Actual source code: dmplexsnes.c

      1: #include <petsc/private/dmpleximpl.h>
      2: #include <petsc/private/snesimpl.h>
      3: #include <petscds.h>
      4: #include <petscblaslapack.h>
      5: #include <petsc/private/petscimpl.h>
      6: #include <petsc/private/petscfeimpl.h>

      8: static void pressure_Private(PetscInt dim, PetscInt Nf, PetscInt NfAux,
      9:                              const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
     10:                              const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
     11:                              PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar p[])
     12: {
     13:   p[0] = u[uOff[1]];
     14: }

     16: /*
     17:   SNESCorrectDiscretePressure_Private - Add a vector in the nullspace to make the continuum integral of the pressure field equal to zero. This is normally used only to evaluate convergence rates for the pressure accurately.

     19:   Collective on SNES

     21:   Input Parameters:
     22: + snes      - The SNES
     23: . pfield    - The field number for pressure
     24: . nullspace - The pressure nullspace
     25: . u         - The solution vector
     26: - ctx       - An optional user context

     28:   Output Parameter:
     29: . u         - The solution with a continuum pressure integral of zero

     31:   Notes:
     32:   If int(u) = a and int(n) = b, then int(u - a/b n) = a - a/b b = 0. We assume that the nullspace is a single vector given explicitly.

     34:   Level: developer

     36: .seealso: SNESConvergedCorrectPressure()
     37: */
     38: static PetscErrorCode SNESCorrectDiscretePressure_Private(SNES snes, PetscInt pfield, MatNullSpace nullspace, Vec u, void *ctx)
     39: {
     40:   DM             dm;
     41:   PetscDS        ds;
     42:   const Vec     *nullvecs;
     43:   PetscScalar    pintd, *intc, *intn;
     44:   MPI_Comm       comm;
     45:   PetscInt       Nf, Nv;

     49:   PetscObjectGetComm((PetscObject) snes, &comm);
     50:   SNESGetDM(snes, &dm);
     51:   if (!dm) SETERRQ(comm, PETSC_ERR_ARG_WRONG, "Cannot compute test without a SNES DM");
     52:   if (!nullspace) SETERRQ(comm, PETSC_ERR_ARG_WRONG, "Cannot compute test without a Jacobian nullspace");
     53:   DMGetDS(dm, &ds);
     54:   PetscDSSetObjective(ds, pfield, pressure_Private);
     55:   MatNullSpaceGetVecs(nullspace, NULL, &Nv, &nullvecs);
     56:   if (Nv != 1) SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Can only handle a single null vector for pressure, not %D", Nv);
     57:   VecDot(nullvecs[0], u, &pintd);
     58:   if (PetscAbsScalar(pintd) > PETSC_SMALL) SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Discrete integral of pressure: %g\n", (double) PetscRealPart(pintd));
     59:   PetscDSGetNumFields(ds, &Nf);
     60:   PetscMalloc2(Nf, &intc, Nf, &intn);
     61:   DMPlexComputeIntegralFEM(dm, nullvecs[0], intn, ctx);
     62:   DMPlexComputeIntegralFEM(dm, u, intc, ctx);
     63:   VecAXPY(u, -intc[pfield]/intn[pfield], nullvecs[0]);
     64: #if defined (PETSC_USE_DEBUG)
     65:   DMPlexComputeIntegralFEM(dm, u, intc, ctx);
     66:   if (PetscAbsScalar(intc[pfield]) > PETSC_SMALL) SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Continuum integral of pressure after correction: %g\n", (double) PetscRealPart(intc[pfield]));
     67: #endif
     68:   PetscFree2(intc, intn);
     69:   return(0);
     70: }

     72: /*@C
     73:    SNESConvergedCorrectPressure - Convergence test that adds a vector in the nullspace to make the continuum integral of the pressure field equal to zero. This is normally used only to evaluate convergence rates for the pressure accurately. The convergence test itself just mimics SNESConvergedDefault().

     75:    Logically Collective on SNES

     77:    Input Parameters:
     78: +  snes - the SNES context
     79: .  it - the iteration (0 indicates before any Newton steps)
     80: .  xnorm - 2-norm of current iterate
     81: .  snorm - 2-norm of current step
     82: .  fnorm - 2-norm of function at current iterate
     83: -  ctx   - Optional user context

     85:    Output Parameter:
     86: .  reason  - SNES_CONVERGED_ITERATING, SNES_CONVERGED_ITS, or SNES_DIVERGED_FNORM_NAN

     88:    Notes:
     89:    In order to use this monitor, you must setup several PETSc structures. First fields must be added to the DM, and a PetscDS must be created with discretizations of those fields. We currently assume that the pressure field has index 1. The pressure field must have a nullspace, likely created using the DMSetNullSpaceConstructor() interface. Last we must be able to integrate the pressure over the domain, so the DM attached to the SNES must be a Plex at this time.

     91:    Level: advanced

     93: .seealso: SNESConvergedDefault(), SNESSetConvergenceTest(), DMSetNullSpaceConstructor()
     94: @*/
     95: PetscErrorCode SNESConvergedCorrectPressure(SNES snes, PetscInt it, PetscReal xnorm, PetscReal gnorm, PetscReal f, SNESConvergedReason *reason, void *ctx)
     96: {
     97:   PetscBool      monitorIntegral = PETSC_FALSE;

    101:   SNESConvergedDefault(snes, it, xnorm, gnorm, f, reason, ctx);
    102:   if (monitorIntegral) {
    103:     Mat          J;
    104:     Vec          u;
    105:     MatNullSpace nullspace;
    106:     const Vec   *nullvecs;
    107:     PetscScalar  pintd;

    109:     SNESGetSolution(snes, &u);
    110:     SNESGetJacobian(snes, &J, NULL, NULL, NULL);
    111:     MatGetNullSpace(J, &nullspace);
    112:     MatNullSpaceGetVecs(nullspace, NULL, NULL, &nullvecs);
    113:     VecDot(nullvecs[0], u, &pintd);
    114:     PetscInfo1(snes, "SNES: Discrete integral of pressure: %g\n", (double) PetscRealPart(pintd));
    115:   }
    116:   if (*reason > 0) {
    117:     Mat          J;
    118:     Vec          u;
    119:     MatNullSpace nullspace;
    120:     PetscInt     pfield = 1;

    122:     SNESGetSolution(snes, &u);
    123:     SNESGetJacobian(snes, &J, NULL, NULL, NULL);
    124:     MatGetNullSpace(J, &nullspace);
    125:     SNESCorrectDiscretePressure_Private(snes, pfield, nullspace, u, ctx);
    126:   }
    127:   return(0);
    128: }

    130: /************************** Interpolation *******************************/

    132: static PetscErrorCode DMSNESConvertPlex(DM dm, DM *plex, PetscBool copy)
    133: {
    134:   PetscBool      isPlex;

    138:   PetscObjectTypeCompare((PetscObject) dm, DMPLEX, &isPlex);
    139:   if (isPlex) {
    140:     *plex = dm;
    141:     PetscObjectReference((PetscObject) dm);
    142:   } else {
    143:     PetscObjectQuery((PetscObject) dm, "dm_plex", (PetscObject *) plex);
    144:     if (!*plex) {
    145:       DMConvert(dm,DMPLEX,plex);
    146:       PetscObjectCompose((PetscObject) dm, "dm_plex", (PetscObject) *plex);
    147:       if (copy) {
    148:         PetscInt    i;
    149:         PetscObject obj;
    150:         const char *comps[3] = {"A","dmAux","dmCh"};

    152:         DMCopyDMSNES(dm, *plex);
    153:         for (i = 0; i < 3; i++) {
    154:           PetscObjectQuery((PetscObject) dm, comps[i], &obj);
    155:           PetscObjectCompose((PetscObject) *plex, comps[i], obj);
    156:         }
    157:       }
    158:     } else {
    159:       PetscObjectReference((PetscObject) *plex);
    160:     }
    161:   }
    162:   return(0);
    163: }

    165: /*@C
    166:   DMInterpolationCreate - Creates a DMInterpolationInfo context

    168:   Collective

    170:   Input Parameter:
    171: . comm - the communicator

    173:   Output Parameter:
    174: . ctx - the context

    176:   Level: beginner

    178: .seealso: DMInterpolationEvaluate(), DMInterpolationAddPoints(), DMInterpolationDestroy()
    179: @*/
    180: PetscErrorCode DMInterpolationCreate(MPI_Comm comm, DMInterpolationInfo *ctx)
    181: {

    186:   PetscNew(ctx);

    188:   (*ctx)->comm   = comm;
    189:   (*ctx)->dim    = -1;
    190:   (*ctx)->nInput = 0;
    191:   (*ctx)->points = NULL;
    192:   (*ctx)->cells  = NULL;
    193:   (*ctx)->n      = -1;
    194:   (*ctx)->coords = NULL;
    195:   return(0);
    196: }

    198: /*@C
    199:   DMInterpolationSetDim - Sets the spatial dimension for the interpolation context

    201:   Not collective

    203:   Input Parameters:
    204: + ctx - the context
    205: - dim - the spatial dimension

    207:   Level: intermediate

    209: .seealso: DMInterpolationGetDim(), DMInterpolationEvaluate(), DMInterpolationAddPoints()
    210: @*/
    211: PetscErrorCode DMInterpolationSetDim(DMInterpolationInfo ctx, PetscInt dim)
    212: {
    214:   if ((dim < 1) || (dim > 3)) SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Invalid dimension for points: %D", dim);
    215:   ctx->dim = dim;
    216:   return(0);
    217: }

    219: /*@C
    220:   DMInterpolationGetDim - Gets the spatial dimension for the interpolation context

    222:   Not collective

    224:   Input Parameter:
    225: . ctx - the context

    227:   Output Parameter:
    228: . dim - the spatial dimension

    230:   Level: intermediate

    232: .seealso: DMInterpolationSetDim(), DMInterpolationEvaluate(), DMInterpolationAddPoints()
    233: @*/
    234: PetscErrorCode DMInterpolationGetDim(DMInterpolationInfo ctx, PetscInt *dim)
    235: {
    238:   *dim = ctx->dim;
    239:   return(0);
    240: }

    242: /*@C
    243:   DMInterpolationSetDof - Sets the number of fields interpolated at a point for the interpolation context

    245:   Not collective

    247:   Input Parameters:
    248: + ctx - the context
    249: - dof - the number of fields

    251:   Level: intermediate

    253: .seealso: DMInterpolationGetDof(), DMInterpolationEvaluate(), DMInterpolationAddPoints()
    254: @*/
    255: PetscErrorCode DMInterpolationSetDof(DMInterpolationInfo ctx, PetscInt dof)
    256: {
    258:   if (dof < 1) SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Invalid number of components: %D", dof);
    259:   ctx->dof = dof;
    260:   return(0);
    261: }

    263: /*@C
    264:   DMInterpolationGetDof - Gets the number of fields interpolated at a point for the interpolation context

    266:   Not collective

    268:   Input Parameter:
    269: . ctx - the context

    271:   Output Parameter:
    272: . dof - the number of fields

    274:   Level: intermediate

    276: .seealso: DMInterpolationSetDof(), DMInterpolationEvaluate(), DMInterpolationAddPoints()
    277: @*/
    278: PetscErrorCode DMInterpolationGetDof(DMInterpolationInfo ctx, PetscInt *dof)
    279: {
    282:   *dof = ctx->dof;
    283:   return(0);
    284: }

    286: /*@C
    287:   DMInterpolationAddPoints - Add points at which we will interpolate the fields

    289:   Not collective

    291:   Input Parameters:
    292: + ctx    - the context
    293: . n      - the number of points
    294: - points - the coordinates for each point, an array of size n * dim

    296:   Note: The coordinate information is copied.

