int main(int argc, char **argv)
{
SNES snes; /* nonlinear solver */
Mat A,J; /* Jacobian,preconditioner matrix */
Vec u,r; /* solution, residual vectors */
AppCtx user; /* user-defined work context */
PetscReal error = 0.0; /* L_2 error in the solution */
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, &user.dm);CHKERRQ(ierr);
ierr = SNESSetDM(snes, user.dm);CHKERRQ(ierr);
ierr = SetupExactSolution(&user);CHKERRQ(ierr);
ierr = SetupQuadrature(&user);CHKERRQ(ierr);
ierr = SetupSection(user.dm, &user);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(user.dm, &u);CHKERRQ(ierr);
ierr = VecDuplicate(u, &r);CHKERRQ(ierr);
ierr = DMSetMatType(user.dm,MATAIJ);CHKERRQ(ierr);
ierr = DMCreateMatrix(user.dm, &J);CHKERRQ(ierr);
A = J;
ierr = DMSNESSetFunctionLocal(user.dm, (PetscErrorCode (*)(DM,Vec,Vec,void*))FormFunctionLocal,&user);CHKERRQ(ierr);
ierr = DMSNESSetJacobianLocal(user.dm, (PetscErrorCode (*)(DM,Vec,Mat,Mat,void*))FormJacobianLocal,&user);CHKERRQ(ierr);
ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
{
PetscReal res;
/* Check discretization error */
ierr = PetscPrintf(PETSC_COMM_WORLD, "Initial guess\n");CHKERRQ(ierr);
ierr = VecView(u, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
/* ierr = ComputeError(u, &error, &user);CHKERRQ(ierr); */
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);
}
ierr = VecDestroy(&u);CHKERRQ(ierr);
ierr = VecDestroy(&r);CHKERRQ(ierr);
ierr = SNESDestroy(&snes);CHKERRQ(ierr);
ierr = DMDestroy(&user.dm);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
int main(int argc, char **argv)
{
SNES snes; /* nonlinear solver */
DM dm; /* problem definition */
Vec u,r; /* solution, residual vectors */
Mat A,J; /* Jacobian matrix */
MatNullSpace nullSpace; /* May be necessary for pressure */
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 = 0, f;
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 = SetupElement(dm, &user);CHKERRQ(ierr);
for (f = 0; f < NUM_FIELDS; ++f) {
PetscInt numComp;
ierr = PetscFEGetNumComponents(user.fe[f], &numComp);CHKERRQ(ierr);
numComponents += numComp;
}
ierr = PetscMalloc(NUM_FIELDS * sizeof(void (*)(const PetscReal[], PetscScalar *)), &user.exactFuncs);CHKERRQ(ierr);
user.fem.bcFuncs = (void (**)(const PetscReal[], PetscScalar *)) user.exactFuncs;
ierr = SetupExactSolution(dm, &user);CHKERRQ(ierr);
ierr = SetupSection(dm, &user);CHKERRQ(ierr);
ierr = DMPlexCreateClosureIndex(dm, NULL);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(dm, &u);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);
ierr = MatShellSetOperation(A, MATOP_MULT, (void (*)(void))FormJacobianAction);CHKERRQ(ierr);
userJ.dm = dm;
userJ.J = J;
userJ.user = &user;
ierr = DMCreateLocalVector(dm, &userJ.u);CHKERRQ(ierr);
ierr = DMPlexProjectFunctionLocal(dm, user.fe, user.exactFuncs, INSERT_BC_VALUES, userJ.u);CHKERRQ(ierr);
ierr = MatShellSetContext(A, &userJ);CHKERRQ(ierr);
} else {
A = J;
}
ierr = CreatePressureNullSpace(dm, &user, &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,MatStructure*,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, INSERT_ALL_VALUES, u);CHKERRQ(ierr);
if (user.showInitial) {ierr = DMVecViewLocal(dm, u, PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);}
if (user.runType == RUN_FULL) {
ierr = DMPlexProjectFunction(dm, user.fe, user.initialGuess, INSERT_VALUES, u);CHKERRQ(ierr);
