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 = SetupFE(dm, user.dim, user.simplex, "displacement", SetupPrimalProblem, &user);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(dm, &u);CHKERRQ(ierr);
ierr = VecSet(u, 0.0);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) u, "displacement");CHKERRQ(ierr);
ierr = DMPlexSetSNESLocalFEM(dm, &user, &user, &user);CHKERRQ(ierr);
ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
ierr = DMSNESCheckFromOptions(snes, u, NULL, NULL);CHKERRQ(ierr);
ierr = SNESSolve(snes, NULL, u);CHKERRQ(ierr);
ierr = SNESGetSolution(snes, &u);CHKERRQ(ierr);
ierr = VecViewFromOptions(u, NULL, "-displacement_view");CHKERRQ(ierr);
/* Cleanup */
ierr = VecDestroy(&u);CHKERRQ(ierr);
ierr = SNESDestroy(&snes);CHKERRQ(ierr);
ierr = DMDestroy(&dm);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
int main(int argc, char **argv)
{
SNES snes; /* nonlinear solver */
DM dm; /* problem definition */
Vec u, r; /* solution and residual */
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);
ierr = PetscBagCreate(PETSC_COMM_WORLD, sizeof(Parameter), &user.bag);CHKERRQ(ierr);
ierr = SetupParameters(&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);
/* Setup problem */
ierr = PetscMalloc(2 * sizeof(void (*)(const PetscReal[], PetscScalar *, void *)), &user.exactFuncs);CHKERRQ(ierr);
ierr = SetupDiscretization(dm, &user);CHKERRQ(ierr);
ierr = DMPlexCreateClosureIndex(dm, NULL);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(dm, &u);CHKERRQ(ierr);
ierr = VecDuplicate(u, &r);CHKERRQ(ierr);
ierr = DMPlexSetSNESLocalFEM(dm,&user,&user,&user);CHKERRQ(ierr);
ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
{
Parameter *param;
void *ctxs[2];
ierr = PetscBagGetData(user.bag, (void **) ¶m);CHKERRQ(ierr);
ctxs[0] = ctxs[1] = param;
ierr = DMProjectFunction(dm, 0.0, user.exactFuncs, ctxs, INSERT_ALL_VALUES, u);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) u, "Exact Solution");CHKERRQ(ierr);
ierr = VecViewFromOptions(u, NULL, "-exact_vec_view");CHKERRQ(ierr);
}
ierr = DMSNESCheckFromOptions(snes, u, NULL, NULL);CHKERRQ(ierr);
ierr = VecSet(u, 0.0);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) u, "Solution");CHKERRQ(ierr);
ierr = SNESSolve(snes, NULL, u);CHKERRQ(ierr);
ierr = VecViewFromOptions(u, NULL, "-sol_vec_view");CHKERRQ(ierr);
ierr = VecDestroy(&u);CHKERRQ(ierr);
ierr = VecDestroy(&r);CHKERRQ(ierr);
ierr = PetscFree(user.exactFuncs);CHKERRQ(ierr);
ierr = DMDestroy(&dm);CHKERRQ(ierr);
ierr = SNESDestroy(&snes);CHKERRQ(ierr);
ierr = PetscBagDestroy(&user.bag);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
int main(int argc, char **argv)
{
DM dm;
SNES snes;
Vec u, r;
AppCtx user;
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 = PetscMalloc(3 * sizeof(void (*)()), &user.exactFuncs);CHKERRQ(ierr);
ierr = SetupDiscretization(dm, &user);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(dm, &u);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) u, "solution");CHKERRQ(ierr);
ierr = VecDuplicate(u, &r);CHKERRQ(ierr);
ierr = DMPlexSetSNESLocalFEM(dm,&user,&user,&user);CHKERRQ(ierr);
ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
ierr = DMProjectFunction(dm, user.exactFuncs, NULL, INSERT_ALL_VALUES, u);CHKERRQ(ierr);
ierr = DMSNESCheckFromOptions(snes, u, user.exactFuncs, NULL);CHKERRQ(ierr);
if (user.runType == RUN_FULL) {
PetscErrorCode (*initialGuess[3])(PetscInt dim, const PetscReal x[], PetscInt Nf, PetscScalar u[], void *ctx);
PetscReal error;
initialGuess[0] = zero;
initialGuess[1] = zero;
initialGuess[2] = zero;
ierr = DMProjectFunction(dm, initialGuess, NULL, INSERT_VALUES, u);CHKERRQ(ierr);
ierr = VecViewFromOptions(u, NULL, "-initial_vec_view");CHKERRQ(ierr);
ierr = DMComputeL2Diff(dm, user.exactFuncs, NULL, u, &error);CHKERRQ(ierr);
if (error < 1.0e-11) {ierr = PetscPrintf(PETSC_COMM_WORLD, "Initial L_2 Error: < 1.0e-11\n");CHKERRQ(ierr);}
else {ierr = PetscPrintf(PETSC_COMM_WORLD, "Initial L_2 Error: %g\n", error);CHKERRQ(ierr);}
ierr = SNESSolve(snes, NULL, u);CHKERRQ(ierr);
ierr = DMComputeL2Diff(dm, user.exactFuncs, NULL, u, &error);CHKERRQ(ierr);
if (error < 1.0e-11) {ierr = PetscPrintf(PETSC_COMM_WORLD, "Final L_2 Error: < 1.0e-11\n");CHKERRQ(ierr);}
else {ierr = PetscPrintf(PETSC_COMM_WORLD, "Final L_2 Error: %g\n", error);CHKERRQ(ierr);}
}
ierr = VecViewFromOptions(u, NULL, "-sol_vec_view");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 **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;
}
/*@
PetscConvEstGetConvRate - Returns an estimate of the convergence rate for the discretization
Not collective
Input Parameter:
. ce - The PetscConvEst object
Output Parameter:
. alpha - The convergence rate for each field
Note: The convergence rate alpha is defined by
$ || u_h - u_exact || < C h^alpha
where u_h is the discrete solution, and h is a measure of the discretization size.