    298:   Level: intermediate

    300: .seealso: DMInterpolationSetDim(), DMInterpolationEvaluate(), DMInterpolationCreate()
    301: @*/
    302: PetscErrorCode DMInterpolationAddPoints(DMInterpolationInfo ctx, PetscInt n, PetscReal points[])
    303: {

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

    311:   PetscMalloc1(n*ctx->dim, &ctx->points);
    312:   PetscArraycpy(ctx->points, points, n*ctx->dim);
    313:   return(0);
    314: }

    316: /*@C
    317:   DMInterpolationSetUp - Compute spatial indices for point location during interpolation

    319:   Collective on ctx

    321:   Input Parameters:
    322: + ctx - the context
    323: . dm  - the DM for the function space used for interpolation
    324: . redundantPoints - If PETSC_TRUE, all processes are passing in the same array of points. Otherwise, points need to be communicated among processes.
    325: - ignoreOutsideDomain - If PETSC_TRUE, ignore points outside the domain, otherwise return an error

    327:   Level: intermediate

    329: .seealso: DMInterpolationEvaluate(), DMInterpolationAddPoints(), DMInterpolationCreate()
    330: @*/
    331: PetscErrorCode DMInterpolationSetUp(DMInterpolationInfo ctx, DM dm, PetscBool redundantPoints, PetscBool ignoreOutsideDomain)
    332: {
    333:   MPI_Comm          comm = ctx->comm;
    334:   PetscScalar       *a;
    335:   PetscInt          p, q, i;
    336:   PetscMPIInt       rank, size;
    337:   PetscErrorCode    ierr;
    338:   Vec               pointVec;
    339:   PetscSF           cellSF;
    340:   PetscLayout       layout;
    341:   PetscReal         *globalPoints;
    342:   PetscScalar       *globalPointsScalar;
    343:   const PetscInt    *ranges;
    344:   PetscMPIInt       *counts, *displs;
    345:   const PetscSFNode *foundCells;
    346:   const PetscInt    *foundPoints;
    347:   PetscMPIInt       *foundProcs, *globalProcs;
    348:   PetscInt          n, N, numFound;

    352:   MPI_Comm_size(comm, &size);
    353:   MPI_Comm_rank(comm, &rank);
    354:   if (ctx->dim < 0) SETERRQ(comm, PETSC_ERR_ARG_WRONGSTATE, "The spatial dimension has not been set");
    355:   /* Locate points */
    356:   n = ctx->nInput;
    357:   if (!redundantPoints) {
    358:     PetscLayoutCreate(comm, &layout);
    359:     PetscLayoutSetBlockSize(layout, 1);
    360:     PetscLayoutSetLocalSize(layout, n);
    361:     PetscLayoutSetUp(layout);
    362:     PetscLayoutGetSize(layout, &N);
    363:     /* Communicate all points to all processes */
    364:     PetscMalloc3(N*ctx->dim,&globalPoints,size,&counts,size,&displs);
    365:     PetscLayoutGetRanges(layout, &ranges);
    366:     for (p = 0; p < size; ++p) {
    367:       counts[p] = (ranges[p+1] - ranges[p])*ctx->dim;
    368:       displs[p] = ranges[p]*ctx->dim;
    369:     }
    370:     MPI_Allgatherv(ctx->points, n*ctx->dim, MPIU_REAL, globalPoints, counts, displs, MPIU_REAL, comm);
    371:   } else {
    372:     N = n;
    373:     globalPoints = ctx->points;
    374:     counts = displs = NULL;
    375:     layout = NULL;
    376:   }
    377: #if 0
    378:   PetscMalloc3(N,&foundCells,N,&foundProcs,N,&globalProcs);
    379:   /* foundCells[p] = m->locatePoint(&globalPoints[p*ctx->dim]); */
    380: #else
    381: #if defined(PETSC_USE_COMPLEX)
    382:   PetscMalloc1(N*ctx->dim,&globalPointsScalar);
    383:   for (i=0; i<N*ctx->dim; i++) globalPointsScalar[i] = globalPoints[i];
    384: #else
    385:   globalPointsScalar = globalPoints;
    386: #endif
    387:   VecCreateSeqWithArray(PETSC_COMM_SELF, ctx->dim, N*ctx->dim, globalPointsScalar, &pointVec);
    388:   PetscMalloc2(N,&foundProcs,N,&globalProcs);
    389:   for (p = 0; p < N; ++p) {foundProcs[p] = size;}
    390:   cellSF = NULL;
    391:   DMLocatePoints(dm, pointVec, DM_POINTLOCATION_REMOVE, &cellSF);
    392:   PetscSFGetGraph(cellSF,NULL,&numFound,&foundPoints,&foundCells);
    393: #endif
    394:   for (p = 0; p < numFound; ++p) {
    395:     if (foundCells[p].index >= 0) foundProcs[foundPoints ? foundPoints[p] : p] = rank;
    396:   }
    397:   /* Let the lowest rank process own each point */
    398:   MPIU_Allreduce(foundProcs, globalProcs, N, MPI_INT, MPI_MIN, comm);
    399:   ctx->n = 0;
    400:   for (p = 0; p < N; ++p) {
    401:     if (globalProcs[p] == size) {
    402:       if (!ignoreOutsideDomain) SETERRQ4(comm, PETSC_ERR_PLIB, "Point %d: %g %g %g not located in mesh", p, (double)globalPoints[p*ctx->dim+0], (double)(ctx->dim > 1 ? globalPoints[p*ctx->dim+1] : 0.0), (double)(ctx->dim > 2 ? globalPoints[p*ctx->dim+2] : 0.0));
    403:       else if (!rank) ++ctx->n;
    404:     } else if (globalProcs[p] == rank) ++ctx->n;
    405:   }
    406:   /* Create coordinates vector and array of owned cells */
    407:   PetscMalloc1(ctx->n, &ctx->cells);
    408:   VecCreate(comm, &ctx->coords);
    409:   VecSetSizes(ctx->coords, ctx->n*ctx->dim, PETSC_DECIDE);
    410:   VecSetBlockSize(ctx->coords, ctx->dim);
    411:   VecSetType(ctx->coords,VECSTANDARD);
    412:   VecGetArray(ctx->coords, &a);
    413:   for (p = 0, q = 0, i = 0; p < N; ++p) {
    414:     if (globalProcs[p] == rank) {
    415:       PetscInt d;

    417:       for (d = 0; d < ctx->dim; ++d, ++i) a[i] = globalPoints[p*ctx->dim+d];
    418:       ctx->cells[q] = foundCells[q].index;
    419:       ++q;
    420:     }
    421:     if (globalProcs[p] == size && !rank) {
    422:       PetscInt d;

    424:       for (d = 0; d < ctx->dim; ++d, ++i) a[i] = 0.;
    425:       ctx->cells[q] = -1;
    426:       ++q;
    427:     }
    428:   }
    429:   VecRestoreArray(ctx->coords, &a);
    430: #if 0
    431:   PetscFree3(foundCells,foundProcs,globalProcs);
    432: #else
    433:   PetscFree2(foundProcs,globalProcs);
    434:   PetscSFDestroy(&cellSF);
    435:   VecDestroy(&pointVec);
    436: #endif
    437:   if ((void*)globalPointsScalar != (void*)globalPoints) {PetscFree(globalPointsScalar);}
    438:   if (!redundantPoints) {PetscFree3(globalPoints,counts,displs);}
    439:   PetscLayoutDestroy(&layout);
    440:   return(0);
    441: }

    443: /*@C
    444:   DMInterpolationGetCoordinates - Gets a Vec with the coordinates of each interpolation point

    446:   Collective on ctx

    448:   Input Parameter:
    449: . ctx - the context

    451:   Output Parameter:
    452: . coordinates  - the coordinates of interpolation points

    454:   Note: The local vector entries correspond to interpolation points lying on this process, according to the associated DM. This is a borrowed vector that the user should not destroy.

    456:   Level: intermediate

    458: .seealso: DMInterpolationEvaluate(), DMInterpolationAddPoints(), DMInterpolationCreate()
    459: @*/
    460: PetscErrorCode DMInterpolationGetCoordinates(DMInterpolationInfo ctx, Vec *coordinates)
    461: {
    464:   if (!ctx->coords) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The interpolation context has not been setup.");
    465:   *coordinates = ctx->coords;
    466:   return(0);
    467: }

    469: /*@C
    470:   DMInterpolationGetVector - Gets a Vec which can hold all the interpolated field values

    472:   Collective on ctx

    474:   Input Parameter:
    475: . ctx - the context

    477:   Output Parameter:
    478: . v  - a vector capable of holding the interpolated field values

    480:   Note: This vector should be returned using DMInterpolationRestoreVector().

    482:   Level: intermediate

    484: .seealso: DMInterpolationRestoreVector(), DMInterpolationEvaluate(), DMInterpolationAddPoints(), DMInterpolationCreate()
    485: @*/
    486: PetscErrorCode DMInterpolationGetVector(DMInterpolationInfo ctx, Vec *v)
    487: {

    492:   if (!ctx->coords) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The interpolation context has not been setup.");
    493:   VecCreate(ctx->comm, v);
    494:   VecSetSizes(*v, ctx->n*ctx->dof, PETSC_DECIDE);
    495:   VecSetBlockSize(*v, ctx->dof);
    496:   VecSetType(*v,VECSTANDARD);
    497:   return(0);
    498: }

    500: /*@C
    501:   DMInterpolationRestoreVector - Returns a Vec which can hold all the interpolated field values

    503:   Collective on ctx

    505:   Input Parameters:
    506: + ctx - the context
    507: - v  - a vector capable of holding the interpolated field values

    509:   Level: intermediate

    511: .seealso: DMInterpolationGetVector(), DMInterpolationEvaluate(), DMInterpolationAddPoints(), DMInterpolationCreate()
    512: @*/
    513: PetscErrorCode DMInterpolationRestoreVector(DMInterpolationInfo ctx, Vec *v)
    514: {

    519:   if (!ctx->coords) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The interpolation context has not been setup.");
    520:   VecDestroy(v);
    521:   return(0);
    522: }

    524: PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Triangle_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
    525: {
    526:   PetscReal      *v0, *J, *invJ, detJ;
    527:   const PetscScalar *coords;
    528:   PetscScalar    *a;
    529:   PetscInt       p;

    533:   PetscMalloc3(ctx->dim,&v0,ctx->dim*ctx->dim,&J,ctx->dim*ctx->dim,&invJ);
    534:   VecGetArrayRead(ctx->coords, &coords);
    535:   VecGetArray(v, &a);
    536:   for (p = 0; p < ctx->n; ++p) {
    537:     PetscInt     c = ctx->cells[p];
    538:     PetscScalar *x = NULL;
    539:     PetscReal    xi[4];
    540:     PetscInt     d, f, comp;

    542:     DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ);
    543:     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %D", (double)detJ, c);
    544:     DMPlexVecGetClosure(dm, NULL, xLocal, c, NULL, &x);
    545:     for (comp = 0; comp < ctx->dof; ++comp) a[p*ctx->dof+comp] = x[0*ctx->dof+comp];

    547:     for (d = 0; d < ctx->dim; ++d) {
    548:       xi[d] = 0.0;
    549:       for (f = 0; f < ctx->dim; ++f) xi[d] += invJ[d*ctx->dim+f]*0.5*PetscRealPart(coords[p*ctx->dim+f] - v0[f]);
    550:       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];
    551:     }
    552:     DMPlexVecRestoreClosure(dm, NULL, xLocal, c, NULL, &x);
    553:   }
    554:   VecRestoreArray(v, &a);
    555:   VecRestoreArrayRead(ctx->coords, &coords);
    556:   PetscFree3(v0, J, invJ);
    557:   return(0);
    558: }

