /*@
    2168:   DMPlexSNESComputeBoundaryFEM - Form the boundary values for the local input X

    2170:   Input Parameters:
    2171: + dm - The mesh
    2172: - user - The user context

    2174:   Output Parameter:
    2175: . X  - Local solution

    2177:   Level: developer

    2179: .seealso: DMPlexComputeJacobianActionFEM()
    2180: @*/
    2181: PetscErrorCode DMPlexSNESComputeBoundaryFEM(DM dm, Vec X, void *user)
    2182: {
    2183:   DM             plex;

    2187:   DMSNESConvertPlex(dm,&plex,PETSC_TRUE);
    2188:   DMPlexInsertBoundaryValues(plex, PETSC_TRUE, X, PETSC_MIN_REAL, NULL, NULL, NULL);
    2189:   DMDestroy(&plex);
    2190:   return(0);
    2191: }

    2195: PetscErrorCode DMPlexComputeJacobian_Internal(DM dm, PetscInt cStart, PetscInt cEnd, PetscReal t, PetscReal X_tShift, Vec X, Vec X_t, Mat Jac, Mat JacP,void *user)
    2196: {
    2197:   DM_Plex          *mesh  = (DM_Plex *) dm->data;
    2198:   const char       *name  = "Jacobian";
    2199:   DM                dmAux, plex;
    2200:   DMLabel           depth;
    2201:   Vec               A, cellgeom;
    2202:   PetscDS           prob, probAux = NULL;
    2203:   PetscQuadrature   quad;
    2204:   PetscSection      section, globalSection, sectionAux;
    2205:   PetscFECellGeom  *cgeom = NULL;
    2206:   PetscScalar      *cgeomScal;
    2207:   PetscScalar      *elemMat, *elemMatP, *elemMatD, *u, *u_t, *a = NULL;
    2208:   PetscInt          dim, Nf, f, fieldI, fieldJ, numCells, c;
    2209:   PetscInt          totDim, totDimBd, totDimAux, numBd, bd;
    2210:   PetscBool         isShell, hasPrec, hasDyn;
    2211:   PetscErrorCode    ierr;

    2214:   PetscLogEventBegin(DMPLEX_JacobianFEM,dm,0,0,0);
    2215:   DMGetDimension(dm, &dim);
    2216:   DMGetDefaultSection(dm, &section);
    2217:   DMGetDefaultGlobalSection(dm, &globalSection);
    2218:   DMGetDS(dm, &prob);
    2219:   PetscDSGetTotalDimension(prob, &totDim);
    2220:   PetscDSGetTotalBdDimension(prob, &totDimBd);
    2221:   PetscDSHasJacobianPreconditioner(prob, &hasPrec);
    2222:   PetscDSHasDynamicJacobian(prob, &hasDyn);
    2223:   hasDyn = hasDyn && (X_tShift != 0.0) ? PETSC_TRUE : PETSC_FALSE;
    2224:   PetscSectionGetNumFields(section, &Nf);
    2225:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
    2226:   numCells = cEnd - cStart;
    2227:   PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);
    2228:   PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);
    2229:   if (dmAux) {
    2230:     DMConvert(dmAux, DMPLEX, &plex);
    2231:     DMGetDefaultSection(plex, &sectionAux);
    2232:     DMGetDS(dmAux, &probAux);
    2233:     PetscDSGetTotalDimension(probAux, &totDimAux);
    2234:   }
    2235:   MatZeroEntries(JacP);
    2236:   PetscMalloc5(numCells*totDim,&u,X_t ? numCells*totDim : 0,&u_t,numCells*totDim*totDim,&elemMat,hasPrec ? numCells*totDim*totDim : 0, &elemMatP,hasDyn ? numCells*totDim*totDim : 0, &elemMatD);
    2237:   if (dmAux) {PetscMalloc1(numCells*totDimAux, &a);}
    2238:   DMPlexSNESGetGeometryFEM(dm, &cellgeom);
    2239:   VecGetArray(cellgeom, &cgeomScal);
    2240:   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
    2241:     DM dmCell;

