void StaggeredStokesOperator::initializeOperatorState(const SAMRAIVectorReal<NDIM, double>& in,
const SAMRAIVectorReal<NDIM, double>& out)
{
IBAMR_TIMER_START(t_initialize_operator_state);
// Deallocate the operator state if the operator is already initialized.
if (d_is_initialized) deallocateOperatorState();
// Setup solution and rhs vectors.
d_x = in.cloneVector(in.getName());
d_b = out.cloneVector(out.getName());
d_x->allocateVectorData();
// Setup the interpolation transaction information.
d_U_fill_pattern = new SideNoCornersFillPattern(SIDEG, false, false, true);
d_P_fill_pattern = new CellNoCornersFillPattern(CELLG, false, false, true);
typedef HierarchyGhostCellInterpolation::InterpolationTransactionComponent InterpolationTransactionComponent;
d_transaction_comps.resize(2);
d_transaction_comps[0] = InterpolationTransactionComponent(d_x->getComponentDescriptorIndex(0),
in.getComponentDescriptorIndex(0),
DATA_REFINE_TYPE,
USE_CF_INTERPOLATION,
DATA_COARSEN_TYPE,
BDRY_EXTRAP_TYPE,
CONSISTENT_TYPE_2_BDRY,
d_U_bc_coefs,
d_U_fill_pattern);
d_transaction_comps[1] = InterpolationTransactionComponent(in.getComponentDescriptorIndex(1),
DATA_REFINE_TYPE,
USE_CF_INTERPOLATION,
DATA_COARSEN_TYPE,
BDRY_EXTRAP_TYPE,
CONSISTENT_TYPE_2_BDRY,
d_P_bc_coef,
d_P_fill_pattern);
// Initialize the interpolation operators.
d_hier_bdry_fill = new HierarchyGhostCellInterpolation();
d_hier_bdry_fill->initializeOperatorState(d_transaction_comps, d_x->getPatchHierarchy());
// Initialize hierarchy math ops object.
if (!d_hier_math_ops_external)
{
d_hier_math_ops = new HierarchyMathOps(d_object_name + "::HierarchyMathOps",
in.getPatchHierarchy(),
in.getCoarsestLevelNumber(),
in.getFinestLevelNumber());
}
#if !defined(NDEBUG)
else
{
TBOX_ASSERT(d_hier_math_ops);
}
#endif
// Indicate the operator is initialized.
d_is_initialized = true;
IBAMR_TIMER_STOP(t_initialize_operator_state);
return;
} // initializeOperatorState
void
INSCollocatedPPMConvectiveOperator::initializeOperatorState(
const SAMRAIVectorReal<NDIM,double>& in,
const SAMRAIVectorReal<NDIM,double>& out)
{
IBAMR_TIMER_START(t_initialize_operator_state);
if (d_is_initialized) deallocateOperatorState();
// Get the hierarchy configuration.
d_hierarchy = in.getPatchHierarchy();
d_coarsest_ln = in.getCoarsestLevelNumber();
d_finest_ln = in.getFinestLevelNumber();
#ifdef DEBUG_CHECK_ASSERTIONS
TBOX_ASSERT(d_hierarchy == out.getPatchHierarchy());
TBOX_ASSERT(d_coarsest_ln == out.getCoarsestLevelNumber());
TBOX_ASSERT(d_finest_ln == out.getFinestLevelNumber());
#else
NULL_USE(out);
#endif
Pointer<CartesianGridGeometry<NDIM> > grid_geom = d_hierarchy->getGridGeometry();
// Setup the coarsen algorithm, operator, and schedules.