    560: PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Tetrahedron_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
    561: {
    562:   PetscReal      *v0, *J, *invJ, detJ;
    563:   const PetscScalar *coords;
    564:   PetscScalar    *a;
    565:   PetscInt       p;

    569:   PetscMalloc3(ctx->dim,&v0,ctx->dim*ctx->dim,&J,ctx->dim*ctx->dim,&invJ);
    570:   VecGetArrayRead(ctx->coords, &coords);
    571:   VecGetArray(v, &a);
    572:   for (p = 0; p < ctx->n; ++p) {
    573:     PetscInt       c = ctx->cells[p];
    574:     const PetscInt order[3] = {2, 1, 3};
    575:     PetscScalar   *x = NULL;
    576:     PetscReal      xi[4];
    577:     PetscInt       d, f, comp;

    579:     DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ);
    580:     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %D", (double)detJ, c);
    581:     DMPlexVecGetClosure(dm, NULL, xLocal, c, NULL, &x);
    582:     for (comp = 0; comp < ctx->dof; ++comp) a[p*ctx->dof+comp] = x[0*ctx->dof+comp];

    584:     for (d = 0; d < ctx->dim; ++d) {
    585:       xi[d] = 0.0;
    586:       for (f = 0; f < ctx->dim; ++f) xi[d] += invJ[d*ctx->dim+f]*0.5*PetscRealPart(coords[p*ctx->dim+f] - v0[f]);
    587:       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];
    588:     }
    589:     DMPlexVecRestoreClosure(dm, NULL, xLocal, c, NULL, &x);
    590:   }
    591:   VecRestoreArray(v, &a);
    592:   VecRestoreArrayRead(ctx->coords, &coords);
    593:   PetscFree3(v0, J, invJ);
    594:   return(0);
    595: }

    597: PETSC_STATIC_INLINE PetscErrorCode QuadMap_Private(SNES snes, Vec Xref, Vec Xreal, void *ctx)
    598: {
    599:   const PetscScalar *vertices = (const PetscScalar*) ctx;
    600:   const PetscScalar x0        = vertices[0];
    601:   const PetscScalar y0        = vertices[1];
    602:   const PetscScalar x1        = vertices[2];
    603:   const PetscScalar y1        = vertices[3];
    604:   const PetscScalar x2        = vertices[4];
    605:   const PetscScalar y2        = vertices[5];
    606:   const PetscScalar x3        = vertices[6];
    607:   const PetscScalar y3        = vertices[7];
    608:   const PetscScalar f_1       = x1 - x0;
    609:   const PetscScalar g_1       = y1 - y0;
    610:   const PetscScalar f_3       = x3 - x0;
    611:   const PetscScalar g_3       = y3 - y0;
    612:   const PetscScalar f_01      = x2 - x1 - x3 + x0;
    613:   const PetscScalar g_01      = y2 - y1 - y3 + y0;
    614:   const PetscScalar *ref;
    615:   PetscScalar       *real;
    616:   PetscErrorCode    ierr;

    619:   VecGetArrayRead(Xref,  &ref);
    620:   VecGetArray(Xreal, &real);
    621:   {
    622:     const PetscScalar p0 = ref[0];
    623:     const PetscScalar p1 = ref[1];

    625:     real[0] = x0 + f_1 * p0 + f_3 * p1 + f_01 * p0 * p1;
    626:     real[1] = y0 + g_1 * p0 + g_3 * p1 + g_01 * p0 * p1;
    627:   }
    628:   PetscLogFlops(28);
    629:   VecRestoreArrayRead(Xref,  &ref);
    630:   VecRestoreArray(Xreal, &real);
    631:   return(0);
    632: }

    634: #include <petsc/private/dmimpl.h>
    635: PETSC_STATIC_INLINE PetscErrorCode QuadJacobian_Private(SNES snes, Vec Xref, Mat J, Mat M, void *ctx)
    636: {
    637:   const PetscScalar *vertices = (const PetscScalar*) ctx;
    638:   const PetscScalar x0        = vertices[0];
    639:   const PetscScalar y0        = vertices[1];
    640:   const PetscScalar x1        = vertices[2];
    641:   const PetscScalar y1        = vertices[3];
    642:   const PetscScalar x2        = vertices[4];
    643:   const PetscScalar y2        = vertices[5];
    644:   const PetscScalar x3        = vertices[6];
    645:   const PetscScalar y3        = vertices[7];
    646:   const PetscScalar f_01      = x2 - x1 - x3 + x0;
    647:   const PetscScalar g_01      = y2 - y1 - y3 + y0;
    648:   const PetscScalar *ref;
    649:   PetscErrorCode    ierr;

    652:   VecGetArrayRead(Xref,  &ref);
    653:   {
    654:     const PetscScalar x       = ref[0];
    655:     const PetscScalar y       = ref[1];
    656:     const PetscInt    rows[2] = {0, 1};
    657:     PetscScalar       values[4];

    659:     values[0] = (x1 - x0 + f_01*y) * 0.5; values[1] = (x3 - x0 + f_01*x) * 0.5;
    660:     values[2] = (y1 - y0 + g_01*y) * 0.5; values[3] = (y3 - y0 + g_01*x) * 0.5;
    661:     MatSetValues(J, 2, rows, 2, rows, values, INSERT_VALUES);
    662:   }
    663:   PetscLogFlops(30);
    664:   VecRestoreArrayRead(Xref,  &ref);
    665:   MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY);
    666:   MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY);
    667:   return(0);
    668: }

    670: PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Quad_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
    671: {
    672:   DM             dmCoord;
    673:   PetscFE        fem = NULL;
    674:   SNES           snes;
    675:   KSP            ksp;
    676:   PC             pc;
    677:   Vec            coordsLocal, r, ref, real;
    678:   Mat            J;
    679:   PetscTabulation    T;
    680:   const PetscScalar *coords;
    681:   PetscScalar    *a;
    682:   PetscReal      xir[2];
    683:   PetscInt       Nf, p;
    684:   const PetscInt dof = ctx->dof;

    688:   DMGetNumFields(dm, &Nf);
    689:   if (Nf) {DMGetField(dm, 0, NULL, (PetscObject *) &fem);}
    690:   DMGetCoordinatesLocal(dm, &coordsLocal);
    691:   DMGetCoordinateDM(dm, &dmCoord);
    692:   SNESCreate(PETSC_COMM_SELF, &snes);
    693:   SNESSetOptionsPrefix(snes, "quad_interp_");
    694:   VecCreate(PETSC_COMM_SELF, &r);
    695:   VecSetSizes(r, 2, 2);
    696:   VecSetType(r,dm->vectype);
    697:   VecDuplicate(r, &ref);
    698:   VecDuplicate(r, &real);
    699:   MatCreate(PETSC_COMM_SELF, &J);
    700:   MatSetSizes(J, 2, 2, 2, 2);
    701:   MatSetType(J, MATSEQDENSE);
    702:   MatSetUp(J);
    703:   SNESSetFunction(snes, r, QuadMap_Private, NULL);
    704:   SNESSetJacobian(snes, J, J, QuadJacobian_Private, NULL);
    705:   SNESGetKSP(snes, &ksp);
    706:   KSPGetPC(ksp, &pc);
    707:   PCSetType(pc, PCLU);
    708:   SNESSetFromOptions(snes);

    710:   VecGetArrayRead(ctx->coords, &coords);
    711:   VecGetArray(v, &a);
    712:   PetscFECreateTabulation(fem, 1, 1, xir, 0, &T);
    713:   for (p = 0; p < ctx->n; ++p) {
    714:     PetscScalar *x = NULL, *vertices = NULL;
    715:     PetscScalar *xi;
    716:     PetscInt     c = ctx->cells[p], comp, coordSize, xSize;

    718:     /* Can make this do all points at once */
    719:     DMPlexVecGetClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);
    720:     if (4*2 != coordSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %D should be %d", coordSize, 4*2);
    721:     DMPlexVecGetClosure(dm, NULL, xLocal, c, &xSize, &x);
    722:     SNESSetFunction(snes, NULL, NULL, (void*) vertices);
    723:     SNESSetJacobian(snes, NULL, NULL, NULL, (void*) vertices);
    724:     VecGetArray(real, &xi);
    725:     xi[0]  = coords[p*ctx->dim+0];
    726:     xi[1]  = coords[p*ctx->dim+1];
    727:     VecRestoreArray(real, &xi);
    728:     SNESSolve(snes, real, ref);
    729:     VecGetArray(ref, &xi);
    730:     xir[0] = PetscRealPart(xi[0]);
    731:     xir[1] = PetscRealPart(xi[1]);
    732:     if (4*dof != xSize) {
    733:       PetscInt d;

    735:       xir[0] = 2.0*xir[0] - 1.0; xir[1] = 2.0*xir[1] - 1.0;
    736:       PetscFEComputeTabulation(fem, 1, xir, 0, T);
    737:       for (comp = 0; comp < dof; ++comp) {
    738:         a[p*dof+comp] = 0.0;
    739:         for (d = 0; d < xSize/dof; ++d) {
    740:           a[p*dof+comp] += x[d*dof+comp]*T->T[0][d*dof+comp];
    741:         }
    742:       }
    743:     } else {
    744:       for (comp = 0; comp < dof; ++comp)
    745:         a[p*dof+comp] = x[0*dof+comp]*(1 - xir[0])*(1 - xir[1]) + x[1*dof+comp]*xir[0]*(1 - xir[1]) + x[2*dof+comp]*xir[0]*xir[1] + x[3*dof+comp]*(1 - xir[0])*xir[1];
    746:     }
    747:     VecRestoreArray(ref, &xi);
    748:     DMPlexVecRestoreClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);
    749:     DMPlexVecRestoreClosure(dm, NULL, xLocal, c, &xSize, &x);
    750:   }
    751:   PetscTabulationDestroy(&T);
    752:   VecRestoreArray(v, &a);
    753:   VecRestoreArrayRead(ctx->coords, &coords);

    755:   SNESDestroy(&snes);
    756:   VecDestroy(&r);
    757:   VecDestroy(&ref);
    758:   VecDestroy(&real);
    759:   MatDestroy(&J);
    760:   return(0);
    761: }