    2243:     VecGetDM(cellgeom,&dmCell);
    2244:     PetscMalloc1(cEnd-cStart,&cgeom);
    2245:     for (c = 0; c < cEnd - cStart; c++) {
    2246:       PetscScalar *thisgeom;

    2248:       DMPlexPointLocalRef(dmCell, c + cStart, cgeomScal, &thisgeom);
    2249:       cgeom[c] = *((PetscFECellGeom *) thisgeom);
    2250:     }
    2251:   }
    2252:   else {
    2253:     cgeom = (PetscFECellGeom *) cgeomScal;
    2254:   }
    2255:   for (c = cStart; c < cEnd; ++c) {
    2256:     PetscScalar *x = NULL,  *x_t = NULL;
    2257:     PetscInt     i;

    2259:     DMPlexVecGetClosure(dm, section, X, c, NULL, &x);
    2260:     for (i = 0; i < totDim; ++i) u[(c-cStart)*totDim+i] = x[i];
    2261:     DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);
    2262:     if (X_t) {
    2263:       DMPlexVecGetClosure(dm, section, X_t, c, NULL, &x_t);
    2264:       for (i = 0; i < totDim; ++i) u_t[(c-cStart)*totDim+i] = x_t[i];
    2265:       DMPlexVecRestoreClosure(dm, section, X_t, c, NULL, &x_t);
    2266:     }
    2267:     if (dmAux) {
    2268:       DMPlexVecGetClosure(plex, sectionAux, A, c, NULL, &x);
    2269:       for (i = 0; i < totDimAux; ++i) a[(c-cStart)*totDimAux+i] = x[i];
    2270:       DMPlexVecRestoreClosure(plex, sectionAux, A, c, NULL, &x);
    2271:     }
    2272:   }
    2273:   PetscMemzero(elemMat, numCells*totDim*totDim * sizeof(PetscScalar));
    2274:   if (hasPrec) {PetscMemzero(elemMatP, numCells*totDim*totDim * sizeof(PetscScalar));}
    2275:   if (hasDyn)  {PetscMemzero(elemMatD, numCells*totDim*totDim * sizeof(PetscScalar));}
    2276:   for (fieldI = 0; fieldI < Nf; ++fieldI) {
    2277:     PetscFE  fe;
    2278:     PetscInt numQuadPoints, Nb;
    2279:     /* Conforming batches */
    2280:     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
    2281:     /* Remainder */
    2282:     PetscInt Nr, offset;