Pointer<CoarsenOperator<NDIM> > coarsen_op = grid_geom->lookupCoarsenOperator(d_u_flux_var, "CONSERVATIVE_COARSEN");
d_coarsen_alg = new CoarsenAlgorithm<NDIM>();
if (d_difference_form == ADVECTIVE || d_difference_form == SKEW_SYMMETRIC) d_coarsen_alg->registerCoarsen(d_u_extrap_idx, d_u_extrap_idx, coarsen_op);
if (d_difference_form == CONSERVATIVE || d_difference_form == SKEW_SYMMETRIC) d_coarsen_alg->registerCoarsen(d_u_flux_idx, d_u_flux_idx, coarsen_op);
d_coarsen_scheds.resize(d_finest_ln+1);
for (int ln = d_coarsest_ln+1; ln <= d_finest_ln; ++ln)
{
Pointer<PatchLevel<NDIM> > level = d_hierarchy->getPatchLevel(ln );
Pointer<PatchLevel<NDIM> > coarser_level = d_hierarchy->getPatchLevel(ln-1);
d_coarsen_scheds[ln] = d_coarsen_alg->createSchedule(coarser_level, level);
}
// Setup the refine algorithm, operator, patch strategy, and schedules.
Pointer<RefineOperator<NDIM> > refine_op = grid_geom->lookupRefineOperator(d_U_var, "CONSERVATIVE_LINEAR_REFINE");
d_ghostfill_alg = new RefineAlgorithm<NDIM>();
d_ghostfill_alg->registerRefine(d_U_scratch_idx, in.getComponentDescriptorIndex(0), d_U_scratch_idx, refine_op);
d_ghostfill_strategy = new CartExtrapPhysBdryOp(d_U_scratch_idx, d_bdry_extrap_type);
d_ghostfill_scheds.resize(d_finest_ln+1);
for (int ln = d_coarsest_ln; ln <= d_finest_ln; ++ln)
{
Pointer<PatchLevel<NDIM> > level = d_hierarchy->getPatchLevel(ln);
d_ghostfill_scheds[ln] = d_ghostfill_alg->createSchedule(level, ln-1, d_hierarchy, d_ghostfill_strategy);
}
// Allocate scratch data.
for (int ln = d_coarsest_ln; ln <= d_finest_ln; ++ln)
{
Pointer<PatchLevel<NDIM> > level = d_hierarchy->getPatchLevel(ln);
if (!level->checkAllocated(d_U_scratch_idx))
{
level->allocatePatchData(d_U_scratch_idx);
level->allocatePatchData(d_u_extrap_idx);
if (d_difference_form == CONSERVATIVE || d_difference_form == SKEW_SYMMETRIC) level->allocatePatchData(d_u_flux_idx);
}
}
d_is_initialized = true;
IBAMR_TIMER_STOP(t_initialize_operator_state);
return;
}// initializeOperatorState
void StaggeredStokesOperator::apply(SAMRAIVectorReal<NDIM, double>& x, SAMRAIVectorReal<NDIM, double>& y)
{
IBAMR_TIMER_START(t_apply);
// Get the vector components.
const int U_idx = x.getComponentDescriptorIndex(0);
const int P_idx = x.getComponentDescriptorIndex(1);
const int A_U_idx = y.getComponentDescriptorIndex(0);
const int A_P_idx = y.getComponentDescriptorIndex(1);
const int U_scratch_idx = d_x->getComponentDescriptorIndex(0);
Pointer<SideVariable<NDIM, double> > U_sc_var = x.getComponentVariable(0);
Pointer<CellVariable<NDIM, double> > P_cc_var = x.getComponentVariable(1);
Pointer<SideVariable<NDIM, double> > A_U_sc_var = y.getComponentVariable(0);
Pointer<CellVariable<NDIM, double> > A_P_cc_var = y.getComponentVariable(1);
// Simultaneously fill ghost cell values for all components.