if (user.showInitial) {ierr = DMVecViewLocal(dm, u, PETSC_VIEWER_STDOUT_SELF);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, u, &error);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: %.3g\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 {
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, u, &error);CHKERRQ(ierr);
if (error >= 1.0e-11) {
ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: %g\n", error);CHKERRQ(ierr);
} else {
ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: < 1.0e-11\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;
MatStructure flag;
PetscBool isNull;
ierr = SNESComputeJacobian(snes, u, &A, &A, &flag);CHKERRQ(ierr);
ierr = MatNullSpaceTest(nullSpace, J, &isNull);CHKERRQ(ierr);
if (!isNull) SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_PLIB, "The null space calculated for the system operator is invalid.");
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);
}
}
if (user.runType == RUN_FULL) {
PetscViewer viewer;
Vec uLocal;
const char *name;
ierr = PetscViewerCreate(PETSC_COMM_WORLD, &viewer);CHKERRQ(ierr);
ierr = PetscViewerSetType(viewer, PETSCVIEWERVTK);CHKERRQ(ierr);
ierr = PetscViewerSetFormat(viewer, PETSC_VIEWER_ASCII_VTK);CHKERRQ(ierr);
ierr = PetscViewerFileSetName(viewer, "ex62_sol.vtk");CHKERRQ(ierr);
ierr = DMGetLocalVector(dm, &uLocal);CHKERRQ(ierr);
ierr = PetscObjectGetName((PetscObject) u, &name);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) uLocal, name);CHKERRQ(ierr);
ierr = DMGlobalToLocalBegin(dm, u, INSERT_VALUES, uLocal);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(dm, u, INSERT_VALUES, uLocal);CHKERRQ(ierr);
ierr = VecView(uLocal, viewer);CHKERRQ(ierr);
ierr = DMRestoreLocalVector(dm, &uLocal);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
}
ierr = PetscFree(user.exactFuncs);CHKERRQ(ierr);
ierr = DestroyElement(&user);CHKERRQ(ierr);
ierr = MatNullSpaceDestroy(&nullSpace);CHKERRQ(ierr);
if (user.jacobianMF) {
ierr = VecDestroy(&userJ.u);CHKERRQ(ierr);
}
if (A != J) {
ierr = MatDestroy(&A);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 = PetscFinalize();
return 0;
}
int main(int argc, char **argv)
{
SNES snes; /* nonlinear solver */
Vec u,r; /* solution, residual vectors */
Mat A,J; /* Jacobian matrix */
MatNullSpace nullSpace; /* May be necessary for pressure */
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 */
const PetscInt numComponents = NUM_BASIS_COMPONENTS_TOTAL;
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, &user.dm);CHKERRQ(ierr);
ierr = SNESSetDM(snes, user.dm);CHKERRQ(ierr);
ierr = SetupExactSolution(user.dm, &user);CHKERRQ(ierr);
ierr = SetupQuadrature(&user);CHKERRQ(ierr);
ierr = SetupSection(user.dm, &user);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(user.dm, &u);CHKERRQ(ierr);
ierr = VecDuplicate(u, &r);CHKERRQ(ierr);
ierr = DMCreateMatrix(user.dm, MATAIJ, &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);
ierr = MatShellSetOperation(A, MATOP_MULT, (void (*)(void))FormJacobianAction);CHKERRQ(ierr);
userJ.dm = user.dm;
userJ.J = J;
userJ.user = &user;
ierr = DMCreateLocalVector(user.dm, &userJ.u);CHKERRQ(ierr);
ierr = DMPlexProjectFunctionLocal(user.dm, numComponents, user.exactFuncs, INSERT_BC_VALUES, userJ.u);CHKERRQ(ierr);
ierr = MatShellSetContext(A, &userJ);CHKERRQ(ierr);
} else {
A = J;
}
ierr = CreatePressureNullSpace(user.dm, &user, &nullSpace);CHKERRQ(ierr);