    763: PETSC_STATIC_INLINE PetscErrorCode HexMap_Private(SNES snes, Vec Xref, Vec Xreal, void *ctx)
    764: {
    765:   const PetscScalar *vertices = (const PetscScalar*) ctx;
    766:   const PetscScalar x0        = vertices[0];
    767:   const PetscScalar y0        = vertices[1];
    768:   const PetscScalar z0        = vertices[2];
    769:   const PetscScalar x1        = vertices[9];
    770:   const PetscScalar y1        = vertices[10];
    771:   const PetscScalar z1        = vertices[11];
    772:   const PetscScalar x2        = vertices[6];
    773:   const PetscScalar y2        = vertices[7];
    774:   const PetscScalar z2        = vertices[8];
    775:   const PetscScalar x3        = vertices[3];
    776:   const PetscScalar y3        = vertices[4];
    777:   const PetscScalar z3        = vertices[5];
    778:   const PetscScalar x4        = vertices[12];
    779:   const PetscScalar y4        = vertices[13];
    780:   const PetscScalar z4        = vertices[14];
    781:   const PetscScalar x5        = vertices[15];
    782:   const PetscScalar y5        = vertices[16];
    783:   const PetscScalar z5        = vertices[17];
    784:   const PetscScalar x6        = vertices[18];
    785:   const PetscScalar y6        = vertices[19];
    786:   const PetscScalar z6        = vertices[20];
    787:   const PetscScalar x7        = vertices[21];
    788:   const PetscScalar y7        = vertices[22];
    789:   const PetscScalar z7        = vertices[23];
    790:   const PetscScalar f_1       = x1 - x0;
    791:   const PetscScalar g_1       = y1 - y0;
    792:   const PetscScalar h_1       = z1 - z0;
    793:   const PetscScalar f_3       = x3 - x0;
    794:   const PetscScalar g_3       = y3 - y0;
    795:   const PetscScalar h_3       = z3 - z0;
    796:   const PetscScalar f_4       = x4 - x0;
    797:   const PetscScalar g_4       = y4 - y0;
    798:   const PetscScalar h_4       = z4 - z0;
    799:   const PetscScalar f_01      = x2 - x1 - x3 + x0;
    800:   const PetscScalar g_01      = y2 - y1 - y3 + y0;
    801:   const PetscScalar h_01      = z2 - z1 - z3 + z0;
    802:   const PetscScalar f_12      = x7 - x3 - x4 + x0;
    803:   const PetscScalar g_12      = y7 - y3 - y4 + y0;
    804:   const PetscScalar h_12      = z7 - z3 - z4 + z0;
    805:   const PetscScalar f_02      = x5 - x1 - x4 + x0;
    806:   const PetscScalar g_02      = y5 - y1 - y4 + y0;
    807:   const PetscScalar h_02      = z5 - z1 - z4 + z0;
    808:   const PetscScalar f_012     = x6 - x0 + x1 - x2 + x3 + x4 - x5 - x7;
    809:   const PetscScalar g_012     = y6 - y0 + y1 - y2 + y3 + y4 - y5 - y7;
    810:   const PetscScalar h_012     = z6 - z0 + z1 - z2 + z3 + z4 - z5 - z7;
    811:   const PetscScalar *ref;
    812:   PetscScalar       *real;
    813:   PetscErrorCode    ierr;

    816:   VecGetArrayRead(Xref,  &ref);
    817:   VecGetArray(Xreal, &real);
    818:   {
    819:     const PetscScalar p0 = ref[0];
    820:     const PetscScalar p1 = ref[1];
    821:     const PetscScalar p2 = ref[2];

    823:     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;
    824:     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;
    825:     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;
    826:   }
    827:   PetscLogFlops(114);
    828:   VecRestoreArrayRead(Xref,  &ref);
    829:   VecRestoreArray(Xreal, &real);
    830:   return(0);
    831: }

    833: PETSC_STATIC_INLINE PetscErrorCode HexJacobian_Private(SNES snes, Vec Xref, Mat J, Mat M, void *ctx)
    834: {
    835:   const PetscScalar *vertices = (const PetscScalar*) ctx;
    836:   const PetscScalar x0        = vertices[0];
    837:   const PetscScalar y0        = vertices[1];
    838:   const PetscScalar z0        = vertices[2];
    839:   const PetscScalar x1        = vertices[9];
    840:   const PetscScalar y1        = vertices[10];
    841:   const PetscScalar z1        = vertices[11];
    842:   const PetscScalar x2        = vertices[6];
    843:   const PetscScalar y2        = vertices[7];
    844:   const PetscScalar z2        = vertices[8];
    845:   const PetscScalar x3        = vertices[3];
    846:   const PetscScalar y3        = vertices[4];
    847:   const PetscScalar z3        = vertices[5];
    848:   const PetscScalar x4        = vertices[12];
    849:   const PetscScalar y4        = vertices[13];
    850:   const PetscScalar z4        = vertices[14];
    851:   const PetscScalar x5        = vertices[15];
    852:   const PetscScalar y5        = vertices[16];
    853:   const PetscScalar z5        = vertices[17];
    854:   const PetscScalar x6        = vertices[18];
    855:   const PetscScalar y6        = vertices[19];
    856:   const PetscScalar z6        = vertices[20];
    857:   const PetscScalar x7        = vertices[21];
    858:   const PetscScalar y7        = vertices[22];
    859:   const PetscScalar z7        = vertices[23];
    860:   const PetscScalar f_xy      = x2 - x1 - x3 + x0;
    861:   const PetscScalar g_xy      = y2 - y1 - y3 + y0;
    862:   const PetscScalar h_xy      = z2 - z1 - z3 + z0;
    863:   const PetscScalar f_yz      = x7 - x3 - x4 + x0;
    864:   const PetscScalar g_yz      = y7 - y3 - y4 + y0;
    865:   const PetscScalar h_yz      = z7 - z3 - z4 + z0;
    866:   const PetscScalar f_xz      = x5 - x1 - x4 + x0;
    867:   const PetscScalar g_xz      = y5 - y1 - y4 + y0;
    868:   const PetscScalar h_xz      = z5 - z1 - z4 + z0;
    869:   const PetscScalar f_xyz     = x6 - x0 + x1 - x2 + x3 + x4 - x5 - x7;
    870:   const PetscScalar g_xyz     = y6 - y0 + y1 - y2 + y3 + y4 - y5 - y7;
    871:   const PetscScalar h_xyz     = z6 - z0 + z1 - z2 + z3 + z4 - z5 - z7;
    872:   const PetscScalar *ref;
    873:   PetscErrorCode    ierr;

    876:   VecGetArrayRead(Xref,  &ref);
    877:   {
    878:     const PetscScalar x       = ref[0];
    879:     const PetscScalar y       = ref[1];
    880:     const PetscScalar z       = ref[2];
    881:     const PetscInt    rows[3] = {0, 1, 2};
    882:     PetscScalar       values[9];

    884:     values[0] = (x1 - x0 + f_xy*y + f_xz*z + f_xyz*y*z) / 2.0;
    885:     values[1] = (x3 - x0 + f_xy*x + f_yz*z + f_xyz*x*z) / 2.0;
    886:     values[2] = (x4 - x0 + f_yz*y + f_xz*x + f_xyz*x*y) / 2.0;
    887:     values[3] = (y1 - y0 + g_xy*y + g_xz*z + g_xyz*y*z) / 2.0;
    888:     values[4] = (y3 - y0 + g_xy*x + g_yz*z + g_xyz*x*z) / 2.0;
    889:     values[5] = (y4 - y0 + g_yz*y + g_xz*x + g_xyz*x*y) / 2.0;
    890:     values[6] = (z1 - z0 + h_xy*y + h_xz*z + h_xyz*y*z) / 2.0;
    891:     values[7] = (z3 - z0 + h_xy*x + h_yz*z + h_xyz*x*z) / 2.0;
    892:     values[8] = (z4 - z0 + h_yz*y + h_xz*x + h_xyz*x*y) / 2.0;

    894:     MatSetValues(J, 3, rows, 3, rows, values, INSERT_VALUES);
    895:   }
    896:   PetscLogFlops(152);
    897:   VecRestoreArrayRead(Xref,  &ref);
    898:   MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY);
    899:   MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY);
    900:   return(0);
    901: }

    903: PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Hex_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
    904: {
    905:   DM             dmCoord;
    906:   SNES           snes;
    907:   KSP            ksp;
    908:   PC             pc;
    909:   Vec            coordsLocal, r, ref, real;
    910:   Mat            J;
    911:   const PetscScalar *coords;
    912:   PetscScalar    *a;
    913:   PetscInt       p;

    917:   DMGetCoordinatesLocal(dm, &coordsLocal);
    918:   DMGetCoordinateDM(dm, &dmCoord);
    919:   SNESCreate(PETSC_COMM_SELF, &snes);
    920:   SNESSetOptionsPrefix(snes, "hex_interp_");
    921:   VecCreate(PETSC_COMM_SELF, &r);
    922:   VecSetSizes(r, 3, 3);
    923:   VecSetType(r,dm->vectype);
    924:   VecDuplicate(r, &ref);
    925:   VecDuplicate(r, &real);
    926:   MatCreate(PETSC_COMM_SELF, &J);
    927:   MatSetSizes(J, 3, 3, 3, 3);
    928:   MatSetType(J, MATSEQDENSE);
    929:   MatSetUp(J);
    930:   SNESSetFunction(snes, r, HexMap_Private, NULL);
    931:   SNESSetJacobian(snes, J, J, HexJacobian_Private, NULL);
    932:   SNESGetKSP(snes, &ksp);
    933:   KSPGetPC(ksp, &pc);
    934:   PCSetType(pc, PCLU);
    935:   SNESSetFromOptions(snes);

    937:   VecGetArrayRead(ctx->coords, &coords);
    938:   VecGetArray(v, &a);
    939:   for (p = 0; p < ctx->n; ++p) {
    940:     PetscScalar *x = NULL, *vertices = NULL;
    941:     PetscScalar *xi;
    942:     PetscReal    xir[3];
    943:     PetscInt     c = ctx->cells[p], comp, coordSize, xSize;

    945:     /* Can make this do all points at once */
    946:     DMPlexVecGetClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);
    947:     if (8*3 != coordSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %D should be %d", coordSize, 8*3);
    948:     DMPlexVecGetClosure(dm, NULL, xLocal, c, &xSize, &x);
    949:     if (8*ctx->dof != xSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %D should be %D", xSize, 8*ctx->dof);
    950:     SNESSetFunction(snes, NULL, NULL, (void*) vertices);
    951:     SNESSetJacobian(snes, NULL, NULL, NULL, (void*) vertices);
    952:     VecGetArray(real, &xi);
    953:     xi[0]  = coords[p*ctx->dim+0];
    954:     xi[1]  = coords[p*ctx->dim+1];
    955:     xi[2]  = coords[p*ctx->dim+2];
    956:     VecRestoreArray(real, &xi);
    957:     SNESSolve(snes, real, ref);
    958:     VecGetArray(ref, &xi);
    959:     xir[0] = PetscRealPart(xi[0]);
    960:     xir[1] = PetscRealPart(xi[1]);
    961:     xir[2] = PetscRealPart(xi[2]);
    962:     for (comp = 0; comp < ctx->dof; ++comp) {
    963:       a[p*ctx->dof+comp] =
    964:         x[0*ctx->dof+comp]*(1-xir[0])*(1-xir[1])*(1-xir[2]) +
    965:         x[3*ctx->dof+comp]*    xir[0]*(1-xir[1])*(1-xir[2]) +
    966:         x[2*ctx->dof+comp]*    xir[0]*    xir[1]*(1-xir[2]) +
    967:         x[1*ctx->dof+comp]*(1-xir[0])*    xir[1]*(1-xir[2]) +
    968:         x[4*ctx->dof+comp]*(1-xir[0])*(1-xir[1])*   xir[2] +
    969:         x[5*ctx->dof+comp]*    xir[0]*(1-xir[1])*   xir[2] +
    970:         x[6*ctx->dof+comp]*    xir[0]*    xir[1]*   xir[2] +
    971:         x[7*ctx->dof+comp]*(1-xir[0])*    xir[1]*   xir[2];
    972:     }
    973:     VecRestoreArray(ref, &xi);
    974:     DMPlexVecRestoreClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);
    975:     DMPlexVecRestoreClosure(dm, NULL, xLocal, c, &xSize, &x);
    976:   }
    977:   VecRestoreArray(v, &a);
    978:   VecRestoreArrayRead(ctx->coords, &coords);

    980:   SNESDestroy(&snes);
    981:   VecDestroy(&r);
    982:   VecDestroy(&ref);
    983:   VecDestroy(&real);
    984:   MatDestroy(&J);
    985:   return(0);
    986: }

    988: /*@C
    989:   DMInterpolationEvaluate - Using the input from dm and x, calculates interpolated field values at the interpolation points.

    991:   Input Parameters:
    992: + ctx - The DMInterpolationInfo context
    993: . dm  - The DM
    994: - x   - The local vector containing the field to be interpolated

    996:   Output Parameters:
    997: . v   - The vector containing the interpolated values

    999:   Note: A suitable v can be obtained using DMInterpolationGetVector().

