static PetscErrorCode DMPlexTSSetupGradient(DM dm, PetscFV fvm, DMTS_Plex *dmplexts)
{
DM dmFace, dmCell;
PetscScalar *fgeom, *cgeom;
PetscSection sectionGrad;
PetscInt dim, pdim, cStart, cEnd, cEndInterior, c;
PetscErrorCode ierr;
PetscFunctionBegin;
if (dmplexts->setupGrad) PetscFunctionReturn(0);
ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
ierr = PetscFVGetNumComponents(fvm, &pdim);CHKERRQ(ierr);
ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
ierr = DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
/* Construct the interpolant corresponding to each face from the leat-square solution over the cell neighborhood */
ierr = VecGetDM(dmplexts->facegeom, &dmFace);CHKERRQ(ierr);
ierr = VecGetDM(dmplexts->cellgeom, &dmCell);CHKERRQ(ierr);
ierr = VecGetArray(dmplexts->facegeom, &fgeom);CHKERRQ(ierr);
ierr = VecGetArray(dmplexts->cellgeom, &cgeom);CHKERRQ(ierr);
ierr = BuildGradientReconstruction(dm, fvm, dmFace, fgeom, dmCell, cgeom);CHKERRQ(ierr);
ierr = VecRestoreArray(dmplexts->facegeom, &fgeom);CHKERRQ(ierr);
ierr = VecRestoreArray(dmplexts->cellgeom, &cgeom);CHKERRQ(ierr);
/* Create storage for gradients */
ierr = DMClone(dm, &dmplexts->dmGrad);CHKERRQ(ierr);
ierr = PetscSectionCreate(PetscObjectComm((PetscObject) dm), §ionGrad);CHKERRQ(ierr);
ierr = PetscSectionSetChart(sectionGrad, cStart, cEnd);CHKERRQ(ierr);
for (c = cStart; c < cEnd; ++c) {ierr = PetscSectionSetDof(sectionGrad, c, pdim*dim);CHKERRQ(ierr);}
ierr = PetscSectionSetUp(sectionGrad);CHKERRQ(ierr);
ierr = DMSetDefaultSection(dmplexts->dmGrad, sectionGrad);CHKERRQ(ierr);
ierr = PetscSectionDestroy(§ionGrad);CHKERRQ(ierr);
dmplexts->setupGrad = PETSC_TRUE;
PetscFunctionReturn(0);
}
static PetscErrorCode CreateAuxiliaryData(DM dm, DM *auxdm, Vec *la, AppCtx *user)
{
PetscErrorCode (**afuncs)(PetscInt, PetscReal, const PetscReal [], PetscInt, PetscScalar *, void *);
PetscInt dim, Nf, f;
PetscErrorCode ierr;
PetscFunctionBeginUser;
ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
ierr = DMGetNumFields(dm, &Nf);CHKERRQ(ierr);
ierr = PetscMalloc1(Nf, &afuncs);CHKERRQ(ierr);
for (f = 0; f < Nf; ++f) afuncs[f] = linear;
ierr = DMClone(dm, auxdm);CHKERRQ(ierr);
ierr = SetupDiscretization(*auxdm, dim, user->cellSimplex, user);CHKERRQ(ierr);
ierr = DMCreateLocalVector(*auxdm, la);CHKERRQ(ierr);
ierr = DMProjectFunctionLocal(dm, 0.0, afuncs, NULL, INSERT_VALUES, *la);CHKERRQ(ierr);
ierr = VecViewFromOptions(*la, NULL, "-local_aux_view");CHKERRQ(ierr);
ierr = PetscFree(afuncs);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
int main(int argc,char **args)
{
Mat Amat;
PetscErrorCode ierr;
SNES snes;
KSP ksp;
MPI_Comm comm;
PetscMPIInt npe,rank;
PetscLogStage stage[7];
PetscBool test_nonzero_cols=PETSC_FALSE,use_nearnullspace=PETSC_TRUE;
Vec xx,bb;
PetscInt iter,i,N,dim=3,cells[3]={1,1,1},max_conv_its,local_sizes[7],run_type=1;
DM dm,distdm,basedm;
PetscBool flg;
char convType[256];
PetscReal Lx,mdisp[10],err[10];
const char * const options[10] = {"-ex56_dm_refine 0",
"-ex56_dm_refine 1",
"-ex56_dm_refine 2",
"-ex56_dm_refine 3",
"-ex56_dm_refine 4",
"-ex56_dm_refine 5",
"-ex56_dm_refine 6",
"-ex56_dm_refine 7",
"-ex56_dm_refine 8",
"-ex56_dm_refine 9"};
PetscFunctionBeginUser;
ierr = PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
comm = PETSC_COMM_WORLD;
ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
ierr = MPI_Comm_size(comm, &npe);CHKERRQ(ierr);
/* options */
ierr = PetscOptionsBegin(comm,NULL,"3D bilinear Q1 elasticity options","");CHKERRQ(ierr);
{
i = 3;
ierr = PetscOptionsIntArray("-cells", "Number of (flux tube) processor in each dimension", "ex56.c", cells, &i, NULL);CHKERRQ(ierr);
Lx = 1.; /* or ne for rod */
max_conv_its = 3;
ierr = PetscOptionsInt("-max_conv_its","Number of iterations in convergence study","",max_conv_its,&max_conv_its,NULL);CHKERRQ(ierr);
if (max_conv_its<=0 || max_conv_its>7) SETERRQ1(PETSC_COMM_WORLD, PETSC_ERR_USER, "Bad number of iterations for convergence test (%D)",max_conv_its);
ierr = PetscOptionsReal("-lx","Length of domain","",Lx,&Lx,NULL);CHKERRQ(ierr);
ierr = PetscOptionsReal("-alpha","material coefficient inside circle","",s_soft_alpha,&s_soft_alpha,NULL);CHKERRQ(ierr);
ierr = PetscOptionsBool("-test_nonzero_cols","nonzero test","",test_nonzero_cols,&test_nonzero_cols,NULL);CHKERRQ(ierr);
ierr = PetscOptionsBool("-use_mat_nearnullspace","MatNearNullSpace API test","",use_nearnullspace,&use_nearnullspace,NULL);CHKERRQ(ierr);
ierr = PetscOptionsInt("-run_type","0: twisting load on cantalever, 1: 3rd order accurate convergence test","",run_type,&run_type,NULL);CHKERRQ(ierr);
i = 3;
ierr = PetscOptionsInt("-mat_block_size","","",i,&i,&flg);CHKERRQ(ierr);
if (!flg || i!=3) SETERRQ2(PETSC_COMM_WORLD, PETSC_ERR_USER, "'-mat_block_size 3' must be set (%D) and = 3 (%D)",flg,flg? i : 3);
}
ierr = PetscOptionsEnd();CHKERRQ(ierr);
ierr = PetscLogStageRegister("Mesh Setup", &stage[6]);CHKERRQ(ierr);
ierr = PetscLogStageRegister("1st Setup", &stage[0]);CHKERRQ(ierr);