ierr = MatSetNullSpace(J, nullSpace);CHKERRQ(ierr);
if (A != J) {
ierr = MatSetNullSpace(A, nullSpace);CHKERRQ(ierr);
}
ierr = DMSNESSetFunctionLocal(user.dm, (PetscErrorCode (*)(DM,Vec,Vec,void*))DMPlexComputeResidualFEM,&user);CHKERRQ(ierr);
ierr = DMSNESSetJacobianLocal(user.dm, (PetscErrorCode (*)(DM,Vec,Mat,Mat,MatStructure*,void*))DMPlexComputeJacobianFEM,&user);CHKERRQ(ierr);
ierr = SNESSetJacobian(snes, A, J, NULL, NULL);CHKERRQ(ierr);
ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
ierr = DMPlexProjectFunction(user.dm, numComponents, user.exactFuncs, INSERT_ALL_VALUES, u);CHKERRQ(ierr);
if (user.showInitial) {ierr = DMVecViewLocal(user.dm, u, PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);}
if (user.runType == RUN_FULL) {
PetscScalar (*initialGuess[numComponents])(const PetscReal x[]);
PetscInt c;
for (c = 0; c < numComponents; ++c) initialGuess[c] = zero;
ierr = DMPlexProjectFunction(user.dm, numComponents, initialGuess, INSERT_VALUES, u);CHKERRQ(ierr);
if (user.showInitial) {ierr = DMVecViewLocal(user.dm, u, PETSC_VIEWER_STDOUT_SELF);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(user.dm, user.fem.quad, user.exactFuncs, u, &error);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: %.3g\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 {
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(user.dm, user.fem.quad, user.exactFuncs, u, &error);CHKERRQ(ierr);
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;
MatStructure flag;
PetscBool isNull;
ierr = SNESComputeJacobian(snes, u, &A, &A, &flag);CHKERRQ(ierr);
ierr = MatNullSpaceTest(nullSpace, J, &isNull);CHKERRQ(ierr);
if (!isNull) SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_PLIB, "The null space calculated for the system operator is invalid.");
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);
}
}
if (user.runType == RUN_FULL) {
PetscViewer viewer;
Vec uLocal;
ierr = PetscViewerCreate(PETSC_COMM_WORLD, &viewer);CHKERRQ(ierr);
ierr = PetscViewerSetType(viewer, PETSCVIEWERVTK);CHKERRQ(ierr);
ierr = PetscViewerSetFormat(viewer, PETSC_VIEWER_ASCII_VTK);CHKERRQ(ierr);
ierr = PetscViewerFileSetName(viewer, "ex62_sol.vtk");CHKERRQ(ierr);
ierr = DMGetLocalVector(user.dm, &uLocal);CHKERRQ(ierr);
ierr = DMGlobalToLocalBegin(user.dm, u, INSERT_VALUES, uLocal);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(user.dm, u, INSERT_VALUES, uLocal);CHKERRQ(ierr);
ierr = PetscObjectReference((PetscObject) user.dm);CHKERRQ(ierr); /* Needed because viewer destroys the DM */
ierr = PetscObjectReference((PetscObject) uLocal);CHKERRQ(ierr); /* Needed because viewer destroys the Vec */
ierr = PetscViewerVTKAddField(viewer, (PetscObject) user.dm, DMPlexVTKWriteAll, PETSC_VTK_POINT_FIELD, (PetscObject) uLocal);CHKERRQ(ierr);
ierr = DMRestoreLocalVector(user.dm, &uLocal);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
}
ierr = DestroyQuadrature(&user);CHKERRQ(ierr);
ierr = MatNullSpaceDestroy(&nullSpace);CHKERRQ(ierr);
if (user.jacobianMF) {
ierr = VecDestroy(&userJ.u);CHKERRQ(ierr);
}
if (A != J) {
ierr = MatDestroy(&A);CHKERRQ(ierr);
}
ierr = MatDestroy(&J);CHKERRQ(ierr);
ierr = VecDestroy(&u);CHKERRQ(ierr);
ierr = VecDestroy(&r);CHKERRQ(ierr);
ierr = SNESDestroy(&snes);CHKERRQ(ierr);
ierr = DMDestroy(&user.dm);CHKERRQ(ierr);
ierr = PetscFinalize();
return 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;
}