    2284:     PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fe);
    2285:     PetscFEGetQuadrature(fe, &quad);
    2286:     PetscFEGetDimension(fe, &Nb);
    2287:     PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);
    2288:     PetscQuadratureGetData(quad, NULL, &numQuadPoints, NULL, NULL);
    2289:     blockSize = Nb*numQuadPoints;
    2290:     batchSize = numBlocks * blockSize;
    2291:     PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);
    2292:     numChunks = numCells / (numBatches*batchSize);
    2293:     Ne        = numChunks*numBatches*batchSize;
    2294:     Nr        = numCells % (numBatches*batchSize);
    2295:     offset    = numCells - Nr;
    2296:     for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
    2297:       PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN, fieldI, fieldJ, Ne, cgeom, u, u_t, probAux, a, elemMat);
    2298:       PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN, fieldI, fieldJ, Nr, &cgeom[offset], &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], &elemMat[offset*totDim*totDim]);
    2299:       if (hasPrec) {
    2300:         PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_PRE, fieldI, fieldJ, Ne, cgeom, u, u_t, probAux, a, elemMatP);
    2301:         PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_PRE, fieldI, fieldJ, Nr, &cgeom[offset], &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], &elemMatP[offset*totDim*totDim]);
    2302:       }
    2303:       if (hasDyn) {
    2304:         PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_DYN, fieldI, fieldJ, Ne, cgeom, u, u_t, probAux, a, elemMatD);
    2305:         PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_DYN, fieldI, fieldJ, Nr, &cgeom[offset], &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], &elemMatD[offset*totDim*totDim]);
    2306:       }
    2307:     }
    2308:   }
    2309:   if (hasDyn) {
    2310:     for (c = 0; c < (cEnd - cStart)*totDim*totDim; ++c) elemMat[c] += X_tShift*elemMatD[c];
    2311:   }
    2312:   for (c = cStart; c < cEnd; ++c) {
    2313:     if (hasPrec) {
    2314:       if (mesh->printFEM > 1) {DMPrintCellMatrix(c, name, totDim, totDim, &elemMat[(c-cStart)*totDim*totDim]);}
    2315:       DMPlexMatSetClosure(dm, section, globalSection, Jac, c, &elemMat[(c-cStart)*totDim*totDim], ADD_VALUES);
    2316:       if (mesh->printFEM > 1) {DMPrintCellMatrix(c, name, totDim, totDim, &elemMatP[(c-cStart)*totDim*totDim]);}
    2317:       DMPlexMatSetClosure(dm, section, globalSection, JacP, c, &elemMatP[(c-cStart)*totDim*totDim], ADD_VALUES);
    2318:     } else {
    2319:       if (mesh->printFEM > 1) {DMPrintCellMatrix(c, name, totDim, totDim, &elemMat[(c-cStart)*totDim*totDim]);}
    2320:       DMPlexMatSetClosure(dm, section, globalSection, JacP, c, &elemMat[(c-cStart)*totDim*totDim], ADD_VALUES);
    2321:     }
    2322:   }
    2323:   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
    2324:     PetscFree(cgeom);
    2325:   }
    2326:   else {
    2327:     cgeom = NULL;
    2328:   }
    2329:   VecRestoreArray(cellgeom, &cgeomScal);
    2330:   PetscFree5(u,u_t,elemMat,elemMatP,elemMatD);
    2331:   if (dmAux) {
    2332:     PetscFree(a);
    2333:     DMDestroy(&plex);
    2334:   }
    2335:   DMPlexGetDepthLabel(dm, &depth);
    2336:   DMGetNumBoundary(dm, &numBd);
    2337:   DMPlexGetDepthLabel(dm, &depth);
    2338:   DMGetNumBoundary(dm, &numBd);
    2339:   for (bd = 0; bd < numBd; ++bd) {
    2340:     const char     *bdLabel;
    2341:     DMLabel         label;
    2342:     IS              pointIS;
    2343:     const PetscInt *points;
    2344:     const PetscInt *values;
    2345:     PetscInt        field, numValues, v, numPoints, p, dep, numFaces;
    2346:     PetscBool       isEssential;
    2347:     PetscObject     obj;
    2348:     PetscClassId    id;

    2350:     DMGetBoundary(dm, bd, &isEssential, NULL, &bdLabel, &field, NULL, NULL, NULL, &numValues, &values, NULL);
    2351:     DMGetField(dm, field, &obj);
    2352:     PetscObjectGetClassId(obj, &id);
    2353:     if ((id != PETSCFE_CLASSID) || isEssential) continue;
    2354:     DMGetLabel(dm, bdLabel, &label);
    2355:     for (v = 0; v < numValues; ++v) {
    2356:       DMLabelGetStratumSize(label, values[v], &numPoints);
    2357:       DMLabelGetStratumIS(label, values[v], &pointIS);
    2358:       if (!pointIS) continue; /* No points with that id on this process */
    2359:       ISGetIndices(pointIS, &points);
    2360:       for (p = 0, numFaces = 0; p < numPoints; ++p) {
    2361:         DMLabelGetValue(depth, points[p], &dep);
    2362:         if (dep == dim-1) ++numFaces;
    2363:       }
    2364:       PetscMalloc3(numFaces*totDimBd,&u,numFaces,&cgeom,numFaces*totDimBd*totDimBd,&elemMat);
    2365:       if (X_t) {PetscMalloc1(numFaces*totDimBd,&u_t);}
    2366:       for (p = 0, f = 0; p < numPoints; ++p) {
    2367:         const PetscInt point = points[p];
    2368:         PetscScalar   *x     = NULL;
    2369:         PetscInt       i;