    1001:   Level: beginner

    1003: .seealso: DMInterpolationGetVector(), DMInterpolationAddPoints(), DMInterpolationCreate()
    1004: @*/
    1005: PetscErrorCode DMInterpolationEvaluate(DMInterpolationInfo ctx, DM dm, Vec x, Vec v)
    1006: {
    1007:   PetscInt       n;

    1014:   VecGetLocalSize(v, &n);
    1015:   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);
    1016:   if (n) {
    1017:     PetscDS        ds;
    1018:     DMPolytopeType ct;
    1019:     PetscBool      done = PETSC_FALSE;

    1021:     DMGetDS(dm, &ds);
    1022:     if (ds) {
    1023:       const PetscScalar *coords;
    1024:       PetscScalar       *interpolant;
    1025:       PetscInt           cdim, d, p, Nf, field, c = 0;

    1027:       DMGetCoordinateDim(dm, &cdim);
    1028:       PetscDSGetNumFields(ds, &Nf);
    1029:       for (field = 0; field < Nf; ++field) {
    1030:         PetscTabulation T;
    1031:         PetscFE         fe;
    1032:         PetscClassId    id;
    1033:         PetscReal       xi[3];
    1034:         PetscInt        Nc, f, fc;

    1036:         PetscDSGetDiscretization(ds, field, (PetscObject *) &fe);
    1037:         PetscObjectGetClassId((PetscObject) fe, &id);
    1038:         if (id != PETSCFE_CLASSID) break;
    1039:         PetscFEGetNumComponents(fe, &Nc);
    1040:         VecGetArrayRead(ctx->coords, &coords);
    1041:         VecGetArrayWrite(v, &interpolant);
    1042:         for (p = 0; p < ctx->n; ++p) {
    1043:           PetscScalar *xa = NULL;
    1044:           PetscReal    pcoords[3];

    1046:           if (ctx->cells[p] < 0) continue;
    1047:           for (d = 0; d < cdim; ++d) pcoords[d] = PetscRealPart(coords[p*cdim+d]);
    1048:           DMPlexCoordinatesToReference(dm, ctx->cells[p], 1, pcoords, xi);
    1049:           DMPlexVecGetClosure(dm, NULL, x, ctx->cells[p], NULL, &xa);
    1050:           PetscFECreateTabulation(fe, 1, 1, xi, 0, &T);
    1051:           {
    1052:             const PetscReal *basis = T->T[0];
    1053:             const PetscInt   Nb    = T->Nb;
    1054:             const PetscInt   Nc    = T->Nc;
    1055:             for (fc = 0; fc < Nc; ++fc) {
    1056:               interpolant[p*ctx->dof+c+fc] = 0.0;
    1057:               for (f = 0; f < Nb; ++f) {
    1058:                 interpolant[p*ctx->dof+c+fc] += xa[f]*basis[(0*Nb + f)*Nc + fc];
    1059:               }
    1060:             }
    1061:           }
    1062:           PetscTabulationDestroy(&T);
    1063:           DMPlexVecRestoreClosure(dm, NULL, x, ctx->cells[p], NULL, &xa);
    1064:         }
    1065:         VecRestoreArrayWrite(v, &interpolant);
    1066:         VecRestoreArrayRead(ctx->coords, &coords);
    1067:         c += Nc;
    1068:       }
    1069:       if (field == Nf) {
    1070:         done = PETSC_TRUE;
    1071:         if (c != ctx->dof) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Total components %D != %D dof specified for interpolation", c, ctx->dof);
    1072:       }
    1073:     }
    1074:     if (!done) {
    1075:       /* TODO Check each cell individually */
    1076:       DMPlexGetCellType(dm, ctx->cells[0], &ct);
    1077:       switch (ct) {
    1078:         case DM_POLYTOPE_TRIANGLE:      DMInterpolate_Triangle_Private(ctx, dm, x, v);break;
    1079:         case DM_POLYTOPE_QUADRILATERAL: DMInterpolate_Quad_Private(ctx, dm, x, v);break;
    1080:         case DM_POLYTOPE_TETRAHEDRON:   DMInterpolate_Tetrahedron_Private(ctx, dm, x, v);break;
    1081:         case DM_POLYTOPE_HEXAHEDRON:    DMInterpolate_Hex_Private(ctx, dm, x, v);break;
    1082:         default: SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_SUP, "No support fpr cell type %s", DMPolytopeTypes[ct]);
    1083:       }
    1084:     }
    1085:   }
    1086:   return(0);
    1087: }

    1089: /*@C
    1090:   DMInterpolationDestroy - Destroys a DMInterpolationInfo context

    1092:   Collective on ctx

    1094:   Input Parameter:
    1095: . ctx - the context

    1097:   Level: beginner

    1099: .seealso: DMInterpolationEvaluate(), DMInterpolationAddPoints(), DMInterpolationCreate()
    1100: @*/
    1101: PetscErrorCode DMInterpolationDestroy(DMInterpolationInfo *ctx)
    1102: {

    1107:   VecDestroy(&(*ctx)->coords);
    1108:   PetscFree((*ctx)->points);
    1109:   PetscFree((*ctx)->cells);
    1110:   PetscFree(*ctx);
    1111:   *ctx = NULL;
    1112:   return(0);
    1113: }

    1115: /*@C
    1116:   SNESMonitorFields - Monitors the residual for each field separately

    1118:   Collective on SNES

    1120:   Input Parameters:
    1121: + snes   - the SNES context
    1122: . its    - iteration number
    1123: . fgnorm - 2-norm of residual
    1124: - vf  - PetscViewerAndFormat of type ASCII

    1126:   Notes:
    1127:   This routine prints the residual norm at each iteration.

    1129:   Level: intermediate

    1131: .seealso: SNESMonitorSet(), SNESMonitorDefault()
    1132: @*/
    1133: PetscErrorCode SNESMonitorFields(SNES snes, PetscInt its, PetscReal fgnorm, PetscViewerAndFormat *vf)
    1134: {
    1135:   PetscViewer        viewer = vf->viewer;
    1136:   Vec                res;
    1137:   DM                 dm;
    1138:   PetscSection       s;
    1139:   const PetscScalar *r;
    1140:   PetscReal         *lnorms, *norms;
    1141:   PetscInt           numFields, f, pStart, pEnd, p;
    1142:   PetscErrorCode     ierr;

    1146:   SNESGetFunction(snes, &res, NULL, NULL);
    1147:   SNESGetDM(snes, &dm);
    1148:   DMGetLocalSection(dm, &s);
    1149:   PetscSectionGetNumFields(s, &numFields);
    1150:   PetscSectionGetChart(s, &pStart, &pEnd);
    1151:   PetscCalloc2(numFields, &lnorms, numFields, &norms);
    1152:   VecGetArrayRead(res, &r);
    1153:   for (p = pStart; p < pEnd; ++p) {
    1154:     for (f = 0; f < numFields; ++f) {
    1155:       PetscInt fdof, foff, d;

    1157:       PetscSectionGetFieldDof(s, p, f, &fdof);
    1158:       PetscSectionGetFieldOffset(s, p, f, &foff);
    1159:       for (d = 0; d < fdof; ++d) lnorms[f] += PetscRealPart(PetscSqr(r[foff+d]));
    1160:     }
    1161:   }
    1162:   VecRestoreArrayRead(res, &r);
    1163:   MPIU_Allreduce(lnorms, norms, numFields, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject) dm));
    1164:   PetscViewerPushFormat(viewer,vf->format);
    1165:   PetscViewerASCIIAddTab(viewer, ((PetscObject) snes)->tablevel);
    1166:   PetscViewerASCIIPrintf(viewer, "%3D SNES Function norm %14.12e [", its, (double) fgnorm);
    1167:   for (f = 0; f < numFields; ++f) {
    1168:     if (f > 0) {PetscViewerASCIIPrintf(viewer, ", ");}
    1169:     PetscViewerASCIIPrintf(viewer, "%14.12e", (double) PetscSqrtReal(norms[f]));
    1170:   }
    1171:   PetscViewerASCIIPrintf(viewer, "]\n");
    1172:   PetscViewerASCIISubtractTab(viewer, ((PetscObject) snes)->tablevel);
    1173:   PetscViewerPopFormat(viewer);
    1174:   PetscFree2(lnorms, norms);
    1175:   return(0);
    1176: }

    1178: /********************* Residual Computation **************************/

    1180: PetscErrorCode DMPlexGetAllCells_Internal(DM plex, IS *cellIS)
    1181: {
    1182:   PetscInt       depth;

    1186:   DMPlexGetDepth(plex, &depth);
    1187:   DMGetStratumIS(plex, "dim", depth, cellIS);
    1188:   if (!*cellIS) {DMGetStratumIS(plex, "depth", depth, cellIS);}
    1189:   return(0);
    1190: }

    1192: /*@
    1193:   DMPlexSNESComputeResidualFEM - Sums the local residual into vector F from the local input X using pointwise functions specified by the user

    1195:   Input Parameters:
    1196: + dm - The mesh
    1197: . X  - Local solution
    1198: - user - The user context

    1200:   Output Parameter:
    1201: . F  - Local output vector

    1203:   Notes:
    1204:   The residual is summed into F; the caller is responsible for using VecZeroEntries() or otherwise ensuring that any data in F is intentional.

    1206:   Level: developer

    1208: .seealso: DMPlexComputeJacobianAction()
    1209: @*/
    1210: PetscErrorCode DMPlexSNESComputeResidualFEM(DM dm, Vec X, Vec F, void *user)
    1211: {
    1212:   DM             plex;
    1213:   IS             allcellIS;
    1214:   PetscInt       Nds, s;

    1218:   DMSNESConvertPlex(dm, &plex, PETSC_TRUE);
    1219:   DMPlexGetAllCells_Internal(plex, &allcellIS);
    1220:   DMGetNumDS(dm, &Nds);
    1221:   for (s = 0; s < Nds; ++s) {
    1222:     PetscDS          ds;
    1223:     IS               cellIS;
    1224:     PetscHashFormKey key;

    1226:     DMGetRegionNumDS(dm, s, &key.label, NULL, &ds);
    1227:     key.value = 0;
    1228:     key.field = 0;
    1229:     if (!key.label) {
    1230:       PetscObjectReference((PetscObject) allcellIS);
    1231:       cellIS = allcellIS;
    1232:     } else {
    1233:       IS pointIS;

    1235:       key.value = 1;
    1236:       DMLabelGetStratumIS(key.label, key.value, &pointIS);
    1237:       ISIntersect_Caching_Internal(allcellIS, pointIS, &cellIS);
    1238:       ISDestroy(&pointIS);
    1239:     }
    1240:     DMPlexComputeResidual_Internal(plex, key, cellIS, PETSC_MIN_REAL, X, NULL, 0.0, F, user);
    1241:     ISDestroy(&cellIS);
    1242:   }
    1243:   ISDestroy(&allcellIS);
    1244:   DMDestroy(&plex);
    1245:   return(0);
    1246: }

    1248: PetscErrorCode DMSNESComputeResidual(DM dm, Vec X, Vec F, void *user)
    1249: {
    1250:   DM             plex;
    1251:   IS             allcellIS;
    1252:   PetscInt       Nds, s;

    1256:   DMSNESConvertPlex(dm, &plex, PETSC_TRUE);
    1257:   DMPlexGetAllCells_Internal(plex, &allcellIS);
    1258:   DMGetNumDS(dm, &Nds);
    1259:   for (s = 0; s < Nds; ++s) {
    1260:     PetscDS ds;
    1261:     DMLabel label;
    1262:     IS      cellIS;

    1264:     DMGetRegionNumDS(dm, s, &label, NULL, &ds);
    1265:     {
    1266:       PetscHMapForm     resmap[2] = {ds->wf->f0, ds->wf->f1};
    1267:       PetscWeakForm     wf;
    1268:       PetscInt          Nm = 2, m, Nk = 0, k, kp, off = 0;
    1269:       PetscHashFormKey *reskeys;