ierr = PetscLogStageRegister("1st Solve", &stage[1]);CHKERRQ(ierr);
/* create DM, Plex calls DMSetup */
ierr = PetscLogStagePush(stage[6]);CHKERRQ(ierr);
ierr = DMPlexCreateHexBoxMesh(comm, dim, cells, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, &dm);CHKERRQ(ierr);
{
DMLabel label;
IS is;
ierr = DMCreateLabel(dm, "boundary");CHKERRQ(ierr);
ierr = DMGetLabel(dm, "boundary", &label);CHKERRQ(ierr);
ierr = DMPlexMarkBoundaryFaces(dm, label);CHKERRQ(ierr);
if (run_type==0) {
ierr = DMGetStratumIS(dm, "boundary", 1, &is);CHKERRQ(ierr);
ierr = DMCreateLabel(dm,"Faces");CHKERRQ(ierr);
if (is) {
PetscInt d, f, Nf;
const PetscInt *faces;
PetscInt csize;
PetscSection cs;
Vec coordinates ;
DM cdm;
ierr = ISGetLocalSize(is, &Nf);CHKERRQ(ierr);
ierr = ISGetIndices(is, &faces);CHKERRQ(ierr);
ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
ierr = DMGetCoordinateDM(dm, &cdm);CHKERRQ(ierr);
ierr = DMGetDefaultSection(cdm, &cs);CHKERRQ(ierr);
/* Check for each boundary face if any component of its centroid is either 0.0 or 1.0 */
for (f = 0; f < Nf; ++f) {
PetscReal faceCoord;
PetscInt b,v;
PetscScalar *coords = NULL;
PetscInt Nv;
ierr = DMPlexVecGetClosure(cdm, cs, coordinates, faces[f], &csize, &coords);CHKERRQ(ierr);
Nv = csize/dim; /* Calculate mean coordinate vector */
for (d = 0; d < dim; ++d) {
faceCoord = 0.0;
for (v = 0; v < Nv; ++v) faceCoord += PetscRealPart(coords[v*dim+d]);
faceCoord /= Nv;
for (b = 0; b < 2; ++b) {
if (PetscAbs(faceCoord - b) < PETSC_SMALL) { /* domain have not been set yet, still [0,1]^3 */
ierr = DMSetLabelValue(dm, "Faces", faces[f], d*2+b+1);CHKERRQ(ierr);
}
}
}
ierr = DMPlexVecRestoreClosure(cdm, cs, coordinates, faces[f], &csize, &coords);CHKERRQ(ierr);
}
ierr = ISRestoreIndices(is, &faces);CHKERRQ(ierr);
}
ierr = ISDestroy(&is);CHKERRQ(ierr);
ierr = DMGetLabel(dm, "Faces", &label);CHKERRQ(ierr);
ierr = DMPlexLabelComplete(dm, label);CHKERRQ(ierr);
}
}
{
PetscInt dimEmbed, i;
PetscInt nCoords;
PetscScalar *coords,bounds[] = {0,Lx,-.5,.5,-.5,.5,}; /* x_min,x_max,y_min,y_max */
Vec coordinates;
if (run_type==1) {
for (i = 0; i < 2*dim; i++) bounds[i] = (i%2) ? 1 : 0;
}
ierr = DMGetCoordinatesLocal(dm,&coordinates);CHKERRQ(ierr);
ierr = DMGetCoordinateDim(dm,&dimEmbed);CHKERRQ(ierr);
if (dimEmbed != dim) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"dimEmbed != dim %D",dimEmbed);CHKERRQ(ierr);
ierr = VecGetLocalSize(coordinates,&nCoords);CHKERRQ(ierr);
if (nCoords % dimEmbed) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Coordinate vector the wrong size");CHKERRQ(ierr);
ierr = VecGetArray(coordinates,&coords);CHKERRQ(ierr);
for (i = 0; i < nCoords; i += dimEmbed) {
PetscInt j;
PetscScalar *coord = &coords[i];
for (j = 0; j < dimEmbed; j++) {
coord[j] = bounds[2 * j] + coord[j] * (bounds[2 * j + 1] - bounds[2 * j]);
}
}
ierr = VecRestoreArray(coordinates,&coords);CHKERRQ(ierr);
ierr = DMSetCoordinatesLocal(dm,coordinates);CHKERRQ(ierr);
}
/* convert to p4est, and distribute */
ierr = PetscOptionsBegin(comm, "", "Mesh conversion options", "DMPLEX");CHKERRQ(ierr);
ierr = PetscOptionsFList("-dm_type","Convert DMPlex to another format (should not be Plex!)","ex56.c",DMList,DMPLEX,convType,256,&flg);CHKERRQ(ierr);
ierr = PetscOptionsEnd();
if (flg) {
DM newdm;
ierr = DMConvert(dm,convType,&newdm);CHKERRQ(ierr);
if (newdm) {
const char *prefix;
PetscBool isForest;
ierr = PetscObjectGetOptionsPrefix((PetscObject)dm,&prefix);CHKERRQ(ierr);
ierr = PetscObjectSetOptionsPrefix((PetscObject)newdm,prefix);CHKERRQ(ierr);
ierr = DMIsForest(newdm,&isForest);CHKERRQ(ierr);
if (isForest) {
} else SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_USER, "Converted to non Forest?");
ierr = DMDestroy(&dm);CHKERRQ(ierr);
dm = newdm;
} else SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_USER, "Convert failed?");
} else {
/* Plex Distribute mesh over processes */
ierr = DMPlexDistribute(dm, 0, NULL, &distdm);CHKERRQ(ierr);
if (distdm) {
const char *prefix;
ierr = PetscObjectGetOptionsPrefix((PetscObject)dm,&prefix);CHKERRQ(ierr);
ierr = PetscObjectSetOptionsPrefix((PetscObject)distdm,prefix);CHKERRQ(ierr);
ierr = DMDestroy(&dm);CHKERRQ(ierr);
dm = distdm;
}
}
ierr = PetscLogStagePop();CHKERRQ(ierr);
basedm = dm; dm = NULL;
for (iter=0 ; iter<max_conv_its ; iter++) {
ierr = PetscLogStagePush(stage[6]);CHKERRQ(ierr);
/* make new DM */
ierr = DMClone(basedm, &dm);CHKERRQ(ierr);
ierr = PetscObjectSetOptionsPrefix((PetscObject) dm, "ex56_");CHKERRQ(ierr);
ierr = PetscObjectSetName( (PetscObject)dm,"Mesh");CHKERRQ(ierr);
ierr = PetscOptionsClearValue(NULL,"-ex56_dm_refine");CHKERRQ(ierr);
ierr = PetscOptionsInsertString(NULL,options[iter]);CHKERRQ(ierr);
ierr = DMSetFromOptions(dm);CHKERRQ(ierr); /* refinement done here in Plex, p4est */
/* snes */
ierr = SNESCreate(comm, &snes);CHKERRQ(ierr);
ierr = SNESSetDM(snes, dm);CHKERRQ(ierr);
/* fem */
{
const PetscInt Ncomp = dim;
const PetscInt components[] = {0,1,2};
const PetscInt Nfid = 1, Npid = 1;