    2371:         DMLabelGetValue(depth, points[p], &dep);
    2372:         if (dep != dim-1) continue;
    2373:         DMPlexComputeCellGeometryFEM(dm, point, NULL, cgeom[f].v0, cgeom[f].J, cgeom[f].invJ, &cgeom[f].detJ);
    2374:         DMPlexComputeCellGeometryFVM(dm, point, NULL, NULL, cgeom[f].n);
    2375:         if (cgeom[f].detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", cgeom[f].detJ, point);
    2376:         DMPlexVecGetClosure(dm, section, X, point, NULL, &x);
    2377:         for (i = 0; i < totDimBd; ++i) u[f*totDimBd+i] = x[i];
    2378:         DMPlexVecRestoreClosure(dm, section, X, point, NULL, &x);
    2379:         if (X_t) {
    2380:           DMPlexVecGetClosure(dm, section, X_t, point, NULL, &x);
    2381:           for (i = 0; i < totDimBd; ++i) u_t[f*totDimBd+i] = x[i];
    2382:           DMPlexVecRestoreClosure(dm, section, X_t, point, NULL, &x);
    2383:         }
    2384:         ++f;
    2385:       }
    2386:       PetscMemzero(elemMat, numFaces*totDimBd*totDimBd * sizeof(PetscScalar));
    2387:       for (fieldI = 0; fieldI < Nf; ++fieldI) {
    2388:         PetscFE  fe;
    2389:         PetscInt numQuadPoints, Nb;
    2390:         /* Conforming batches */
    2391:         PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
    2392:         /* Remainder */
    2393:         PetscInt Nr, offset;

    2395:         PetscDSGetBdDiscretization(prob, fieldI, (PetscObject *) &fe);
    2396:         PetscFEGetQuadrature(fe, &quad);
    2397:         PetscFEGetDimension(fe, &Nb);
    2398:         PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);
    2399:         PetscQuadratureGetData(quad, NULL, &numQuadPoints, NULL, NULL);
    2400:         blockSize = Nb*numQuadPoints;
    2401:         batchSize = numBlocks * blockSize;
    2402:          PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);
    2403:         numChunks = numFaces / (numBatches*batchSize);
    2404:         Ne        = numChunks*numBatches*batchSize;
    2405:         Nr        = numFaces % (numBatches*batchSize);
    2406:         offset    = numFaces - Nr;
    2407:         for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
    2408:           PetscFEIntegrateBdJacobian(fe, prob, fieldI, fieldJ, Ne, cgeom, u, u_t, NULL, NULL, elemMat);
    2409:           PetscFEIntegrateBdJacobian(fe, prob, fieldI, fieldJ, Nr, &cgeom[offset], &u[offset*totDimBd], u_t ? &u_t[offset*totDimBd] : NULL, NULL, NULL, &elemMat[offset*totDimBd*totDimBd]);
    2410:         }
    2411:       }
    2412:       for (p = 0, f = 0; p < numPoints; ++p) {
    2413:         const PetscInt point = points[p];

    2415:         DMLabelGetValue(depth, point, &dep);
    2416:         if (dep != dim-1) continue;
    2417:         if (mesh->printFEM > 1) {DMPrintCellMatrix(point, "BdJacobian", totDimBd, totDimBd, &elemMat[f*totDimBd*totDimBd]);}
    2418:         DMPlexMatSetClosure(dm, section, globalSection, JacP, point, &elemMat[f*totDimBd*totDimBd], ADD_VALUES);
    2419:         ++f;
    2420:       }
    2421:       ISRestoreIndices(pointIS, &points);
    2422:       ISDestroy(&pointIS);
    2423:       PetscFree3(u,cgeom,elemMat);
    2424:       if (X_t) {PetscFree(u_t);}
    2425:     }
    2426:   }
    2427:   if (hasPrec) {
    2428:     MatAssemblyBegin(Jac, MAT_FINAL_ASSEMBLY);
    2429:     MatAssemblyEnd(Jac, MAT_FINAL_ASSEMBLY);
    2430:   }
    2431:   MatAssemblyBegin(JacP, MAT_FINAL_ASSEMBLY);
    2432:   MatAssemblyEnd(JacP, MAT_FINAL_ASSEMBLY);
    2433:   if (mesh->printFEM) {
    2434:     PetscPrintf(PETSC_COMM_WORLD, "%s:\n", name);
    2435:     MatChop(JacP, 1.0e-10);
    2436:     MatView(JacP, PETSC_VIEWER_STDOUT_WORLD);
    2437:   }
    2438:   PetscLogEventEnd(DMPLEX_JacobianFEM,dm,0,0,0);
    2439:   PetscObjectTypeCompare((PetscObject) Jac, MATSHELL, &isShell);
    2440:   if (isShell) {
    2441:     JacActionCtx *jctx;