typedef HierarchyGhostCellInterpolation::InterpolationTransactionComponent InterpolationTransactionComponent;
std::vector<InterpolationTransactionComponent> transaction_comps(2);
transaction_comps[0] = InterpolationTransactionComponent(U_scratch_idx,
U_idx,
DATA_REFINE_TYPE,
USE_CF_INTERPOLATION,
DATA_COARSEN_TYPE,
BDRY_EXTRAP_TYPE,
CONSISTENT_TYPE_2_BDRY,
d_U_bc_coefs,
d_U_fill_pattern);
transaction_comps[1] = InterpolationTransactionComponent(P_idx,
DATA_REFINE_TYPE,
USE_CF_INTERPOLATION,
DATA_COARSEN_TYPE,
BDRY_EXTRAP_TYPE,
CONSISTENT_TYPE_2_BDRY,
d_P_bc_coef,
d_P_fill_pattern);
d_hier_bdry_fill->resetTransactionComponents(transaction_comps);
d_hier_bdry_fill->setHomogeneousBc(d_homogeneous_bc);
StaggeredStokesPhysicalBoundaryHelper::setupBcCoefObjects(
d_U_bc_coefs, d_P_bc_coef, U_scratch_idx, P_idx, d_homogeneous_bc);
d_hier_bdry_fill->fillData(d_solution_time);
StaggeredStokesPhysicalBoundaryHelper::resetBcCoefObjects(d_U_bc_coefs, d_P_bc_coef);
// d_bc_helper->enforceDivergenceFreeConditionAtBoundary(U_scratch_idx);
d_hier_bdry_fill->resetTransactionComponents(d_transaction_comps);
// Compute the action of the operator:
//
// A*[U;P] := [A_U;A_P] = [(C*I+D*L)*U + Grad P; -Div U]
d_hier_math_ops->grad(A_U_idx,
A_U_sc_var,
/*cf_bdry_synch*/ false,
1.0,
P_idx,
P_cc_var,
d_no_fill,
d_new_time);
d_hier_math_ops->laplace(A_U_idx,
A_U_sc_var,
d_U_problem_coefs,
U_scratch_idx,
U_sc_var,
d_no_fill,
d_new_time,
1.0,
A_U_idx,
A_U_sc_var);
d_hier_math_ops->div(A_P_idx,
A_P_cc_var,
-1.0,
U_scratch_idx,
U_sc_var,
d_no_fill,
d_new_time,
/*cf_bdry_synch*/ true);
d_bc_helper->copyDataAtDirichletBoundaries(A_U_idx, U_scratch_idx);
IBAMR_TIMER_STOP(t_apply);
return;
} // apply
void
IBImplicitModHelmholtzPETScLevelSolver::initializeSolverState(
const SAMRAIVectorReal<NDIM,double>& x,
const SAMRAIVectorReal<NDIM,double>& b)
{
IBAMR_TIMER_START(t_initialize_solver_state);
// Rudimentary error checking.
#ifdef DEBUG_CHECK_ASSERTIONS
if (x.getNumberOfComponents() != b.getNumberOfComponents())
{
TBOX_ERROR(d_object_name << "::initializeSolverState()\n"
<< " vectors must have the same number of components" << std::endl);
}
const Pointer<PatchHierarchy<NDIM> >& patch_hierarchy = x.getPatchHierarchy();
if (patch_hierarchy != b.getPatchHierarchy())
{
TBOX_ERROR(d_object_name << "::initializeSolverState()\n"
<< " vectors must have the same hierarchy" << std::endl);
}
const int coarsest_ln = x.getCoarsestLevelNumber();
if (coarsest_ln < 0)
{
TBOX_ERROR(d_object_name << "::initializeSolverState()\n"
<< " coarsest level number must not be negative" << std::endl);
}
if (coarsest_ln != b.getCoarsestLevelNumber())
{
TBOX_ERROR(d_object_name << "::initializeSolverState()\n"
<< " vectors must have same coarsest level number" << std::endl);
}
const int finest_ln = x.getFinestLevelNumber();
if (finest_ln < coarsest_ln)
{
TBOX_ERROR(d_object_name << "::initializeSolverState()\n"
<< " finest level number must be >= coarsest level number" << std::endl);
}
if (finest_ln != b.getFinestLevelNumber())
{
TBOX_ERROR(d_object_name << "::initializeSolverState()\n"
<< " vectors must have same finest level number" << std::endl);
}
for (int ln = coarsest_ln; ln <= finest_ln; ++ln)
{
if (patch_hierarchy->getPatchLevel(ln).isNull())
{
TBOX_ERROR(d_object_name << "::initializeSolverState()\n"
<< " hierarchy level " << ln << " does not exist" << std::endl);
}
}
if (coarsest_ln != finest_ln)
{
TBOX_ERROR(d_object_name << "::initializeSolverState()\n"
<< " coarsest_ln != finest_ln in IBImplicitModHelmholtzPETScLevelSolver" << std::endl);
}
#endif
// Deallocate the solver state if the solver is already initialized.