const PetscInt fid[] = {1}; /* The fixed faces (x=0) */
const PetscInt pid[] = {2}; /* The faces with loading (x=L_x) */
PetscFE fe;
PetscDS prob;
DM cdm = dm;
ierr = PetscFECreateDefault(dm, dim, dim, PETSC_FALSE, NULL, PETSC_DECIDE, &fe);CHKERRQ(ierr); /* elasticity */
ierr = PetscObjectSetName((PetscObject) fe, "deformation");CHKERRQ(ierr);
/* FEM prob */
ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
ierr = PetscDSSetDiscretization(prob, 0, (PetscObject) fe);CHKERRQ(ierr);
/* setup problem */
if (run_type==1) {
ierr = PetscDSSetJacobian(prob, 0, 0, NULL, NULL, NULL, g3_uu_3d);CHKERRQ(ierr);
ierr = PetscDSSetResidual(prob, 0, f0_u_x4, f1_u_3d);CHKERRQ(ierr);
} else {
ierr = PetscDSSetJacobian(prob, 0, 0, NULL, NULL, NULL, g3_uu_3d_alpha);CHKERRQ(ierr);
ierr = PetscDSSetResidual(prob, 0, f0_u, f1_u_3d_alpha);CHKERRQ(ierr);
ierr = PetscDSSetBdResidual(prob, 0, f0_bd_u_3d, f1_bd_u);CHKERRQ(ierr);
}
/* bcs */
if (run_type==1) {
PetscInt id = 1;
ierr = DMAddBoundary(dm, DM_BC_ESSENTIAL, "wall", "boundary", 0, 0, NULL, (void (*)()) zero, 1, &id, NULL);CHKERRQ(ierr);
} else {
ierr = PetscDSAddBoundary(prob, DM_BC_ESSENTIAL, "fixed", "Faces", 0, Ncomp, components, (void (*)()) zero, Nfid, fid, NULL);CHKERRQ(ierr);
ierr = PetscDSAddBoundary(prob, DM_BC_NATURAL, "traction", "Faces", 0, Ncomp, components, NULL, Npid, pid, NULL);CHKERRQ(ierr);
}
while (cdm) {
ierr = DMSetDS(cdm,prob);CHKERRQ(ierr);
ierr = DMGetCoarseDM(cdm, &cdm);CHKERRQ(ierr);
}
ierr = PetscFEDestroy(&fe);CHKERRQ(ierr);
}
/* vecs & mat */
ierr = DMCreateGlobalVector(dm,&xx);CHKERRQ(ierr);
ierr = VecDuplicate(xx, &bb);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) bb, "b");CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) xx, "u");CHKERRQ(ierr);
ierr = DMCreateMatrix(dm, &Amat);CHKERRQ(ierr);
ierr = VecGetSize(bb,&N);CHKERRQ(ierr);
local_sizes[iter] = N;
ierr = PetscPrintf(PETSC_COMM_WORLD,"[%d]%s %d global equations, %d vertices\n",rank,PETSC_FUNCTION_NAME,N,N/dim);CHKERRQ(ierr);
if (use_nearnullspace && N/dim > 1) {
/* Set up the near null space (a.k.a. rigid body modes) that will be used by the multigrid preconditioner */
DM subdm;
MatNullSpace nearNullSpace;
PetscInt fields = 0;
PetscObject deformation;
ierr = DMCreateSubDM(dm, 1, &fields, NULL, &subdm);CHKERRQ(ierr);
ierr = DMPlexCreateRigidBody(subdm, &nearNullSpace);CHKERRQ(ierr);
ierr = DMGetField(dm, 0, &deformation);CHKERRQ(ierr);
ierr = PetscObjectCompose(deformation, "nearnullspace", (PetscObject) nearNullSpace);CHKERRQ(ierr);
ierr = DMDestroy(&subdm);CHKERRQ(ierr);
ierr = MatNullSpaceDestroy(&nearNullSpace);CHKERRQ(ierr); /* created by DM and destroyed by Mat */
}
ierr = DMPlexSetSNESLocalFEM(dm,NULL,NULL,NULL);CHKERRQ(ierr);
ierr = SNESSetJacobian(snes, Amat, Amat, NULL, NULL);CHKERRQ(ierr);
ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
ierr = DMSetUp(dm);CHKERRQ(ierr);
ierr = PetscLogStagePop();CHKERRQ(ierr);
ierr = PetscLogStagePush(stage[0]);CHKERRQ(ierr);
/* ksp */
ierr = SNESGetKSP(snes, &ksp);CHKERRQ(ierr);
ierr = KSPSetComputeSingularValues(ksp,PETSC_TRUE);CHKERRQ(ierr);
/* test BCs */
ierr = VecZeroEntries(xx);CHKERRQ(ierr);
if (test_nonzero_cols) {
if (rank==0) ierr = VecSetValue(xx,0,1.0,INSERT_VALUES);CHKERRQ(ierr);
ierr = VecAssemblyBegin(xx);CHKERRQ(ierr);
ierr = VecAssemblyEnd(xx);CHKERRQ(ierr);
}
ierr = VecZeroEntries(bb);CHKERRQ(ierr);
ierr = VecGetSize(bb,&i);CHKERRQ(ierr);
local_sizes[iter] = i;
ierr = PetscPrintf(PETSC_COMM_WORLD,"[%d]%s %d equations in vector, %d vertices\n",rank,PETSC_FUNCTION_NAME,i,i/dim);CHKERRQ(ierr);
/* setup solver, dummy solve to really setup */
if (0) {
ierr = KSPSetTolerances(ksp,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,1);CHKERRQ(ierr);
ierr = SNESSolve(snes, bb, xx);CHKERRQ(ierr);
ierr = KSPSetTolerances(ksp,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,50);CHKERRQ(ierr);
ierr = VecZeroEntries(xx);CHKERRQ(ierr);
}
ierr = PetscLogStagePop();CHKERRQ(ierr);
/* solve */
ierr = PetscLogStagePush(stage[1]);CHKERRQ(ierr);
ierr = SNESSolve(snes, bb, xx);CHKERRQ(ierr);
ierr = PetscLogStagePop();CHKERRQ(ierr);
ierr = VecNorm(xx,NORM_INFINITY,&mdisp[iter]);CHKERRQ(ierr);
ierr = DMViewFromOptions(dm, NULL, "-dm_view");CHKERRQ(ierr);
{
PetscViewer viewer = NULL;
PetscViewerFormat fmt;
ierr = PetscOptionsGetViewer(comm,"ex56_","-vec_view",&viewer,&fmt,&flg);CHKERRQ(ierr);
if (flg) {
ierr = PetscViewerPushFormat(viewer,fmt);CHKERRQ(ierr);
ierr = VecView(xx,viewer);CHKERRQ(ierr);
ierr = VecView(bb,viewer);CHKERRQ(ierr);
ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
}
ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
}
/* Free work space */
ierr = DMDestroy(&dm);CHKERRQ(ierr);
ierr = SNESDestroy(&snes);CHKERRQ(ierr);
ierr = VecDestroy(&xx);CHKERRQ(ierr);
ierr = VecDestroy(&bb);CHKERRQ(ierr);
ierr = MatDestroy(&Amat);CHKERRQ(ierr);
}
ierr = DMDestroy(&basedm);CHKERRQ(ierr);
if (run_type==1) {
err[0] = 59.975208 - mdisp[0]; /* error with what I think is the exact solution */
} else {