    2443:     MatShellGetContext(Jac, &jctx);
    2444:     VecCopy(X, jctx->u);
    2445:   }
    2446:   return(0);
    2447: }

    2451: /*@
    2452:   DMPlexSNESComputeJacobianFEM - Form the local portion of the Jacobian matrix J at the local solution X using pointwise functions specified by the user.

    2454:   Input Parameters:
    2455: + dm - The mesh
    2456: . X  - Local input vector
    2457: - user - The user context

    2459:   Output Parameter:
    2460: . Jac  - Jacobian matrix

    2462:   Note:
    2463:   The first member of the user context must be an FEMContext.

    2465:   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
    2466:   like a GPU, or vectorize on a multicore machine.

    2468:   Level: developer

    2470: .seealso: FormFunctionLocal()
    2471: @*/
    2472: PetscErrorCode DMPlexSNESComputeJacobianFEM(DM dm, Vec X, Mat Jac, Mat JacP,void *user)
    2473: {
    2474:   PetscInt       cStart, cEnd, cEndInterior;
    2475:   DM             plex;

    2479:   DMSNESConvertPlex(dm,&plex,PETSC_TRUE);
    2480:   DMPlexGetHeightStratum(plex, 0, &cStart, &cEnd);
    2481:   DMPlexGetHybridBounds(plex, &cEndInterior, NULL, NULL, NULL);
    2482:   cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
    2483:   DMPlexComputeJacobian_Internal(plex, cStart, cEnd, 0.0, 0.0, X, NULL, Jac, JacP, user);
    2484:   DMDestroy(&plex);
    2485:   return(0);
    2486: }

    2490: /*@
    2491:   DMPlexSetSNESLocalFEM - Use DMPlex's internal FEM routines to compute SNES boundary values, residual, and Jacobian.

    2493:   Input Parameters:
    2494: + dm - The DM object
    2495: . boundaryctx - the user context that will be passed to pointwise evaluation of boundary values (see DMAddBoundary())
    2496: . residualctx - the user context that will be passed to pointwise evaluation of finite element residual computations (see PetscDSSetResidual())
    2497: - jacobianctx - the user context that will be passed to pointwise evaluation of finite element Jacobian construction (see PetscDSSetJacobian())

    2499:   Level: developer
    2500: @*/
    2501: PetscErrorCode DMPlexSetSNESLocalFEM(DM dm, void *boundaryctx, void *residualctx, void *jacobianctx)
    2502: {

    2506:   DMSNESSetBoundaryLocal(dm,DMPlexSNESComputeBoundaryFEM,boundaryctx);
    2507:   DMSNESSetFunctionLocal(dm,DMPlexSNESComputeResidualFEM,residualctx);
    2508:   DMSNESSetJacobianLocal(dm,DMPlexSNESComputeJacobianFEM,jacobianctx);
    2509:   return(0);
    2510: }

    2514: PetscErrorCode DMSNESCheckFromOptions_Internal(SNES snes, DM dm, Vec u, Vec sol, PetscErrorCode (**exactFuncs)(PetscInt, PetscReal, const PetscReal x[], PetscInt, PetscScalar *u, void *ctx), void **ctxs)
    2515: {
    2516:   Mat            J, M;
    2517:   Vec            r, b;
    2518:   MatNullSpace   nullSpace;
    2519:   PetscReal     *error, res = 0.0;
    2520:   PetscInt       numFields;