    1271:       /* Get unique residual keys */
    1272:       for (m = 0; m < Nm; ++m) {
    1273:         PetscInt Nkm;
    1274:         PetscHMapFormGetSize(resmap[m], &Nkm);
    1275:         Nk  += Nkm;
    1276:       }
    1277:       PetscMalloc1(Nk, &reskeys);
    1278:       for (m = 0; m < Nm; ++m) {
    1279:         PetscHMapFormGetKeys(resmap[m], &off, reskeys);
    1280:       }
    1281:       if (off != Nk) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Number of keys %D should be %D", off, Nk);
    1282:       PetscHashFormKeySort(Nk, reskeys);
    1283:       for (k = 0, kp = 1; kp < Nk; ++kp) {
    1284:         if ((reskeys[k].label != reskeys[kp].label) || (reskeys[k].value != reskeys[kp].value)) {
    1285:           ++k;
    1286:           if (kp != k) reskeys[k] = reskeys[kp];
    1287:         }
    1288:       }
    1289:       Nk = k;

    1291:       PetscDSGetWeakForm(ds, &wf);
    1292:       for (k = 0; k < Nk; ++k) {
    1293:         DMLabel  label = reskeys[k].label;
    1294:         PetscInt val   = reskeys[k].value;

    1296:         if (!label) {
    1297:           PetscObjectReference((PetscObject) allcellIS);
    1298:           cellIS = allcellIS;
    1299:         } else {
    1300:           IS pointIS;

    1302:           DMLabelGetStratumIS(label, val, &pointIS);
    1303:           ISIntersect_Caching_Internal(allcellIS, pointIS, &cellIS);
    1304:           ISDestroy(&pointIS);
    1305:         }
    1306:         DMPlexComputeResidual_Internal(plex, reskeys[k], cellIS, PETSC_MIN_REAL, X, NULL, 0.0, F, user);
    1307:         ISDestroy(&cellIS);
    1308:       }
    1309:       PetscFree(reskeys);
    1310:     }
    1311:   }
    1312:   ISDestroy(&allcellIS);
    1313:   DMDestroy(&plex);
    1314:   return(0);
    1315: }

    1317: /*@
    1318:   DMPlexSNESComputeBoundaryFEM - Form the boundary values for the local input X

    1320:   Input Parameters:
    1321: + dm - The mesh
    1322: - user - The user context

    1324:   Output Parameter:
    1325: . X  - Local solution

    1327:   Level: developer

    1329: .seealso: DMPlexComputeJacobianAction()
    1330: @*/
    1331: PetscErrorCode DMPlexSNESComputeBoundaryFEM(DM dm, Vec X, void *user)
    1332: {
    1333:   DM             plex;

    1337:   DMSNESConvertPlex(dm,&plex,PETSC_TRUE);
    1338:   DMPlexInsertBoundaryValues(plex, PETSC_TRUE, X, PETSC_MIN_REAL, NULL, NULL, NULL);
    1339:   DMDestroy(&plex);
    1340:   return(0);
    1341: }

    1343: /*@
    1344:   DMPlexComputeJacobianAction - Form the local portion of the Jacobian action Z = J(X) Y at the local solution X using pointwise functions specified by the user.

    1346:   Input Parameters:
    1347: + dm - The mesh
    1348: . cellIS - index set for the cells or NULL to use entire depth=dim stratum
    1349: . t  - The time
    1350: . X_tShift - The multiplier for the Jacobian with respect to X_t
    1351: . X  - Local solution vector
    1352: . X_t  - Time-derivative of the local solution vector
    1353: . Y  - Local input vector
    1354: - user - The user context

    1356:   Output Parameter:
    1357: . Z - Local output vector

    1359:   Note:
    1360:   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
    1361:   like a GPU, or vectorize on a multicore machine.

    1363:   Level: developer

    1365: .seealso: DMPlexSNESComputeResidualFEM()
    1366: @*/
    1367: PetscErrorCode DMPlexComputeJacobianAction(DM dm, IS cellIS, PetscReal t, PetscReal X_tShift, Vec X, Vec X_t, Vec Y, Vec Z, void *user)
    1368: {
    1369:   DM_Plex          *mesh  = (DM_Plex *) dm->data;
    1370:   const char       *name  = "Jacobian";
    1371:   DM                dmAux, plex, plexAux = NULL;
    1372:   DMEnclosureType   encAux;
    1373:   Vec               A;
    1374:   PetscDS           prob, probAux = NULL;
    1375:   PetscQuadrature   quad;
    1376:   PetscSection      section, globalSection, sectionAux;
    1377:   PetscScalar      *elemMat, *elemMatD, *u, *u_t, *a = NULL, *y, *z;
    1378:   PetscInt          Nf, fieldI, fieldJ;
    1379:   PetscInt          totDim, totDimAux = 0;
    1380:   const PetscInt   *cells;
    1381:   PetscInt          cStart, cEnd, numCells, c;
    1382:   PetscBool         hasDyn;
    1383:   DMField           coordField;
    1384:   PetscHashFormKey  key;
    1385:   PetscErrorCode    ierr;

    1388:   PetscLogEventBegin(DMPLEX_JacobianFEM,dm,0,0,0);
    1389:   DMSNESConvertPlex(dm, &plex, PETSC_TRUE);
    1390:   if (!cellIS) {
    1391:     PetscInt depth;

    1393:     DMPlexGetDepth(plex, &depth);
    1394:     DMGetStratumIS(plex, "dim", depth, &cellIS);
    1395:     if (!cellIS) {DMGetStratumIS(plex, "depth", depth, &cellIS);}
    1396:   } else {
    1397:     PetscObjectReference((PetscObject) cellIS);
    1398:   }
    1399:   key.label = NULL;
    1400:   key.value = 0;
    1401:   DMGetLocalSection(dm, &section);
    1402:   DMGetGlobalSection(dm, &globalSection);
    1403:   ISGetLocalSize(cellIS, &numCells);
    1404:   ISGetPointRange(cellIS, &cStart, &cEnd, &cells);
    1405:   DMGetCellDS(dm, cells ? cells[cStart] : cStart, &prob);
    1406:   PetscDSGetNumFields(prob, &Nf);
    1407:   PetscDSGetTotalDimension(prob, &totDim);
    1408:   PetscDSHasDynamicJacobian(prob, &hasDyn);
    1409:   hasDyn = hasDyn && (X_tShift != 0.0) ? PETSC_TRUE : PETSC_FALSE;
    1410:   PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);
    1411:   PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);
    1412:   if (dmAux) {
    1413:     DMGetEnclosureRelation(dmAux, dm, &encAux);
    1414:     DMConvert(dmAux, DMPLEX, &plexAux);
    1415:     DMGetLocalSection(plexAux, &sectionAux);
    1416:     DMGetDS(dmAux, &probAux);
    1417:     PetscDSGetTotalDimension(probAux, &totDimAux);
    1418:   }
    1419:   VecSet(Z, 0.0);
    1420:   PetscMalloc6(numCells*totDim,&u,X_t ? numCells*totDim : 0,&u_t,numCells*totDim*totDim,&elemMat,hasDyn ? numCells*totDim*totDim : 0, &elemMatD,numCells*totDim,&y,totDim,&z);
    1421:   if (dmAux) {PetscMalloc1(numCells*totDimAux, &a);}
    1422:   DMGetCoordinateField(dm, &coordField);
    1423:   for (c = cStart; c < cEnd; ++c) {
    1424:     const PetscInt cell = cells ? cells[c] : c;
    1425:     const PetscInt cind = c - cStart;
    1426:     PetscScalar   *x = NULL,  *x_t = NULL;
    1427:     PetscInt       i;

    1429:     DMPlexVecGetClosure(dm, section, X, cell, NULL, &x);
    1430:     for (i = 0; i < totDim; ++i) u[cind*totDim+i] = x[i];
    1431:     DMPlexVecRestoreClosure(dm, section, X, cell, NULL, &x);
    1432:     if (X_t) {
    1433:       DMPlexVecGetClosure(dm, section, X_t, cell, NULL, &x_t);
    1434:       for (i = 0; i < totDim; ++i) u_t[cind*totDim+i] = x_t[i];
    1435:       DMPlexVecRestoreClosure(dm, section, X_t, cell, NULL, &x_t);
    1436:     }
    1437:     if (dmAux) {
    1438:       PetscInt subcell;
    1439:       DMGetEnclosurePoint(dmAux, dm, encAux, cell, &subcell);
    1440:       DMPlexVecGetClosure(plexAux, sectionAux, A, subcell, NULL, &x);
    1441:       for (i = 0; i < totDimAux; ++i) a[cind*totDimAux+i] = x[i];
    1442:       DMPlexVecRestoreClosure(plexAux, sectionAux, A, subcell, NULL, &x);
    1443:     }
    1444:     DMPlexVecGetClosure(dm, section, Y, cell, NULL, &x);
    1445:     for (i = 0; i < totDim; ++i) y[cind*totDim+i] = x[i];
    1446:     DMPlexVecRestoreClosure(dm, section, Y, cell, NULL, &x);
    1447:   }
    1448:   PetscArrayzero(elemMat, numCells*totDim*totDim);
    1449:   if (hasDyn)  {PetscArrayzero(elemMatD, numCells*totDim*totDim);}
    1450:   for (fieldI = 0; fieldI < Nf; ++fieldI) {
    1451:     PetscFE  fe;
    1452:     PetscInt Nb;
    1453:     /* Conforming batches */
    1454:     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
    1455:     /* Remainder */
    1456:     PetscInt Nr, offset, Nq;
    1457:     PetscQuadrature qGeom = NULL;
    1458:     PetscInt    maxDegree;
    1459:     PetscFEGeom *cgeomFEM, *chunkGeom = NULL, *remGeom = NULL;

    1461:     PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fe);
    1462:     PetscFEGetQuadrature(fe, &quad);
    1463:     PetscFEGetDimension(fe, &Nb);
    1464:     PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);
    1465:     DMFieldGetDegree(coordField,cellIS,NULL,&maxDegree);
    1466:     if (maxDegree <= 1) {DMFieldCreateDefaultQuadrature(coordField,cellIS,&qGeom);}
    1467:     if (!qGeom) {
    1468:       PetscFEGetQuadrature(fe,&qGeom);
    1469:       PetscObjectReference((PetscObject)qGeom);
    1470:     }
    1471:     PetscQuadratureGetData(qGeom, NULL, NULL, &Nq, NULL, NULL);
    1472:     DMSNESGetFEGeom(coordField,cellIS,qGeom,PETSC_FALSE,&cgeomFEM);
    1473:     blockSize = Nb;
    1474:     batchSize = numBlocks * blockSize;
    1475:     PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);
    1476:     numChunks = numCells / (numBatches*batchSize);
    1477:     Ne        = numChunks*numBatches*batchSize;
    1478:     Nr        = numCells % (numBatches*batchSize);
    1479:     offset    = numCells - Nr;
    1480:     PetscFEGeomGetChunk(cgeomFEM,0,offset,&chunkGeom);
    1481:     PetscFEGeomGetChunk(cgeomFEM,offset,numCells,&remGeom);
    1482:     for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
    1483:       key.field = fieldI*Nf + fieldJ;
    1484:       PetscFEIntegrateJacobian(prob, PETSCFE_JACOBIAN, key, Ne, chunkGeom, u, u_t, probAux, a, t, X_tShift, elemMat);
    1485:       PetscFEIntegrateJacobian(prob, PETSCFE_JACOBIAN, key, Nr, remGeom, &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], t, X_tShift, &elemMat[offset*totDim*totDim]);
    1486:       if (hasDyn) {
    1487:         PetscFEIntegrateJacobian(prob, PETSCFE_JACOBIAN_DYN, key, Ne, chunkGeom, u, u_t, probAux, a, t, X_tShift, elemMatD);
    1488:         PetscFEIntegrateJacobian(prob, PETSCFE_JACOBIAN_DYN, key, Nr, remGeom, &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], t, X_tShift, &elemMatD[offset*totDim*totDim]);
    1489:       }
    1490:     }
    1491:     PetscFEGeomRestoreChunk(cgeomFEM,offset,numCells,&remGeom);
    1492:     PetscFEGeomRestoreChunk(cgeomFEM,0,offset,&chunkGeom);
    1493:     DMSNESRestoreFEGeom(coordField,cellIS,qGeom,PETSC_FALSE,&cgeomFEM);
    1494:     PetscQuadratureDestroy(&qGeom);
    1495:   }
    1496:   if (hasDyn) {
    1497:     for (c = 0; c < numCells*totDim*totDim; ++c) elemMat[c] += X_tShift*elemMatD[c];
    1498:   }
    1499:   for (c = cStart; c < cEnd; ++c) {
    1500:     const PetscInt     cell = cells ? cells[c] : c;
    1501:     const PetscInt     cind = c - cStart;
    1502:     const PetscBLASInt M = totDim, one = 1;
    1503:     const PetscScalar  a = 1.0, b = 0.0;