We solve a series of problems on refined meshes, calculate an error based upon the exact solution in the DS,
and then fit the result to our model above using linear regression.
Options database keys:
. -snes_convergence_estimate : Execute convergence estimation and print out the rate
Level: intermediate
.keywords: PetscConvEst, convergence
.seealso: PetscConvEstSetSolver(), PetscConvEstCreate(), PetscConvEstGetConvRate()
@*/
PetscErrorCode PetscConvEstGetConvRate(PetscConvEst ce, PetscReal alpha[])
{
DM *dm;
PetscObject disc;
MPI_Comm comm;
const char *uname, *dmname;
void *ctx;
Vec u;
PetscReal t = 0.0, *x, *y, slope, intercept;
PetscInt *dof, dim, Nr = ce->Nr, r, f, oldlevel, oldnlev;
PetscLogEvent event;
PetscErrorCode ierr;
PetscFunctionBegin;
ierr = PetscObjectGetComm((PetscObject) ce, &comm);CHKERRQ(ierr);
ierr = DMGetDimension(ce->idm, &dim);CHKERRQ(ierr);
ierr = DMGetApplicationContext(ce->idm, &ctx);CHKERRQ(ierr);
ierr = DMPlexSetRefinementUniform(ce->idm, PETSC_TRUE);CHKERRQ(ierr);
ierr = DMGetRefineLevel(ce->idm, &oldlevel);CHKERRQ(ierr);
ierr = PetscMalloc2((Nr+1), &dm, (Nr+1)*ce->Nf, &dof);CHKERRQ(ierr);
dm[0] = ce->idm;
for (f = 0; f < ce->Nf; ++f) alpha[f] = 0.0;
/* Loop over meshes */
ierr = PetscLogEventRegister("ConvEst Error", PETSC_OBJECT_CLASSID, &event);CHKERRQ(ierr);
for (r = 0; r <= Nr; ++r) {
PetscLogStage stage;
char stageName[PETSC_MAX_PATH_LEN];
ierr = PetscSNPrintf(stageName, PETSC_MAX_PATH_LEN-1, "ConvEst Refinement Level %D", r);CHKERRQ(ierr);
ierr = PetscLogStageRegister(stageName, &stage);CHKERRQ(ierr);
ierr = PetscLogStagePush(stage);CHKERRQ(ierr);
if (r > 0) {
ierr = DMRefine(dm[r-1], MPI_COMM_NULL, &dm[r]);CHKERRQ(ierr);
ierr = DMSetCoarseDM(dm[r], dm[r-1]);CHKERRQ(ierr);
ierr = DMCopyDisc(ce->idm, dm[r]);CHKERRQ(ierr);
ierr = DMCopyTransform(ce->idm, dm[r]);CHKERRQ(ierr);
ierr = PetscObjectGetName((PetscObject) dm[r-1], &dmname);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) dm[r], dmname);CHKERRQ(ierr);
for (f = 0; f <= ce->Nf; ++f) {
PetscErrorCode (*nspconstr)(DM, PetscInt, MatNullSpace *);
ierr = DMGetNullSpaceConstructor(dm[r-1], f, &nspconstr);CHKERRQ(ierr);
ierr = DMSetNullSpaceConstructor(dm[r], f, nspconstr);CHKERRQ(ierr);
}
}
ierr = DMViewFromOptions(dm[r], NULL, "-conv_dm_view");CHKERRQ(ierr);
/* Create solution */
ierr = DMCreateGlobalVector(dm[r], &u);CHKERRQ(ierr);
ierr = DMGetField(dm[r], 0, NULL, &disc);CHKERRQ(ierr);
ierr = PetscObjectGetName(disc, &uname);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) u, uname);CHKERRQ(ierr);
/* Setup solver */
ierr = SNESReset(ce->snes);CHKERRQ(ierr);
ierr = SNESSetDM(ce->snes, dm[r]);CHKERRQ(ierr);
ierr = DMPlexSetSNESLocalFEM(dm[r], ctx, ctx, ctx);CHKERRQ(ierr);
ierr = SNESSetFromOptions(ce->snes);CHKERRQ(ierr);
/* Create initial guess */
ierr = DMProjectFunction(dm[r], t, ce->initGuess, ce->ctxs, INSERT_VALUES, u);CHKERRQ(ierr);