err[0] = 171.038 - mdisp[0];
}
for (iter=1 ; iter<max_conv_its ; iter++) {
if (run_type==1) {
err[iter] = 59.975208 - mdisp[iter];
} else {
err[iter] = 171.038 - mdisp[iter];
}
PetscPrintf(PETSC_COMM_WORLD,"[%d]%s %D) N=%12D, max displ=%9.7e, disp diff=%9.2e, error=%4.3e, rate=%3.2g\n",
rank,PETSC_FUNCTION_NAME,iter,local_sizes[iter],mdisp[iter],
mdisp[iter]-mdisp[iter-1],err[iter],log(err[iter-1]/err[iter])/log(2.));
}
ierr = PetscFinalize();
return ierr;
}
static PetscErrorCode DMPlexTSSetupGeometry(DM dm, PetscFV fvm, DMTS_Plex *dmplexts)
{
DM dmFace, dmCell;
DMLabel ghostLabel;
PetscSection sectionFace, sectionCell;
PetscSection coordSection;
Vec coordinates;
PetscReal minradius;
PetscScalar *fgeom, *cgeom;
PetscInt dim, cStart, cEnd, cEndInterior, c, fStart, fEnd, f;
PetscErrorCode ierr;
PetscFunctionBegin;
if (dmplexts->setupGeom) PetscFunctionReturn(0);
ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
/* Make cell centroids and volumes */
ierr = DMClone(dm, &dmCell);CHKERRQ(ierr);
ierr = DMSetCoordinateSection(dmCell, coordSection);CHKERRQ(ierr);
ierr = DMSetCoordinatesLocal(dmCell, coordinates);CHKERRQ(ierr);
ierr = PetscSectionCreate(PetscObjectComm((PetscObject) dm), §ionCell);CHKERRQ(ierr);
ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
ierr = DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
ierr = PetscSectionSetChart(sectionCell, cStart, cEnd);CHKERRQ(ierr);
for (c = cStart; c < cEnd; ++c) {ierr = PetscSectionSetDof(sectionCell, c, sizeof(CellGeom)/sizeof(PetscScalar));CHKERRQ(ierr);}
ierr = PetscSectionSetUp(sectionCell);CHKERRQ(ierr);
ierr = DMSetDefaultSection(dmCell, sectionCell);CHKERRQ(ierr);
ierr = PetscSectionDestroy(§ionCell);CHKERRQ(ierr);
ierr = DMCreateLocalVector(dmCell, &dmplexts->cellgeom);CHKERRQ(ierr);
ierr = VecGetArray(dmplexts->cellgeom, &cgeom);CHKERRQ(ierr);
for (c = cStart; c < cEndInterior; ++c) {
CellGeom *cg;
ierr = DMPlexPointLocalRef(dmCell, c, cgeom, &cg);CHKERRQ(ierr);
ierr = PetscMemzero(cg, sizeof(*cg));CHKERRQ(ierr);
ierr = DMPlexComputeCellGeometryFVM(dmCell, c, &cg->volume, cg->centroid, NULL);CHKERRQ(ierr);
}
/* Compute face normals and minimum cell radius */
ierr = DMClone(dm, &dmFace);CHKERRQ(ierr);
ierr = PetscSectionCreate(PetscObjectComm((PetscObject) dm), §ionFace);CHKERRQ(ierr);
ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
ierr = PetscSectionSetChart(sectionFace, fStart, fEnd);CHKERRQ(ierr);
for (f = fStart; f < fEnd; ++f) {ierr = PetscSectionSetDof(sectionFace, f, sizeof(FaceGeom)/sizeof(PetscScalar));CHKERRQ(ierr);}
ierr = PetscSectionSetUp(sectionFace);CHKERRQ(ierr);
ierr = DMSetDefaultSection(dmFace, sectionFace);CHKERRQ(ierr);
ierr = PetscSectionDestroy(§ionFace);CHKERRQ(ierr);
ierr = DMCreateLocalVector(dmFace, &dmplexts->facegeom);CHKERRQ(ierr);
ierr = VecGetArray(dmplexts->facegeom, &fgeom);CHKERRQ(ierr);
ierr = DMPlexGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
minradius = PETSC_MAX_REAL;
for (f = fStart; f < fEnd; ++f) {
FaceGeom *fg;
PetscReal area;
PetscInt ghost, d;
ierr = DMLabelGetValue(ghostLabel, f, &ghost);CHKERRQ(ierr);
if (ghost >= 0) continue;
ierr = DMPlexPointLocalRef(dmFace, f, fgeom, &fg);CHKERRQ(ierr);
ierr = DMPlexComputeCellGeometryFVM(dm, f, &area, fg->centroid, fg->normal);CHKERRQ(ierr);
for (d = 0; d < dim; ++d) fg->normal[d] *= area;
/* Flip face orientation if necessary to match ordering in support, and Update minimum radius */
{
CellGeom *cL, *cR;
const PetscInt *cells;
PetscReal *lcentroid, *rcentroid;
PetscReal v[3];
ierr = DMPlexGetSupport(dm, f, &cells);CHKERRQ(ierr);
ierr = DMPlexPointLocalRead(dmCell, cells[0], cgeom, &cL);CHKERRQ(ierr);
ierr = DMPlexPointLocalRead(dmCell, cells[1], cgeom, &cR);CHKERRQ(ierr);
lcentroid = cells[0] >= cEndInterior ? fg->centroid : cL->centroid;
rcentroid = cells[1] >= cEndInterior ? fg->centroid : cR->centroid;
WaxpyD(dim, -1, lcentroid, rcentroid, v);
if (DotRealD(dim, fg->normal, v) < 0) {
for (d = 0; d < dim; ++d) fg->normal[d] = -fg->normal[d];
}
if (DotRealD(dim, fg->normal, v) <= 0) {
if (dim == 2) SETERRQ5(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Direction for face %d could not be fixed, normal (%g,%g) v (%g,%g)", f, (double) fg->normal[0], (double) fg->normal[1], (double) v[0], (double) v[1]);
if (dim == 3) SETERRQ7(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Direction for face %d could not be fixed, normal (%g,%g,%g) v (%g,%g,%g)", f, (double) fg->normal[0], (double) fg->normal[1], (double) fg->normal[2], (double) v[0], (double) v[1], (double) v[2]);
SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Direction for face %d could not be fixed", f);
}
if (cells[0] < cEndInterior) {
WaxpyD(dim, -1, fg->centroid, cL->centroid, v);
minradius = PetscMin(minradius, NormD(dim, v));
}
if (cells[1] < cEndInterior) {
WaxpyD(dim, -1, fg->centroid, cR->centroid, v);
minradius = PetscMin(minradius, NormD(dim, v));
}
}
}
ierr = MPI_Allreduce(&minradius, &dmplexts->minradius, 1, MPIU_REAL, MPI_MIN, PetscObjectComm((PetscObject)dm));CHKERRQ(ierr);