    2524:   VecDuplicate(u, &r);
    2525:   DMCreateMatrix(dm, &J);
    2526:   M    = J;
    2527:   /* TODO Null space for J */
    2528:   /* Check discretization error */
    2529:   DMGetNumFields(dm, &numFields);
    2530:   PetscMalloc1(PetscMax(1, numFields), &error);
    2531:   if (numFields > 1) {
    2532:     PetscInt f;

    2534:     DMComputeL2FieldDiff(dm, 0.0, exactFuncs, ctxs, u, error);
    2535:     PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: [");
    2536:     for (f = 0; f < numFields; ++f) {
    2537:       if (f) {PetscPrintf(PETSC_COMM_WORLD, ", ");}
    2538:       if (error[f] >= 1.0e-11) {PetscPrintf(PETSC_COMM_WORLD, "%g", error[f]);}
    2539:       else                     {PetscPrintf(PETSC_COMM_WORLD, "< 1.0e-11");}
    2540:     }
    2541:     PetscPrintf(PETSC_COMM_WORLD, "]\n");
    2542:   } else {
    2543:     DMComputeL2Diff(dm, 0.0, exactFuncs, ctxs, u, &error[0]);
    2544:     if (error[0] >= 1.0e-11) {PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: %g\n", error[0]);}
    2545:     else                     {PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: < 1.0e-11\n");}
    2546:   }
    2547:   PetscFree(error);
    2548:   /* Check residual */
    2549:   SNESComputeFunction(snes, u, r);
    2550:   VecNorm(r, NORM_2, &res);
    2551:   PetscPrintf(PETSC_COMM_WORLD, "L_2 Residual: %g\n", res);
    2552:   VecChop(r, 1.0e-10);
    2553:   PetscObjectSetName((PetscObject) r, "Initial Residual");
    2554:   PetscObjectSetOptionsPrefix((PetscObject)r,"res_");
    2555:   VecViewFromOptions(r, NULL, "-vec_view");
    2556:   /* Check Jacobian */
    2557:   SNESComputeJacobian(snes, u, M, M);
    2558:   MatGetNullSpace(J, &nullSpace);
    2559:   if (nullSpace) {
    2560:     PetscBool isNull;
    2561:     MatNullSpaceTest(nullSpace, J, &isNull);
    2562:     if (!isNull) SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_PLIB, "The null space calculated for the system operator is invalid.");
    2563:   }
    2564:   VecDuplicate(u, &b);
    2565:   VecSet(r, 0.0);
    2566:   SNESComputeFunction(snes, r, b);
    2567:   MatMult(M, u, r);
    2568:   VecAXPY(r, 1.0, b);
    2569:   VecDestroy(&b);
    2570:   VecNorm(r, NORM_2, &res);
    2571:   PetscPrintf(PETSC_COMM_WORLD, "Linear L_2 Residual: %g\n", res);
    2572:   VecChop(r, 1.0e-10);
    2573:   PetscObjectSetName((PetscObject) r, "Au - b = Au + F(0)");
    2574:   PetscObjectSetOptionsPrefix((PetscObject)r,"linear_res_");
    2575:   VecViewFromOptions(r, NULL, "-vec_view");
    2576:   VecDestroy(&r);
    2577:   MatNullSpaceDestroy(&nullSpace);
    2578:   MatDestroy(&J);
    2579:   return(0);
    2580: }

    2584: PetscErrorCode DMSNESCheckFromOptions(SNES snes, Vec u, PetscErrorCode (**exactFuncs)(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx), void **ctxs)
    2585: {
    2586:   DM             dm;
    2587:   Vec            sol;
    2588:   PetscBool      check;

    2592:   PetscOptionsHasName(((PetscObject)snes)->options,((PetscObject)snes)->prefix, "-dmsnes_check", &check);
    2593:   if (!check) return(0);
    2594:   SNESGetDM(snes, &dm);
    2595:   VecDuplicate(u, &sol);
    2596:   SNESSetSolution(snes, sol);
    2597:   DMSNESCheckFromOptions_Internal(snes, dm, u, sol, exactFuncs, ctxs);
    2598:   VecDestroy(&sol);
    2599:   return(0);
    2600: }