if (d_is_initialized) deallocateSolverState();
// Get the hierarchy information.
d_hierarchy = x.getPatchHierarchy();
d_level_num = x.getCoarsestLevelNumber();
#ifdef DEBUG_CHECK_ASSERTIONS
TBOX_ASSERT(d_level_num == x.getFinestLevelNumber());
#endif
const int x_idx = x.getComponentDescriptorIndex(0);
Pointer<SideVariable<NDIM,double> > x_var = x.getComponentVariable(0);
const int b_idx = b.getComponentDescriptorIndex(0);
Pointer<SideVariable<NDIM,double> > b_var = b.getComponentVariable(0);
// Allocate DOF index data.
VariableDatabase<NDIM>* var_db = VariableDatabase<NDIM>::getDatabase();
Pointer<SideDataFactory<NDIM,double> > x_fac =
var_db->getPatchDescriptor()->getPatchDataFactory(x_idx);
const int depth = x_fac->getDefaultDepth();
Pointer<SideDataFactory<NDIM,int> > dof_index_fac =
var_db->getPatchDescriptor()->getPatchDataFactory(d_dof_index_idx);
dof_index_fac->setDefaultDepth(depth);
Pointer<PatchLevel<NDIM> > level = d_hierarchy->getPatchLevel(d_level_num);
if (!level->checkAllocated(d_dof_index_idx)) level->allocatePatchData(d_dof_index_idx);
// Setup PETSc objects.
int ierr;
PETScVecUtilities::constructPatchLevelVec(d_petsc_x, x_idx, x_var, level);
PETScVecUtilities::constructPatchLevelVec(d_petsc_b, b_idx, b_var, level);
PETScVecUtilities::constructPatchLevelDOFIndices(d_dof_index_idx, d_dof_index_var, x_idx, x_var, level);
const double C = d_poisson_spec.cIsZero() ? 0.0 : d_poisson_spec.getCConstant();
const double D = d_poisson_spec.getDConstant();
PETScMatUtilities::constructPatchLevelLaplaceOp(d_petsc_mat, C, D, x_idx, x_var, d_dof_index_idx, d_dof_index_var, level, d_dof_index_fill);
if (d_SJR_mat != PETSC_NULL)
{
ierr = PETScMatOps::MatAXPY(d_petsc_mat, 1.0, d_SJR_mat); IBTK_CHKERRQ(ierr);
}
ierr = MatSetBlockSize(d_petsc_mat, NDIM); IBTK_CHKERRQ(ierr);
ierr = KSPCreate(PETSC_COMM_WORLD, &d_petsc_ksp); IBTK_CHKERRQ(ierr);
ierr = KSPSetOperators(d_petsc_ksp, d_petsc_mat, d_petsc_mat, SAME_PRECONDITIONER); IBTK_CHKERRQ(ierr);
if (!d_options_prefix.empty())
{
ierr = KSPSetOptionsPrefix(d_petsc_ksp, d_options_prefix.c_str()); IBTK_CHKERRQ(ierr);
}
ierr = KSPSetFromOptions(d_petsc_ksp); IBTK_CHKERRQ(ierr);
// Indicate that the solver is initialized.
d_is_initialized = true;
IBAMR_TIMER_STOP(t_initialize_solver_state);
return;
}// initializeSolverState
void
FACPreconditioner::facCycle_McCormick(
SAMRAIVectorReal<double>& e,
SAMRAIVectorReal<double>& r,
SAMRAIVectorReal<double>& u,
int lmax,
int lmin,
int ln)
{
/*
* The steps 1-4 in this function correspond to McCormick's steps
* those in his description.
*
* 1. If on the coarsest level, solve it.
* 2. Presmoothing.
* 3. Recurse to next lower level.
* 4. Postsmoothing.
*/
/*
* Step 1.
*/
if (ln == lmin) {
/*
* Solve coarsest level.
*/
d_fac_operator->solveCoarsestLevel(e,
r,
ln);
} else {
int i, num_components = e.getNumberOfComponents();
/*
* Step 2a.