    1505:     PetscStackCallBLAS("BLASgemv", BLASgemv_("N", &M, &M, &a, &elemMat[cind*totDim*totDim], &M, &y[cind*totDim], &one, &b, z, &one));
    1506:     if (mesh->printFEM > 1) {
    1507:       DMPrintCellMatrix(c, name, totDim, totDim, &elemMat[cind*totDim*totDim]);
    1508:       DMPrintCellVector(c, "Y",  totDim, &y[cind*totDim]);
    1509:       DMPrintCellVector(c, "Z",  totDim, z);
    1510:     }
    1511:     DMPlexVecSetClosure(dm, section, Z, cell, z, ADD_VALUES);
    1512:   }
    1513:   PetscFree6(u,u_t,elemMat,elemMatD,y,z);
    1514:   if (mesh->printFEM) {
    1515:     PetscPrintf(PetscObjectComm((PetscObject)Z), "Z:\n");
    1516:     VecView(Z, NULL);
    1517:   }
    1518:   PetscFree(a);
    1519:   ISDestroy(&cellIS);
    1520:   DMDestroy(&plexAux);
    1521:   DMDestroy(&plex);
    1522:   PetscLogEventEnd(DMPLEX_JacobianFEM,dm,0,0,0);
    1523:   return(0);
    1524: }

    1526: /*@
    1527:   DMPlexSNESComputeJacobianFEM - Form the local portion of the Jacobian matrix J at the local solution X using pointwise functions specified by the user.

    1529:   Input Parameters:
    1530: + dm - The mesh
    1531: . X  - Local input vector
    1532: - user - The user context

    1534:   Output Parameter:
    1535: . Jac  - Jacobian matrix

    1537:   Note:
    1538:   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
    1539:   like a GPU, or vectorize on a multicore machine.

    1541:   Level: developer

    1543: .seealso: FormFunctionLocal()
    1544: @*/
    1545: PetscErrorCode DMPlexSNESComputeJacobianFEM(DM dm, Vec X, Mat Jac, Mat JacP,void *user)
    1546: {
    1547:   DM             plex;
    1548:   IS             allcellIS;
    1549:   PetscBool      hasJac, hasPrec;
    1550:   PetscInt       Nds, s;

    1554:   DMSNESConvertPlex(dm, &plex, PETSC_TRUE);
    1555:   DMPlexGetAllCells_Internal(plex, &allcellIS);
    1556:   DMGetNumDS(dm, &Nds);
    1557:   for (s = 0; s < Nds; ++s) {
    1558:     PetscDS          ds;
    1559:     IS               cellIS;
    1560:     PetscHashFormKey key;

    1562:     DMGetRegionNumDS(dm, s, &key.label, NULL, &ds);
    1563:     key.value = 0;
    1564:     key.field = 0;
    1565:     if (!key.label) {
    1566:       PetscObjectReference((PetscObject) allcellIS);
    1567:       cellIS = allcellIS;
    1568:     } else {
    1569:       IS pointIS;

    1571:       key.value = 1;
    1572:       DMLabelGetStratumIS(key.label, key.value, &pointIS);
    1573:       ISIntersect_Caching_Internal(allcellIS, pointIS, &cellIS);
    1574:       ISDestroy(&pointIS);
    1575:     }
    1576:     if (!s) {
    1577:       PetscDSHasJacobian(ds, &hasJac);
    1578:       PetscDSHasJacobianPreconditioner(ds, &hasPrec);
    1579:       if (hasJac && hasPrec) {MatZeroEntries(Jac);}
    1580:       MatZeroEntries(JacP);
    1581:     }
    1582:     DMPlexComputeJacobian_Internal(plex, key, cellIS, 0.0, 0.0, X, NULL, Jac, JacP, user);
    1583:     ISDestroy(&cellIS);
    1584:   }
    1585:   ISDestroy(&allcellIS);
    1586:   DMDestroy(&plex);
    1587:   return(0);
    1588: }

    1590: /*
    1591:      MatComputeNeumannOverlap - Computes an unassembled (Neumann) local overlapping Mat in nonlinear context.

    1593:    Input Parameters:
    1594: +     X - SNES linearization point
    1595: .     ovl - index set of overlapping subdomains

    1597:    Output Parameter:
    1598: .     J - unassembled (Neumann) local matrix

    1600:    Level: intermediate

    1602: .seealso: DMCreateNeumannOverlap(), MATIS, PCHPDDMSetAuxiliaryMat()
    1603: */
    1604: static PetscErrorCode MatComputeNeumannOverlap_Plex(Mat J, PetscReal t, Vec X, Vec X_t, PetscReal s, IS ovl, void *ctx)
    1605: {
    1606:   SNES           snes;
    1607:   Mat            pJ;
    1608:   DM             ovldm,origdm;
    1609:   DMSNES         sdm;
    1610:   PetscErrorCode (*bfun)(DM,Vec,void*);
    1611:   PetscErrorCode (*jfun)(DM,Vec,Mat,Mat,void*);
    1612:   void           *bctx,*jctx;

    1616:   PetscObjectQuery((PetscObject)ovl,"_DM_Overlap_HPDDM_MATIS",(PetscObject*)&pJ);
    1617:   if (!pJ) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Missing overlapping Mat");
    1618:   PetscObjectQuery((PetscObject)ovl,"_DM_Original_HPDDM",(PetscObject*)&origdm);
    1619:   if (!origdm) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Missing original DM");
    1620:   MatGetDM(pJ,&ovldm);
    1621:   DMSNESGetBoundaryLocal(origdm,&bfun,&bctx);
    1622:   DMSNESSetBoundaryLocal(ovldm,bfun,bctx);
    1623:   DMSNESGetJacobianLocal(origdm,&jfun,&jctx);
    1624:   DMSNESSetJacobianLocal(ovldm,jfun,jctx);
    1625:   PetscObjectQuery((PetscObject)ovl,"_DM_Overlap_HPDDM_SNES",(PetscObject*)&snes);
    1626:   if (!snes) {
    1627:     SNESCreate(PetscObjectComm((PetscObject)ovl),&snes);
    1628:     SNESSetDM(snes,ovldm);
    1629:     PetscObjectCompose((PetscObject)ovl,"_DM_Overlap_HPDDM_SNES",(PetscObject)snes);
    1630:     PetscObjectDereference((PetscObject)snes);
    1631:   }
    1632:   DMGetDMSNES(ovldm,&sdm);
    1633:   VecLockReadPush(X);
    1634:   PetscStackPush("SNES user Jacobian function");
    1635:   (*sdm->ops->computejacobian)(snes,X,pJ,pJ,sdm->jacobianctx);
    1636:   PetscStackPop;
    1637:   VecLockReadPop(X);
    1638:   /* this is a no-hop, just in case we decide to change the placeholder for the local Neumann matrix */
    1639:   {
    1640:     Mat locpJ;

    1642:     MatISGetLocalMat(pJ,&locpJ);
    1643:     MatCopy(locpJ,J,SAME_NONZERO_PATTERN);
    1644:   }
    1645:   return(0);
    1646: }

    1648: /*@
    1649:   DMPlexSetSNESLocalFEM - Use DMPlex's internal FEM routines to compute SNES boundary values, residual, and Jacobian.

    1651:   Input Parameters:
    1652: + dm - The DM object
    1653: . boundaryctx - the user context that will be passed to pointwise evaluation of boundary values (see PetscDSAddBoundary())
    1654: . residualctx - the user context that will be passed to pointwise evaluation of finite element residual computations (see PetscDSSetResidual())
    1655: - jacobianctx - the user context that will be passed to pointwise evaluation of finite element Jacobian construction (see PetscDSSetJacobian())

    1657:   Level: developer
    1658: @*/
    1659: PetscErrorCode DMPlexSetSNESLocalFEM(DM dm, void *boundaryctx, void *residualctx, void *jacobianctx)
    1660: {

    1664:   DMSNESSetBoundaryLocal(dm,DMPlexSNESComputeBoundaryFEM,boundaryctx);
    1665:   DMSNESSetFunctionLocal(dm,DMPlexSNESComputeResidualFEM,residualctx);
    1666:   DMSNESSetJacobianLocal(dm,DMPlexSNESComputeJacobianFEM,jacobianctx);
    1667:   PetscObjectComposeFunction((PetscObject)dm,"MatComputeNeumannOverlap_C",MatComputeNeumannOverlap_Plex);
    1668:   return(0);
    1669: }

    1671: /*@C
    1672:   DMSNESCheckDiscretization - Check the discretization error of the exact solution

    1674:   Input Parameters:
    1675: + snes - the SNES object
    1676: . dm   - the DM
    1677: . t    - the time
    1678: . u    - a DM vector
    1679: - tol  - A tolerance for the check, or -1 to print the results instead

    1681:   Output Parameters:
    1682: . error - An array which holds the discretization error in each field, or NULL

    1684:   Note: The user must call PetscDSSetExactSolution() beforehand

    1686:   Level: developer

    1688: .seealso: DNSNESCheckFromOptions(), DMSNESCheckResidual(), DMSNESCheckJacobian(), PetscDSSetExactSolution()
    1689: @*/
    1690: PetscErrorCode DMSNESCheckDiscretization(SNES snes, DM dm, PetscReal t, Vec u, PetscReal tol, PetscReal error[])
    1691: {
    1692:   PetscErrorCode (**exacts)(PetscInt, PetscReal, const PetscReal x[], PetscInt, PetscScalar *u, void *ctx);
    1693:   void            **ectxs;
    1694:   PetscReal        *err;
    1695:   MPI_Comm          comm;
    1696:   PetscInt          Nf, f;
    1697:   PetscErrorCode    ierr;

    1705:   DMComputeExactSolution(dm, t, u, NULL);
    1706:   VecViewFromOptions(u, NULL, "-vec_view");

    1708:   PetscObjectGetComm((PetscObject) snes, &comm);
    1709:   DMGetNumFields(dm, &Nf);
    1710:   PetscCalloc3(Nf, &exacts, Nf, &ectxs, PetscMax(1, Nf), &err);
    1711:   {
    1712:     PetscInt Nds, s;

    1714:     DMGetNumDS(dm, &Nds);
    1715:     for (s = 0; s < Nds; ++s) {
    1716:       PetscDS         ds;
    1717:       DMLabel         label;
    1718:       IS              fieldIS;
    1719:       const PetscInt *fields;
    1720:       PetscInt        dsNf, f;