/* Compute centroids of ghost cells */
for (c = cEndInterior; c < cEnd; ++c) {
FaceGeom *fg;
const PetscInt *cone, *support;
PetscInt coneSize, supportSize, s;
ierr = DMPlexGetConeSize(dmCell, c, &coneSize);CHKERRQ(ierr);
if (coneSize != 1) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Ghost cell %d has cone size %d != 1", c, coneSize);
ierr = DMPlexGetCone(dmCell, c, &cone);CHKERRQ(ierr);
ierr = DMPlexGetSupportSize(dmCell, cone[0], &supportSize);CHKERRQ(ierr);
if (supportSize != 2) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Face %d has support size %d != 1", cone[0], supportSize);
ierr = DMPlexGetSupport(dmCell, cone[0], &support);CHKERRQ(ierr);
ierr = DMPlexPointLocalRef(dmFace, cone[0], fgeom, &fg);CHKERRQ(ierr);
for (s = 0; s < 2; ++s) {
/* Reflect ghost centroid across plane of face */
if (support[s] == c) {
const CellGeom *ci;
CellGeom *cg;
PetscReal c2f[3], a;
ierr = DMPlexPointLocalRead(dmCell, support[(s+1)%2], cgeom, &ci);CHKERRQ(ierr);
WaxpyD(dim, -1, ci->centroid, fg->centroid, c2f); /* cell to face centroid */
a = DotRealD(dim, c2f, fg->normal)/DotRealD(dim, fg->normal, fg->normal);
ierr = DMPlexPointLocalRef(dmCell, support[s], cgeom, &cg);CHKERRQ(ierr);
WaxpyD(dim, 2*a, fg->normal, ci->centroid, cg->centroid);
cg->volume = ci->volume;
}
}
}
ierr = VecRestoreArray(dmplexts->facegeom, &fgeom);CHKERRQ(ierr);
ierr = VecRestoreArray(dmplexts->cellgeom, &cgeom);CHKERRQ(ierr);
ierr = DMDestroy(&dmCell);CHKERRQ(ierr);
ierr = DMDestroy(&dmFace);CHKERRQ(ierr);
dmplexts->setupGeom = PETSC_TRUE;
PetscFunctionReturn(0);
}
int main(int argc, char **argv)
{
DM dm; /* Problem specification */
DM dmAux; /* Material specification */
SNES snes; /* nonlinear solver */
Vec u,r; /* solution, residual vectors */
Mat A,J; /* Jacobian matrix */
MatNullSpace nullSpace; /* May be necessary for Neumann conditions */
AppCtx user; /* user-defined work context */
JacActionCtx userJ; /* context for Jacobian MF action */
PetscInt its; /* iterations for convergence */
PetscReal error = 0.0; /* L_2 error in the solution */
PetscInt numComponents;
PetscErrorCode ierr;
ierr = PetscInitialize(&argc, &argv, NULL, help);CHKERRQ(ierr);
ierr = ProcessOptions(PETSC_COMM_WORLD, &user);CHKERRQ(ierr);
ierr = SNESCreate(PETSC_COMM_WORLD, &snes);CHKERRQ(ierr);
ierr = CreateMesh(PETSC_COMM_WORLD, &user, &dm);CHKERRQ(ierr);
ierr = SNESSetDM(snes, dm);CHKERRQ(ierr);
ierr = DMSetApplicationContext(dm, &user);CHKERRQ(ierr);
user.fem.fe = user.fe;
ierr = PetscFECreateDefault(dm, user.dim, 1, PETSC_TRUE, NULL, -1, &user.fe[0]);CHKERRQ(ierr);
if (user.bcType != NEUMANN) {
user.fem.feBd = NULL; user.feBd[0] = NULL;
} else {
user.fem.feBd = user.feBd;
ierr = PetscFECreateDefault(dm, user.dim-1, 1, PETSC_TRUE, "bd_", -1, &user.feBd[0]);CHKERRQ(ierr);
}
ierr = PetscFEGetNumComponents(user.fe[0], &numComponents);CHKERRQ(ierr);
ierr = PetscMalloc(NUM_FIELDS * sizeof(void (*)(const PetscReal[], PetscScalar *, void *)), &user.exactFuncs);CHKERRQ(ierr);
ierr = SetupProblem(dm, &user);CHKERRQ(ierr);
ierr = SetupSection(dm, &user);CHKERRQ(ierr);
/* Setup Material */
ierr = DMClone(dm, &dmAux);CHKERRQ(ierr);
ierr = DMPlexCopyCoordinates(dm, dmAux);CHKERRQ(ierr);
if (user.variableCoefficient != COEFF_FIELD) {
user.fem.feAux = NULL; user.feAux[0] = NULL;
} else {
PetscQuadrature q;
user.fem.feAux = user.feAux;
ierr = PetscFECreateDefault(dmAux, user.dim, 1, PETSC_TRUE, "mat_", -1, &user.feAux[0]);CHKERRQ(ierr);
ierr = PetscFEGetQuadrature(user.fe[0], &q);CHKERRQ(ierr);
ierr = PetscFESetQuadrature(user.feAux[0], q);CHKERRQ(ierr);
}
ierr = SetupMaterialSection(dmAux, &user);CHKERRQ(ierr);
ierr = SetupMaterial(dm, dmAux, &user);CHKERRQ(ierr);
ierr = DMDestroy(&dmAux);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(dm, &u);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) u, "potential");CHKERRQ(ierr);
ierr = VecDuplicate(u, &r);CHKERRQ(ierr);
ierr = DMSetMatType(dm,MATAIJ);CHKERRQ(ierr);
ierr = DMCreateMatrix(dm, &J);CHKERRQ(ierr);
if (user.jacobianMF) {
PetscInt M, m, N, n;
ierr = MatGetSize(J, &M, &N);CHKERRQ(ierr);
ierr = MatGetLocalSize(J, &m, &n);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD, &A);CHKERRQ(ierr);
ierr = MatSetSizes(A, m, n, M, N);CHKERRQ(ierr);
ierr = MatSetType(A, MATSHELL);CHKERRQ(ierr);
ierr = MatSetUp(A);CHKERRQ(ierr);
#if 0
ierr = MatShellSetOperation(A, MATOP_MULT, (void (*)(void))FormJacobianAction);CHKERRQ(ierr);
#endif
userJ.dm = dm;
userJ.J = J;
userJ.user = &user;
ierr = DMCreateLocalVector(dm, &userJ.u);CHKERRQ(ierr);
ierr = DMPlexProjectFunctionLocal(dm, user.fe, user.exactFuncs, NULL, INSERT_BC_VALUES, userJ.u);CHKERRQ(ierr);
ierr = MatShellSetContext(A, &userJ);CHKERRQ(ierr);
} else {
A = J;
}
if (user.bcType == NEUMANN) {
ierr = MatNullSpaceCreate(PetscObjectComm((PetscObject) dm), PETSC_TRUE, 0, NULL, &nullSpace);CHKERRQ(ierr);
ierr = MatSetNullSpace(J, nullSpace);CHKERRQ(ierr);
if (A != J) {
ierr = MatSetNullSpace(A, nullSpace);CHKERRQ(ierr);