*/
d_fac_operator->computeCompositeResidualOnLevel(*d_tmp_residual,
e,
r,
ln,
true);
for (i = 0; i < num_components; ++i) {
int tmp_id = d_tmp_error->getComponentDescriptorIndex(i);
d_controlled_level_ops[i]->resetLevels(ln,
ln);
d_controlled_level_ops[i]->setToScalar(tmp_id,
0.0);
}
/*
* Step 2b.
*/
d_fac_operator->smoothError(*d_tmp_error,
*d_tmp_residual,
ln,
d_presmoothing_sweeps);
/*
* Step 2c.
*/
for (i = 0; i < num_components; ++i) {
int tmp_id = d_tmp_error->getComponentDescriptorIndex(i);
int id = e.getComponentDescriptorIndex(i);
d_controlled_level_ops[i]->resetLevels(ln,
ln);
d_controlled_level_ops[i]->add(id,
id,
tmp_id);
}
/*
* Step 3a.
*/
d_fac_operator->computeCompositeResidualOnLevel(*d_tmp_residual,
e,
r,
ln,
true);
d_fac_operator->restrictResidual(*d_tmp_residual,
*d_tmp_residual,
ln - 1);
/*
* Step 3b.
*/
for (i = 0; i < num_components; ++i) {
int tmp_id = e.getComponentDescriptorIndex(i);
d_controlled_level_ops[i]->resetLevels(ln - 1,
ln - 1);
d_controlled_level_ops[i]->setToScalar(tmp_id,
0.0);
}
/*
* Step 3c.
*/
facCycle_McCormick(e,
r,
u,
lmax,
lmin,
ln - 1);
/*
* Step 3d.
*/
d_fac_operator->prolongErrorAndCorrect(e,
e,
ln);
/*
* Step 4a.
*/
d_fac_operator->computeCompositeResidualOnLevel(*d_tmp_residual,
e,
r,
ln,
true);
for (i = 0; i < num_components; ++i) {
int tmp_id = d_tmp_error->getComponentDescriptorIndex(i);
d_controlled_level_ops[i]->resetLevels(ln,
ln);
d_controlled_level_ops[i]->setToScalar(tmp_id,
0.0);
}
/*
* Step 4b.
*/
d_fac_operator->smoothError(*d_tmp_error,
*d_tmp_residual,
ln,
d_postsmoothing_sweeps);
/*
* Step 4c.
*/
for (i = 0; i < num_components; ++i) {
int tmp_id = d_tmp_error->getComponentDescriptorIndex(i);
int id = e.getComponentDescriptorIndex(i);
d_controlled_level_ops[i]->resetLevels(ln,
ln);
d_controlled_level_ops[i]->add(id,
id,
tmp_id);
}
}
}
bool
FACPreconditioner::solveSystem(
SAMRAIVectorReal<double>& u,
SAMRAIVectorReal<double>& f)
{
d_residual_norm = tbox::MathUtilities<double>::getSignalingNaN();
d_avg_convergence_factor = tbox::MathUtilities<double>::getSignalingNaN();
/*
* Set the solution-vector-dependent data if not preset.
*/
bool clear_hierarchy_configuration_when_done = false;
if (!d_patch_hierarchy) {
clear_hierarchy_configuration_when_done = true;
initializeSolverState(u, f);
} else {
#ifdef DEBUG_CHECK_ASSERTIONS
if (!checkVectorStateCompatibility(u, f)) {
TBOX_ERROR(d_object_name << ": Incompatible vectors for\n"
<< "current state in solveSystem.\n");
}
#endif
}
t_solve_system->start();
d_error_vector->setToScalar(0.0, false);
if (d_tmp_error) {
d_tmp_error->setToScalar(0.0, false);
}
d_residual_vector->setToScalar(0.0);
const double initial_residual_norm = d_residual_norm =
computeFullCompositeResidual(*d_residual_vector,
u,
f);
/*
* Above step has the side effect of filling the residual
* vector d_residual_vector.
