PetscErrorCode SetupDiscretization(DM dm, AppCtx *user)
{
DM cdm = dm;
const PetscInt dim = 2;
PetscFE fe[3];
PetscQuadrature q;
PetscInt f;
MPI_Comm comm;
PetscErrorCode ierr;
PetscFunctionBeginUser;
/* Create finite element */
ierr = PetscObjectGetComm((PetscObject) dm, &comm);CHKERRQ(ierr);
ierr = PetscFECreateDefault(comm, dim, 1, PETSC_TRUE, "potential_", -1, &fe[0]);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) fe[0], "potential");CHKERRQ(ierr);
ierr = PetscFEGetQuadrature(fe[0], &q);CHKERRQ(ierr);
ierr = PetscFECreateDefault(comm, dim, 1, PETSC_TRUE, "charge_", -1, &fe[1]);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) fe[1], "charge");CHKERRQ(ierr);
ierr = PetscFESetQuadrature(fe[1], q);CHKERRQ(ierr);
ierr = PetscFECreateDefault(comm, dim, 1, PETSC_TRUE, "multiplier_", -1, &fe[2]);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) fe[2], "multiplier");CHKERRQ(ierr);
ierr = PetscFESetQuadrature(fe[2], q);CHKERRQ(ierr);
/* Set discretization and boundary conditions for each mesh */
for (f = 0; f < 3; ++f) {ierr = DMSetField(dm, f, NULL, (PetscObject) fe[f]);CHKERRQ(ierr);}
ierr = DMCreateDS(cdm);CHKERRQ(ierr);
ierr = SetupProblem(dm, user);CHKERRQ(ierr);
while (cdm) {
ierr = DMCopyDisc(dm, cdm);CHKERRQ(ierr);
ierr = DMGetCoarseDM(cdm, &cdm);CHKERRQ(ierr);
}
for (f = 0; f < 3; ++f) {ierr = PetscFEDestroy(&fe[f]);CHKERRQ(ierr);}
PetscFunctionReturn(0);
}
PetscErrorCode SetupDiscretization(DM dm, AppCtx *user)
{
DM cdm = dm;
const PetscInt dim = user->dim;
PetscFE fe[2];
PetscQuadrature q;
Parameter *param;
MPI_Comm comm;
PetscErrorCode ierr;
PetscFunctionBeginUser;
/* Create finite element */
ierr = PetscObjectGetComm((PetscObject) dm, &comm);CHKERRQ(ierr);
ierr = PetscFECreateDefault(comm, dim, dim, user->simplex, "vel_", PETSC_DEFAULT, &fe[0]);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) fe[0], "velocity");CHKERRQ(ierr);
ierr = PetscFEGetQuadrature(fe[0], &q);CHKERRQ(ierr);
ierr = PetscFECreateDefault(comm, dim, 1, user->simplex, "pres_", PETSC_DEFAULT, &fe[1]);CHKERRQ(ierr);
ierr = PetscFESetQuadrature(fe[1], q);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) fe[1], "pressure");CHKERRQ(ierr);
/* Set discretization and boundary conditions for each mesh */
ierr = DMSetField(dm, 0, NULL, (PetscObject) fe[0]);CHKERRQ(ierr);
ierr = DMSetField(dm, 1, NULL, (PetscObject) fe[1]);CHKERRQ(ierr);
ierr = DMCreateDS(dm);CHKERRQ(ierr);
ierr = SetupProblem(dm, user);CHKERRQ(ierr);
ierr = PetscBagGetData(user->bag, (void **) ¶m);CHKERRQ(ierr);
while (cdm) {
ierr = DMCopyDisc(dm, cdm);CHKERRQ(ierr);
ierr = DMPlexCreateBasisRotation(cdm, param->alpha, 0.0, 0.0);CHKERRQ(ierr);
ierr = DMGetCoarseDM(cdm, &cdm);CHKERRQ(ierr);
}
ierr = PetscFEDestroy(&fe[0]);CHKERRQ(ierr);
ierr = PetscFEDestroy(&fe[1]);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode SetupFE(DM dm, PetscInt Nc, PetscBool simplex, const char name[], PetscErrorCode (*setup)(DM, AppCtx *), void *ctx)
{
AppCtx *user = (AppCtx *) ctx;
DM cdm = dm;
PetscFE fe;
char prefix[PETSC_MAX_PATH_LEN];
PetscInt dim;
PetscErrorCode ierr;
PetscFunctionBegin;
/* Create finite element */
ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
ierr = PetscSNPrintf(prefix, PETSC_MAX_PATH_LEN, "%s_", name);CHKERRQ(ierr);
ierr = PetscFECreateDefault(PetscObjectComm((PetscObject) dm), dim, Nc, simplex, name ? prefix : NULL, -1, &fe);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) fe, name);CHKERRQ(ierr);
/* Set discretization and boundary conditions for each mesh */
ierr = DMSetField(dm, 0, NULL, (PetscObject) fe);CHKERRQ(ierr);
ierr = DMCreateDS(dm);CHKERRQ(ierr);
ierr = (*setup)(dm, user);CHKERRQ(ierr);
while (cdm) {
ierr = DMCopyDisc(dm, cdm);CHKERRQ(ierr);
if (user->useNearNullspace) {ierr = DMSetNearNullSpaceConstructor(cdm, 0, CreateElasticityNullSpace);CHKERRQ(ierr);}
/* TODO: Check whether the boundary of coarse meshes is marked */
ierr = DMGetCoarseDM(cdm, &cdm);CHKERRQ(ierr);
}
ierr = PetscFEDestroy(&fe);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
static PetscErrorCode SetupDiscretization(DM dm, const char name[], PetscErrorCode (*setup)(DM, AppCtx *), AppCtx *user)
{
DM cdm = dm;
PetscFE fe;
char prefix[PETSC_MAX_PATH_LEN];
PetscErrorCode ierr;
PetscFunctionBeginUser;
/* Create finite element */
ierr = PetscSNPrintf(prefix, PETSC_MAX_PATH_LEN, "%s_", name);CHKERRQ(ierr);
ierr = PetscFECreateDefault(PetscObjectComm((PetscObject) dm), user->dim, 1, user->simplex, name ? prefix : NULL, -1, &fe);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) fe, name);CHKERRQ(ierr);
/* Set discretization and boundary conditions for each mesh */
ierr = DMSetField(dm, 0, NULL, (PetscObject) fe);CHKERRQ(ierr);
ierr = DMCreateDS(dm);CHKERRQ(ierr);
ierr = (*setup)(dm, user);CHKERRQ(ierr);
while (cdm) {
ierr = DMCopyDisc(dm,cdm);CHKERRQ(ierr);
/* TODO: Check whether the boundary of coarse meshes is marked */
ierr = DMGetCoarseDM(cdm, &cdm);CHKERRQ(ierr);
}
ierr = PetscFEDestroy(&fe);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*@
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);
}