ierr = SNESSolve(ce->snes, NULL, u);CHKERRQ(ierr);
ierr = PetscLogEventBegin(event, ce, 0, 0, 0);CHKERRQ(ierr);
ierr = DMComputeL2FieldDiff(dm[r], t, ce->exactSol, ce->ctxs, u, &ce->errors[r*ce->Nf]);CHKERRQ(ierr);
ierr = PetscLogEventEnd(event, ce, 0, 0, 0);CHKERRQ(ierr);
for (f = 0; f < ce->Nf; ++f) {
PetscSection s, fs;
PetscInt lsize;
/* Could use DMGetOutputDM() to add in Dirichlet dofs */
ierr = DMGetSection(dm[r], &s);CHKERRQ(ierr);
ierr = PetscSectionGetField(s, f, &fs);CHKERRQ(ierr);
ierr = PetscSectionGetConstrainedStorageSize(fs, &lsize);CHKERRQ(ierr);
ierr = MPI_Allreduce(&lsize, &dof[r*ce->Nf+f], 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject) ce->snes));CHKERRQ(ierr);
ierr = PetscLogEventSetDof(event, f, dof[r*ce->Nf+f]);CHKERRQ(ierr);
ierr = PetscLogEventSetError(event, f, ce->errors[r*ce->Nf+f]);CHKERRQ(ierr);
}
/* Monitor */
if (ce->monitor) {
PetscReal *errors = &ce->errors[r*ce->Nf];
ierr = PetscPrintf(comm, "L_2 Error: ");CHKERRQ(ierr);
if (ce->Nf > 1) {ierr = PetscPrintf(comm, "[");CHKERRQ(ierr);}
for (f = 0; f < ce->Nf; ++f) {
if (f > 0) {ierr = PetscPrintf(comm, ", ");CHKERRQ(ierr);}
if (errors[f] < 1.0e-11) {ierr = PetscPrintf(comm, "< 1e-11");CHKERRQ(ierr);}
else {ierr = PetscPrintf(comm, "%g", (double)errors[f]);CHKERRQ(ierr);}
}
if (ce->Nf > 1) {ierr = PetscPrintf(comm, "]");CHKERRQ(ierr);}
ierr = PetscPrintf(comm, "\n");CHKERRQ(ierr);
}
if (!r) {
/* PCReset() does not wipe out the level structure */
KSP ksp;
PC pc;
ierr = SNESGetKSP(ce->snes, &ksp);CHKERRQ(ierr);
ierr = KSPGetPC(ksp, &pc);CHKERRQ(ierr);
ierr = PCMGGetLevels(pc, &oldnlev);CHKERRQ(ierr);
}
/* Cleanup */
ierr = VecDestroy(&u);CHKERRQ(ierr);
ierr = PetscLogStagePop();CHKERRQ(ierr);
}
for (r = 1; r <= Nr; ++r) {
ierr = DMDestroy(&dm[r]);CHKERRQ(ierr);
}
/* Fit convergence rate */
ierr = PetscMalloc2(Nr+1, &x, Nr+1, &y);CHKERRQ(ierr);
for (f = 0; f < ce->Nf; ++f) {
for (r = 0; r <= Nr; ++r) {
x[r] = PetscLog10Real(dof[r*ce->Nf+f]);
y[r] = PetscLog10Real(ce->errors[r*ce->Nf+f]);
}
ierr = PetscLinearRegression(Nr+1, x, y, &slope, &intercept);CHKERRQ(ierr);
/* Since h^{-dim} = N, lg err = s lg N + b = -s dim lg h + b */
alpha[f] = -slope * dim;
}
ierr = PetscFree2(x, y);CHKERRQ(ierr);
ierr = PetscFree2(dm, dof);CHKERRQ(ierr);
/* Restore solver */
ierr = SNESReset(ce->snes);CHKERRQ(ierr);
{
/* PCReset() does not wipe out the level structure */
KSP ksp;
PC pc;
ierr = SNESGetKSP(ce->snes, &ksp);CHKERRQ(ierr);
ierr = KSPGetPC(ksp, &pc);CHKERRQ(ierr);
ierr = PCMGSetLevels(pc, oldnlev, NULL);CHKERRQ(ierr);
ierr = DMSetRefineLevel(ce->idm, oldlevel);CHKERRQ(ierr); /* The damn DMCoarsen() calls in PCMG can reset this */
}
ierr = SNESSetDM(ce->snes, ce->idm);CHKERRQ(ierr);
ierr = DMPlexSetSNESLocalFEM(ce->idm, ctx, ctx, ctx);CHKERRQ(ierr);
ierr = SNESSetFromOptions(ce->snes);CHKERRQ(ierr);
PetscFunctionReturn(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;
}