*/
double effective_residual_tolerance = d_residual_tolerance;
if (d_relative_residual_tolerance >= 0) {
double tmp = d_fac_operator->computeResidualNorm(f,
d_finest_ln,
d_coarsest_ln);
tmp *= d_relative_residual_tolerance;
if (effective_residual_tolerance < tmp) effective_residual_tolerance =
tmp;
}
if (static_cast<int>(d_convergence_factor.size()) < d_max_iterations)
d_convergence_factor.resize(d_max_iterations);
d_number_iterations = 0;
/*
* Use a do loop instead of a while loop until convergence.
* It is important to go through the loop at least once
* because the residual norm can be less than the tolerance
* when the solution is 0 and the rhs is less than the tolerance.
*/
do {
/*
* In zeroing the error vector, also zero out the ghost values.
* This gives the FAC operator an oportunity to bypass the
* ghost filling if it decides that the ghost values do not
* change.
*/
d_error_vector->setToScalar(0.0, false);
/*
* Both the recursive and non-recursive fac cycling functions
* were coded to find the problem due presmoothing. Both give
* the same results, but the problem due to presmoothing still
* exists. BTNG.
*/
if (d_algorithm_choice == "default") {
facCycle_Recursive(*d_error_vector,
*d_residual_vector,
u,
d_finest_ln,
d_coarsest_ln,
d_finest_ln);
} else if (d_algorithm_choice == "mccormick-s4.3") {
facCycle_McCormick(*d_error_vector,
*d_residual_vector,
u,
d_finest_ln,
d_coarsest_ln,
d_finest_ln);
} else if (d_algorithm_choice == "pernice") {
facCycle(*d_error_vector,
*d_residual_vector,
u,
d_finest_ln,
d_coarsest_ln);
}
int i, num_components = d_error_vector->getNumberOfComponents();
/*
* u += e
*/
for (i = 0; i < num_components; ++i) {
int soln_id = u.getComponentDescriptorIndex(i);
int err_id = d_error_vector->getComponentDescriptorIndex(i);
d_controlled_level_ops[i]->resetLevels(d_coarsest_ln, d_finest_ln);
d_controlled_level_ops[i]->add(soln_id,
soln_id,
err_id);
}
/*
* Synchronize solution across levels by coarsening the
* more accurate fine-level solutions.
*/
for (int ln = d_finest_ln - 1; ln >= d_coarsest_ln; --ln) {
d_fac_operator->restrictSolution(u,
u,
ln);
}
/*
* Compute convergence factor and new residual norm.
* 1. Temporarily save pre-cycle residual norm in
* convergence factor stack.
* 2. Compute post-cycle residual norm.
* 3. Set convergence factor to ratio of post-cycle to pre-cycle
* residual norms.
*/
d_convergence_factor[d_number_iterations] = d_residual_norm;
d_residual_norm = computeFullCompositeResidual(*d_residual_vector,
u,
f);
// Disable Intel warning on real comparison
#ifdef __INTEL_COMPILER
#pragma warning (disable:1572)
#endif
if (d_convergence_factor[d_number_iterations] != 0) {
d_convergence_factor[d_number_iterations] =
d_residual_norm / d_convergence_factor[d_number_iterations];
} else {
d_convergence_factor[d_number_iterations] = 0;
}
/*
* Increment the iteration counter.
* The rest of this block expects it to have the incremented value.
* In particular, d_fac_operator->postprocessOneCycle does.
*/
++d_number_iterations;
/*
* Compute the convergence factors because they may be accessed
* from the operator's postprocessOneCycle function.
*/
d_net_convergence_factor = d_residual_norm
/ (initial_residual_norm + 1e-20);
d_avg_convergence_factor = pow(d_net_convergence_factor,
1.0 / d_number_iterations);
d_fac_operator->postprocessOneCycle(d_number_iterations - 1,
u,
*d_residual_vector);
} while ((d_residual_norm > effective_residual_tolerance)
&& (d_number_iterations < d_max_iterations));
t_solve_system->stop();
if (clear_hierarchy_configuration_when_done) {
deallocateSolverState();
}
return d_residual_norm < effective_residual_tolerance;
}
void
INSStaggeredVCStokesOperator::apply(
const bool /*homogeneous_bc*/,
SAMRAIVectorReal<NDIM,double>& x,
SAMRAIVectorReal<NDIM,double>& y)
{
IBAMR_TIMER_START(t_apply);
// Get the vector components.