    1722:       DMGetRegionNumDS(dm, s, &label, &fieldIS, &ds);
    1723:       PetscDSGetNumFields(ds, &dsNf);
    1724:       ISGetIndices(fieldIS, &fields);
    1725:       for (f = 0; f < dsNf; ++f) {
    1726:         const PetscInt field = fields[f];
    1727:         PetscDSGetExactSolution(ds, field, &exacts[field], &ectxs[field]);
    1728:       }
    1729:       ISRestoreIndices(fieldIS, &fields);
    1730:     }
    1731:   }
    1732:   if (Nf > 1) {
    1733:     DMComputeL2FieldDiff(dm, t, exacts, ectxs, u, err);
    1734:     if (tol >= 0.0) {
    1735:       for (f = 0; f < Nf; ++f) {
    1736:         if (err[f] > tol) SETERRQ3(comm, PETSC_ERR_ARG_WRONG, "L_2 Error %g for field %D exceeds tolerance %g", (double) err[f], f, (double) tol);
    1737:       }
    1738:     } else if (error) {
    1739:       for (f = 0; f < Nf; ++f) error[f] = err[f];
    1740:     } else {
    1741:       PetscPrintf(comm, "L_2 Error: [");
    1742:       for (f = 0; f < Nf; ++f) {
    1743:         if (f) {PetscPrintf(comm, ", ");}
    1744:         PetscPrintf(comm, "%g", (double)err[f]);
    1745:       }
    1746:       PetscPrintf(comm, "]\n");
    1747:     }
    1748:   } else {
    1749:     DMComputeL2Diff(dm, t, exacts, ectxs, u, &err[0]);
    1750:     if (tol >= 0.0) {
    1751:       if (err[0] > tol) SETERRQ2(comm, PETSC_ERR_ARG_WRONG, "L_2 Error %g exceeds tolerance %g", (double) err[0], (double) tol);
    1752:     } else if (error) {
    1753:       error[0] = err[0];
    1754:     } else {
    1755:       PetscPrintf(comm, "L_2 Error: %g\n", (double) err[0]);
    1756:     }
    1757:   }
    1758:   PetscFree3(exacts, ectxs, err);
    1759:   return(0);
    1760: }

    1762: /*@C
    1763:   DMSNESCheckResidual - Check the residual of the exact solution

    1765:   Input Parameters:
    1766: + snes - the SNES object
    1767: . dm   - the DM
    1768: . u    - a DM vector
    1769: - tol  - A tolerance for the check, or -1 to print the results instead

    1771:   Output Parameters:
    1772: . residual - The residual norm of the exact solution, or NULL

    1774:   Level: developer

    1776: .seealso: DNSNESCheckFromOptions(), DMSNESCheckDiscretization(), DMSNESCheckJacobian()
    1777: @*/
    1778: PetscErrorCode DMSNESCheckResidual(SNES snes, DM dm, Vec u, PetscReal tol, PetscReal *residual)
    1779: {
    1780:   MPI_Comm       comm;
    1781:   Vec            r;
    1782:   PetscReal      res;

    1790:   PetscObjectGetComm((PetscObject) snes, &comm);
    1791:   DMComputeExactSolution(dm, 0.0, u, NULL);
    1792:   VecDuplicate(u, &r);
    1793:   SNESComputeFunction(snes, u, r);
    1794:   VecNorm(r, NORM_2, &res);
    1795:   if (tol >= 0.0) {
    1796:     if (res > tol) SETERRQ2(comm, PETSC_ERR_ARG_WRONG, "L_2 Residual %g exceeds tolerance %g", (double) res, (double) tol);
    1797:   } else if (residual) {
    1798:     *residual = res;
    1799:   } else {
    1800:     PetscPrintf(comm, "L_2 Residual: %g\n", (double)res);
    1801:     VecChop(r, 1.0e-10);
    1802:     PetscObjectSetName((PetscObject) r, "Initial Residual");
    1803:     PetscObjectSetOptionsPrefix((PetscObject)r,"res_");
    1804:     VecViewFromOptions(r, NULL, "-vec_view");
    1805:   }
    1806:   VecDestroy(&r);
    1807:   return(0);
    1808: }

    1810: /*@C
    1811:   DMSNESCheckJacobian - Check the Jacobian of the exact solution against the residual using the Taylor Test

    1813:   Input Parameters:
    1814: + snes - the SNES object
    1815: . dm   - the DM
    1816: . u    - a DM vector
    1817: - tol  - A tolerance for the check, or -1 to print the results instead

    1819:   Output Parameters:
    1820: + isLinear - Flag indicaing that the function looks linear, or NULL
    1821: - convRate - The rate of convergence of the linear model, or NULL

    1823:   Level: developer

    1825: .seealso: DNSNESCheckFromOptions(), DMSNESCheckDiscretization(), DMSNESCheckResidual()
    1826: @*/
    1827: PetscErrorCode DMSNESCheckJacobian(SNES snes, DM dm, Vec u, PetscReal tol, PetscBool *isLinear, PetscReal *convRate)
    1828: {
    1829:   MPI_Comm       comm;
    1830:   PetscDS        ds;
    1831:   Mat            J, M;
    1832:   MatNullSpace   nullspace;
    1833:   PetscReal      slope, intercept;
    1834:   PetscBool      hasJac, hasPrec, isLin = PETSC_FALSE;

    1843:   PetscObjectGetComm((PetscObject) snes, &comm);
    1844:   DMComputeExactSolution(dm, 0.0, u, NULL);
    1845:   /* Create and view matrices */
    1846:   DMCreateMatrix(dm, &J);
    1847:   DMGetDS(dm, &ds);
    1848:   PetscDSHasJacobian(ds, &hasJac);
    1849:   PetscDSHasJacobianPreconditioner(ds, &hasPrec);
    1850:   if (hasJac && hasPrec) {
    1851:     DMCreateMatrix(dm, &M);
    1852:     SNESComputeJacobian(snes, u, J, M);
    1853:     PetscObjectSetName((PetscObject) M, "Preconditioning Matrix");
    1854:     PetscObjectSetOptionsPrefix((PetscObject) M, "jacpre_");
    1855:     MatViewFromOptions(M, NULL, "-mat_view");
    1856:     MatDestroy(&M);
    1857:   } else {
    1858:     SNESComputeJacobian(snes, u, J, J);
    1859:   }
    1860:   PetscObjectSetName((PetscObject) J, "Jacobian");
    1861:   PetscObjectSetOptionsPrefix((PetscObject) J, "jac_");
    1862:   MatViewFromOptions(J, NULL, "-mat_view");
    1863:   /* Check nullspace */
    1864:   MatGetNullSpace(J, &nullspace);
    1865:   if (nullspace) {
    1866:     PetscBool isNull;
    1867:     MatNullSpaceTest(nullspace, J, &isNull);
    1868:     if (!isNull) SETERRQ(comm, PETSC_ERR_PLIB, "The null space calculated for the system operator is invalid.");
    1869:   }
    1870:   /* Taylor test */
    1871:   {
    1872:     PetscRandom rand;
    1873:     Vec         du, uhat, r, rhat, df;
    1874:     PetscReal   h;
    1875:     PetscReal  *es, *hs, *errors;
    1876:     PetscReal   hMax = 1.0, hMin = 1e-6, hMult = 0.1;
    1877:     PetscInt    Nv, v;

    1879:     /* Choose a perturbation direction */
    1880:     PetscRandomCreate(comm, &rand);
    1881:     VecDuplicate(u, &du);
    1882:     VecSetRandom(du, rand);
    1883:     PetscRandomDestroy(&rand);
    1884:     VecDuplicate(u, &df);
    1885:     MatMult(J, du, df);
    1886:     /* Evaluate residual at u, F(u), save in vector r */
    1887:     VecDuplicate(u, &r);
    1888:     SNESComputeFunction(snes, u, r);
    1889:     /* Look at the convergence of our Taylor approximation as we approach u */
    1890:     for (h = hMax, Nv = 0; h >= hMin; h *= hMult, ++Nv);
    1891:     PetscCalloc3(Nv, &es, Nv, &hs, Nv, &errors);
    1892:     VecDuplicate(u, &uhat);
    1893:     VecDuplicate(u, &rhat);
    1894:     for (h = hMax, Nv = 0; h >= hMin; h *= hMult, ++Nv) {
    1895:       VecWAXPY(uhat, h, du, u);
    1896:       /* F(\hat u) \approx F(u) + J(u) (uhat - u) = F(u) + h * J(u) du */
    1897:       SNESComputeFunction(snes, uhat, rhat);
    1898:       VecAXPBYPCZ(rhat, -1.0, -h, 1.0, r, df);
    1899:       VecNorm(rhat, NORM_2, &errors[Nv]);

    1901:       es[Nv] = PetscLog10Real(errors[Nv]);
    1902:       hs[Nv] = PetscLog10Real(h);
    1903:     }
    1904:     VecDestroy(&uhat);
    1905:     VecDestroy(&rhat);
    1906:     VecDestroy(&df);
    1907:     VecDestroy(&r);
    1908:     VecDestroy(&du);
    1909:     for (v = 0; v < Nv; ++v) {
    1910:       if ((tol >= 0) && (errors[v] > tol)) break;
    1911:       else if (errors[v] > PETSC_SMALL)    break;
    1912:     }
    1913:     if (v == Nv) isLin = PETSC_TRUE;
    1914:     PetscLinearRegression(Nv, hs, es, &slope, &intercept);
    1915:     PetscFree3(es, hs, errors);
    1916:     /* Slope should be about 2 */
    1917:     if (tol >= 0) {
    1918:       if (!isLin && PetscAbsReal(2 - slope) > tol) SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Taylor approximation convergence rate should be 2, not %0.2f", (double) slope);
    1919:     } else if (isLinear || convRate) {
    1920:       if (isLinear) *isLinear = isLin;
    1921:       if (convRate) *convRate = slope;
    1922:     } else {
    1923:       if (!isLin) {PetscPrintf(comm, "Taylor approximation converging at order %3.2f\n", (double) slope);}
    1924:       else        {PetscPrintf(comm, "Function appears to be linear\n");}
    1925:     }
    1926:   }
    1927:   MatDestroy(&J);
    1928:   return(0);
    1929: }

    1931: PetscErrorCode DMSNESCheck_Internal(SNES snes, DM dm, Vec u)
    1932: {

    1936:   DMSNESCheckDiscretization(snes, dm, 0.0, u, -1.0, NULL);
    1937:   DMSNESCheckResidual(snes, dm, u, -1.0, NULL);
    1938:   DMSNESCheckJacobian(snes, dm, u, -1.0, NULL, NULL);
    1939:   return(0);
    1940: }

    1942: /*@C
    1943:   DMSNESCheckFromOptions - Check the residual and Jacobian functions using the exact solution by outputting some diagnostic information

    1945:   Input Parameters:
    1946: + snes - the SNES object
    1947: - u    - representative SNES vector

    1949:   Note: The user must call PetscDSSetExactSolution() beforehand

    1951:   Level: developer
    1952: @*/
    1953: PetscErrorCode DMSNESCheckFromOptions(SNES snes, Vec u)
    1954: {
    1955:   DM             dm;
    1956:   Vec            sol;
    1957:   PetscBool      check;

    1961:   PetscOptionsHasName(((PetscObject)snes)->options,((PetscObject)snes)->prefix, "-dmsnes_check", &check);
    1962:   if (!check) return(0);
    1963:   SNESGetDM(snes, &dm);
    1964:   VecDuplicate(u, &sol);
    1965:   SNESSetSolution(snes, sol);
    1966:   DMSNESCheck_Internal(snes, dm, sol);
    1967:   VecDestroy(&sol);
    1968:   return(0);
    1969: }