}
}
ierr = DMSNESSetFunctionLocal(dm, (PetscErrorCode (*)(DM,Vec,Vec,void*)) DMPlexComputeResidualFEM, &user);CHKERRQ(ierr);
ierr = DMSNESSetJacobianLocal(dm, (PetscErrorCode (*)(DM,Vec,Mat,Mat,void*)) DMPlexComputeJacobianFEM, &user);CHKERRQ(ierr);
ierr = SNESSetJacobian(snes, A, J, NULL, NULL);CHKERRQ(ierr);
ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
ierr = DMPlexProjectFunction(dm, user.fe, user.exactFuncs, NULL, INSERT_ALL_VALUES, u);CHKERRQ(ierr);
if (user.checkpoint) {
#if defined(PETSC_HAVE_HDF5)
ierr = PetscViewerHDF5PushGroup(user.checkpoint, "/fields");CHKERRQ(ierr);
ierr = VecLoad(u, user.checkpoint);CHKERRQ(ierr);
ierr = PetscViewerHDF5PopGroup(user.checkpoint);CHKERRQ(ierr);
#endif
}
ierr = PetscViewerDestroy(&user.checkpoint);CHKERRQ(ierr);
if (user.showInitial) {
Vec lv;
ierr = DMGetLocalVector(dm, &lv);CHKERRQ(ierr);
ierr = DMGlobalToLocalBegin(dm, u, INSERT_VALUES, lv);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(dm, u, INSERT_VALUES, lv);CHKERRQ(ierr);
ierr = DMPrintLocalVec(dm, "Local function", 1.0e-10, lv);CHKERRQ(ierr);
ierr = DMRestoreLocalVector(dm, &lv);CHKERRQ(ierr);
}
if (user.runType == RUN_FULL) {
void (*initialGuess[numComponents])(const PetscReal x[], PetscScalar *, void *ctx);
PetscInt c;
for (c = 0; c < numComponents; ++c) initialGuess[c] = zero;
ierr = DMPlexProjectFunction(dm, user.fe, initialGuess, NULL, INSERT_VALUES, u);CHKERRQ(ierr);
if (user.debug) {
ierr = PetscPrintf(PETSC_COMM_WORLD, "Initial guess\n");CHKERRQ(ierr);
ierr = VecView(u, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
ierr = SNESSolve(snes, NULL, u);CHKERRQ(ierr);
ierr = SNESGetIterationNumber(snes, &its);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD, "Number of SNES iterations = %D\n", its);CHKERRQ(ierr);
ierr = DMPlexComputeL2Diff(dm, user.fe, user.exactFuncs, NULL, u, &error);CHKERRQ(ierr);
if (error < 1.0e-11) {ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: < 1.0e-11\n");CHKERRQ(ierr);}
else {ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: %g\n", error);CHKERRQ(ierr);}
if (user.showSolution) {
ierr = PetscPrintf(PETSC_COMM_WORLD, "Solution\n");CHKERRQ(ierr);
ierr = VecChop(u, 3.0e-9);CHKERRQ(ierr);
ierr = VecView(u, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
} else if (user.runType == RUN_PERF) {
PetscReal res = 0.0;
ierr = SNESComputeFunction(snes, u, r);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD, "Initial Residual\n");CHKERRQ(ierr);
ierr = VecChop(r, 1.0e-10);CHKERRQ(ierr);
ierr = VecNorm(r, NORM_2, &res);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Residual: %g\n", res);CHKERRQ(ierr);
} else {
PetscReal res = 0.0;
/* Check discretization error */
ierr = PetscPrintf(PETSC_COMM_WORLD, "Initial guess\n");CHKERRQ(ierr);
ierr = VecView(u, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = DMPlexComputeL2Diff(dm, user.fe, user.exactFuncs, NULL, u, &error);CHKERRQ(ierr);
if (error < 1.0e-11) {ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: < 1.0e-11\n");CHKERRQ(ierr);}
else {ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: %g\n", error);CHKERRQ(ierr);}
/* Check residual */
ierr = SNESComputeFunction(snes, u, r);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD, "Initial Residual\n");CHKERRQ(ierr);
ierr = VecChop(r, 1.0e-10);CHKERRQ(ierr);
ierr = VecView(r, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = VecNorm(r, NORM_2, &res);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Residual: %g\n", res);CHKERRQ(ierr);
/* Check Jacobian */
{
Vec b;
ierr = SNESComputeJacobian(snes, u, A, A);CHKERRQ(ierr);
ierr = VecDuplicate(u, &b);CHKERRQ(ierr);
ierr = VecSet(r, 0.0);CHKERRQ(ierr);
ierr = SNESComputeFunction(snes, r, b);CHKERRQ(ierr);
ierr = MatMult(A, u, r);CHKERRQ(ierr);
ierr = VecAXPY(r, 1.0, b);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD, "Au - b = Au + F(0)\n");CHKERRQ(ierr);
ierr = VecChop(r, 1.0e-10);CHKERRQ(ierr);
ierr = VecView(r, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = VecNorm(r, NORM_2, &res);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD, "Linear L_2 Residual: %g\n", res);CHKERRQ(ierr);
}
}
ierr = VecViewFromOptions(u, NULL, "-vec_view");CHKERRQ(ierr);
if (user.bcType == NEUMANN) {
ierr = MatNullSpaceDestroy(&nullSpace);CHKERRQ(ierr);
}
if (user.jacobianMF) {
ierr = VecDestroy(&userJ.u);CHKERRQ(ierr);
}
if (A != J) {ierr = MatDestroy(&A);CHKERRQ(ierr);}
ierr = PetscFEDestroy(&user.fe[0]);CHKERRQ(ierr);
ierr = PetscFEDestroy(&user.feBd[0]);CHKERRQ(ierr);
ierr = PetscFEDestroy(&user.feAux[0]);CHKERRQ(ierr);
ierr = MatDestroy(&J);CHKERRQ(ierr);
ierr = VecDestroy(&u);CHKERRQ(ierr);
ierr = VecDestroy(&r);CHKERRQ(ierr);
ierr = SNESDestroy(&snes);CHKERRQ(ierr);
ierr = DMDestroy(&dm);CHKERRQ(ierr);
ierr = PetscFree(user.exactFuncs);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
int main(int argc, char **argv)
{
DM dm; /* Problem specification */
SNES snes; /* Nonlinear solver */
Vec u; /* Solutions */
AppCtx user; /* User-defined work context */
PetscErrorCode ierr;
ierr = PetscInitialize(&argc, &argv, NULL,help);if (ierr) return ierr;
ierr = ProcessOptions(PETSC_COMM_WORLD, &user);CHKERRQ(ierr);
/* Primal system */
ierr = SNESCreate(PETSC_COMM_WORLD, &snes);CHKERRQ(ierr);
ierr = CreateMesh(PETSC_COMM_WORLD, &user, &dm);CHKERRQ(ierr);
ierr = SNESSetDM(snes, dm);CHKERRQ(ierr);
ierr = SetupDiscretization(dm, "potential", SetupPrimalProblem, &user);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(dm, &u);CHKERRQ(ierr);
ierr = VecSet(u, 0.0);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) u, "potential");CHKERRQ(ierr);
ierr = DMPlexSetSNESLocalFEM(dm, &user, &user, &user);CHKERRQ(ierr);
ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
ierr = SNESSolve(snes, NULL, u);CHKERRQ(ierr);
ierr = SNESGetSolution(snes, &u);CHKERRQ(ierr);
ierr = VecViewFromOptions(u, NULL, "-potential_view");CHKERRQ(ierr);
if (user.spectral) {
PetscInt planeDir[2] = {0, 1};
PetscReal planeCoord[2] = {0., 1.};
ierr = ComputeSpectral(dm, u, 2, planeDir, planeCoord, &user);CHKERRQ(ierr);
}
/* Adjoint system */
if (user.adjoint) {
DM dmAdj;
SNES snesAdj;
Vec uAdj;
ierr = SNESCreate(PETSC_COMM_WORLD, &snesAdj);CHKERRQ(ierr);
ierr = PetscObjectSetOptionsPrefix((PetscObject) snesAdj, "adjoint_");CHKERRQ(ierr);
ierr = DMClone(dm, &dmAdj);CHKERRQ(ierr);
ierr = SNESSetDM(snesAdj, dmAdj);CHKERRQ(ierr);
ierr = SetupDiscretization(dmAdj, "adjoint", SetupAdjointProblem, &user);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(dmAdj, &uAdj);CHKERRQ(ierr);
ierr = VecSet(uAdj, 0.0);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) uAdj, "adjoint");CHKERRQ(ierr);
ierr = DMPlexSetSNESLocalFEM(dmAdj, &user, &user, &user);CHKERRQ(ierr);
ierr = SNESSetFromOptions(snesAdj);CHKERRQ(ierr);
ierr = SNESSolve(snesAdj, NULL, uAdj);CHKERRQ(ierr);
ierr = SNESGetSolution(snesAdj, &uAdj);CHKERRQ(ierr);
ierr = VecViewFromOptions(uAdj, NULL, "-adjoint_view");CHKERRQ(ierr);
/* Error representation */
{
DM dmErr, dmErrAux, dms[2];
Vec errorEst, errorL2, uErr, uErrLoc, uAdjLoc, uAdjProj;
IS *subis;
PetscReal errorEstTot, errorL2Norm, errorL2Tot;
PetscInt N, i;
PetscErrorCode (*funcs[1])(PetscInt, PetscReal, const PetscReal [], PetscInt, PetscScalar *, void *) = {trig_u};
void (*identity[1])(PetscInt, PetscInt, PetscInt,
const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[],
const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[],
PetscReal, const PetscReal[], PetscInt, const PetscScalar[], PetscScalar[]) = {f0_identityaux_u};
void *ctxs[1] = {0};
ctxs[0] = &user;
ierr = DMClone(dm, &dmErr);CHKERRQ(ierr);
ierr = SetupDiscretization(dmErr, "error", SetupErrorProblem, &user);CHKERRQ(ierr);
ierr = DMGetGlobalVector(dmErr, &errorEst);CHKERRQ(ierr);
ierr = DMGetGlobalVector(dmErr, &errorL2);CHKERRQ(ierr);
/* Compute auxiliary data (solution and projection of adjoint solution) */
ierr = DMGetLocalVector(dmAdj, &uAdjLoc);CHKERRQ(ierr);
ierr = DMGlobalToLocalBegin(dmAdj, uAdj, INSERT_VALUES, uAdjLoc);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(dmAdj, uAdj, INSERT_VALUES, uAdjLoc);CHKERRQ(ierr);
ierr = DMGetGlobalVector(dm, &uAdjProj);CHKERRQ(ierr);
ierr = PetscObjectCompose((PetscObject) dm, "dmAux", (PetscObject) dmAdj);CHKERRQ(ierr);
ierr = PetscObjectCompose((PetscObject) dm, "A", (PetscObject) uAdjLoc);CHKERRQ(ierr);
ierr = DMProjectField(dm, 0.0, u, identity, INSERT_VALUES, uAdjProj);CHKERRQ(ierr);
ierr = PetscObjectCompose((PetscObject) dm, "dmAux", NULL);CHKERRQ(ierr);
ierr = PetscObjectCompose((PetscObject) dm, "A", NULL);CHKERRQ(ierr);
ierr = DMRestoreLocalVector(dmAdj, &uAdjLoc);CHKERRQ(ierr);
/* Attach auxiliary data */
dms[0] = dm; dms[1] = dm;
ierr = DMCreateSuperDM(dms, 2, &subis, &dmErrAux);CHKERRQ(ierr);
if (0) {
PetscSection sec;
ierr = DMGetSection(dms[0], &sec);CHKERRQ(ierr);
ierr = PetscSectionView(sec, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = DMGetSection(dms[1], &sec);CHKERRQ(ierr);
ierr = PetscSectionView(sec, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = DMGetSection(dmErrAux, &sec);CHKERRQ(ierr);
ierr = PetscSectionView(sec, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
ierr = DMViewFromOptions(dmErrAux, NULL, "-dm_err_view");CHKERRQ(ierr);
ierr = ISViewFromOptions(subis[0], NULL, "-super_is_view");CHKERRQ(ierr);
ierr = ISViewFromOptions(subis[1], NULL, "-super_is_view");CHKERRQ(ierr);
ierr = DMGetGlobalVector(dmErrAux, &uErr);CHKERRQ(ierr);
ierr = VecViewFromOptions(u, NULL, "-map_vec_view");CHKERRQ(ierr);
ierr = VecViewFromOptions(uAdjProj, NULL, "-map_vec_view");CHKERRQ(ierr);
ierr = VecViewFromOptions(uErr, NULL, "-map_vec_view");CHKERRQ(ierr);
ierr = VecISCopy(uErr, subis[0], SCATTER_FORWARD, u);CHKERRQ(ierr);
ierr = VecISCopy(uErr, subis[1], SCATTER_FORWARD, uAdjProj);CHKERRQ(ierr);
ierr = DMRestoreGlobalVector(dm, &uAdjProj);CHKERRQ(ierr);
for (i = 0; i < 2; ++i) {ierr = ISDestroy(&subis[i]);CHKERRQ(ierr);}
ierr = PetscFree(subis);CHKERRQ(ierr);
ierr = DMGetLocalVector(dmErrAux, &uErrLoc);CHKERRQ(ierr);
ierr = DMGlobalToLocalBegin(dm, uErr, INSERT_VALUES, uErrLoc);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(dm, uErr, INSERT_VALUES, uErrLoc);CHKERRQ(ierr);
ierr = DMRestoreGlobalVector(dmErrAux, &uErr);CHKERRQ(ierr);
ierr = PetscObjectCompose((PetscObject) dmAdj, "dmAux", (PetscObject) dmErrAux);CHKERRQ(ierr);
ierr = PetscObjectCompose((PetscObject) dmAdj, "A", (PetscObject) uErrLoc);CHKERRQ(ierr);
/* Compute cellwise error estimate */
ierr = VecSet(errorEst, 0.0);CHKERRQ(ierr);
ierr = DMPlexComputeCellwiseIntegralFEM(dmAdj, uAdj, errorEst, &user);CHKERRQ(ierr);
ierr = PetscObjectCompose((PetscObject) dmAdj, "dmAux", NULL);CHKERRQ(ierr);
ierr = PetscObjectCompose((PetscObject) dmAdj, "A", NULL);CHKERRQ(ierr);
ierr = DMRestoreLocalVector(dmErrAux, &uErrLoc);CHKERRQ(ierr);
ierr = DMDestroy(&dmErrAux);CHKERRQ(ierr);
/* Plot cellwise error vector */
ierr = VecViewFromOptions(errorEst, NULL, "-error_view");CHKERRQ(ierr);
/* Compute ratio of estimate (sum over cells) with actual L_2 error */
ierr = DMComputeL2Diff(dm, 0.0, funcs, ctxs, u, &errorL2Norm);CHKERRQ(ierr);
ierr = DMPlexComputeL2DiffVec(dm, 0.0, funcs, ctxs, u, errorL2);CHKERRQ(ierr);
ierr = VecViewFromOptions(errorL2, NULL, "-l2_error_view");CHKERRQ(ierr);
ierr = VecNorm(errorL2, NORM_INFINITY, &errorL2Tot);CHKERRQ(ierr);
ierr = VecNorm(errorEst, NORM_INFINITY, &errorEstTot);CHKERRQ(ierr);
ierr = VecGetSize(errorEst, &N);CHKERRQ(ierr);
ierr = VecPointwiseDivide(errorEst, errorEst, errorL2);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) errorEst, "Error ratio");CHKERRQ(ierr);
ierr = VecViewFromOptions(errorEst, NULL, "-error_ratio_view");CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD, "N: %D L2 error: %g Error Ratio: %g/%g = %g\n", N, (double) errorL2Norm, (double) errorEstTot, (double) PetscSqrtReal(errorL2Tot), (double) errorEstTot/PetscSqrtReal(errorL2Tot));CHKERRQ(ierr);
ierr = DMRestoreGlobalVector(dmErr, &errorEst);CHKERRQ(ierr);
ierr = DMRestoreGlobalVector(dmErr, &errorL2);CHKERRQ(ierr);
ierr = DMDestroy(&dmErr);CHKERRQ(ierr);
}
ierr = DMDestroy(&dmAdj);CHKERRQ(ierr);
ierr = VecDestroy(&uAdj);CHKERRQ(ierr);
ierr = SNESDestroy(&snesAdj);CHKERRQ(ierr);
}
/* Cleanup */
ierr = VecDestroy(&u);CHKERRQ(ierr);
ierr = SNESDestroy(&snes);CHKERRQ(ierr);
ierr = DMDestroy(&dm);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
PetscErrorCode SetupDiscretization(DM dm, AppCtx *user)
{
DM cdm = dm;
const PetscInt dim = user->dim;
const PetscInt id = 1;
PetscFE feAux = NULL;
PetscFE feBd = NULL;
PetscFE feCh = NULL;
PetscFE fe;
PetscDS prob;
PetscErrorCode ierr;
PetscFunctionBeginUser;
/* Create finite element */
ierr = PetscFECreateDefault(dm, dim, 1, PETSC_TRUE, NULL, -1, &fe);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) fe, "potential");CHKERRQ(ierr);
if (user->bcType == NEUMANN) {
ierr = PetscFECreateDefault(dm, dim-1, 1, PETSC_TRUE, "bd_", -1, &feBd);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) feBd, "potential");CHKERRQ(ierr);
}
if (user->variableCoefficient == COEFF_FIELD) {
PetscQuadrature q;
ierr = PetscFECreateDefault(dm, dim, 1, PETSC_TRUE, "mat_", -1, &feAux);CHKERRQ(ierr);
ierr = PetscFEGetQuadrature(fe, &q);CHKERRQ(ierr);
ierr = PetscFESetQuadrature(feAux, q);CHKERRQ(ierr);
}
if (user->check) {ierr = PetscFECreateDefault(dm, dim, 1, PETSC_TRUE, "ch_", -1, &feCh);CHKERRQ(ierr);}
/* Set discretization and boundary conditions for each mesh */
while (cdm) {
ierr = DMGetDS(cdm, &prob);CHKERRQ(ierr);
ierr = PetscDSSetDiscretization(prob, 0, (PetscObject) fe);CHKERRQ(ierr);
ierr = PetscDSSetBdDiscretization(prob, 0, (PetscObject) feBd);CHKERRQ(ierr);
if (feAux) {
DM dmAux;
PetscDS probAux;
ierr = DMClone(cdm, &dmAux);CHKERRQ(ierr);
ierr = DMPlexCopyCoordinates(cdm, dmAux);CHKERRQ(ierr);
ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
ierr = PetscDSSetDiscretization(probAux, 0, (PetscObject) feAux);CHKERRQ(ierr);
ierr = PetscObjectCompose((PetscObject) dm, "dmAux", (PetscObject) dmAux);CHKERRQ(ierr);
ierr = SetupMaterial(cdm, dmAux, user);CHKERRQ(ierr);
ierr = DMDestroy(&dmAux);CHKERRQ(ierr);
}
if (feCh) {
DM dmCh;
PetscDS probCh;
ierr = DMClone(cdm, &dmCh);CHKERRQ(ierr);
ierr = DMPlexCopyCoordinates(cdm, dmCh);CHKERRQ(ierr);
ierr = DMGetDS(dmCh, &probCh);CHKERRQ(ierr);
ierr = PetscDSSetDiscretization(probCh, 0, (PetscObject) feCh);CHKERRQ(ierr);
ierr = PetscObjectCompose((PetscObject) dm, "dmCh", (PetscObject) dmCh);CHKERRQ(ierr);
ierr = DMDestroy(&dmCh);CHKERRQ(ierr);
}
ierr = SetupProblem(cdm, user);CHKERRQ(ierr);
ierr = DMPlexAddBoundary(cdm, user->bcType == DIRICHLET, "wall", user->bcType == NEUMANN ? "boundary" : "marker", 0, user->exactFuncs[0], 1, &id, user);CHKERRQ(ierr);
ierr = DMPlexGetCoarseDM(cdm, &cdm);CHKERRQ(ierr);
}
ierr = PetscFEDestroy(&fe);CHKERRQ(ierr);
ierr = PetscFEDestroy(&feBd);CHKERRQ(ierr);
ierr = PetscFEDestroy(&feAux);CHKERRQ(ierr);
ierr = PetscFEDestroy(&feCh);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