// const int U_in_idx = x.getComponentDescriptorIndex(0);
// const int P_in_idx = x.getComponentDescriptorIndex(1);
const int U_out_idx = y.getComponentDescriptorIndex(0);
const int P_out_idx = y.getComponentDescriptorIndex(1);
const int U_scratch_idx = d_x_scratch->getComponentDescriptorIndex(0);
const int P_scratch_idx = d_x_scratch->getComponentDescriptorIndex(1);
const Pointer<Variable<NDIM> >& U_out_var = y.getComponentVariable(0);
const Pointer<Variable<NDIM> >& P_out_var = y.getComponentVariable(1);
Pointer<SideVariable<NDIM,double> > U_out_sc_var = U_out_var;
Pointer<CellVariable<NDIM,double> > P_out_cc_var = P_out_var;
const Pointer<Variable<NDIM> >& U_scratch_var = d_x_scratch->getComponentVariable(0);
const Pointer<Variable<NDIM> >& P_scratch_var = d_x_scratch->getComponentVariable(1);
Pointer<SideVariable<NDIM,double> > U_scratch_sc_var = U_scratch_var;
Pointer<CellVariable<NDIM,double> > P_scratch_cc_var = P_scratch_var;
d_x_scratch->copyVector(Pointer<SAMRAIVectorReal<NDIM,double> >(&x,false));
// Reset the interpolation operators and fill the data.
typedef HierarchyGhostCellInterpolation::InterpolationTransactionComponent InterpolationTransactionComponent;
InterpolationTransactionComponent U_scratch_component(U_scratch_idx, U_DATA_COARSEN_TYPE, BDRY_EXTRAP_TYPE, CONSISTENT_TYPE_2_BDRY);
InterpolationTransactionComponent P_scratch_component(P_scratch_idx, P_DATA_COARSEN_TYPE, BDRY_EXTRAP_TYPE, CONSISTENT_TYPE_2_BDRY);
InterpolationTransactionComponent mu_component(d_mu_data_idx, MU_DATA_COARSEN_TYPE, BDRY_EXTRAP_TYPE, CONSISTENT_TYPE_2_BDRY);
std::vector<InterpolationTransactionComponent> U_P_MU_components(3);
U_P_MU_components[0] = U_scratch_component;
U_P_MU_components[1] = P_scratch_component;
U_P_MU_components[2] = mu_component;
d_U_P_MU_bdry_fill_op->resetTransactionComponents(U_P_MU_components);
d_U_P_MU_bdry_fill_op->fillData(d_new_time);
// Setup hierarchy data ops object for U.
HierarchyDataOpsManager<NDIM>* hier_ops_manager = HierarchyDataOpsManager<NDIM>::getManager();
Pointer<PatchHierarchy<NDIM> > hierarchy = y.getPatchHierarchy();
Pointer<HierarchySideDataOpsReal<NDIM,double> > hier_sc_data_ops =
hier_ops_manager->getOperationsDouble(U_out_var, hierarchy, true);
// Compute the action of the operator:
// A*[u;p] = [(rho/dt)*u-0.5*div*(mu*(grad u + (grad u)^T)) + grad p; -div u].
//
static const bool cf_bdry_synch = true;
d_hier_math_ops->pointwiseMultiply(
U_out_idx, U_out_sc_var,
d_rho_data_idx, d_rho_var,
U_scratch_idx, U_scratch_sc_var,
0.0, -1, NULL);
d_hier_math_ops->vc_laplace(
U_out_idx, U_out_sc_var,
-0.5, 0.0, d_mu_data_idx, d_mu_var,
U_scratch_idx, U_scratch_sc_var, d_no_fill_op, d_new_time,
1.0/d_dt, U_out_idx, U_out_sc_var);
d_hier_math_ops->grad(
U_out_idx, U_out_sc_var,
cf_bdry_synch,
1.0, P_scratch_idx, P_scratch_cc_var, d_no_fill_op, d_new_time,
1.0, U_out_idx, U_out_sc_var);
d_hier_math_ops->div(
P_out_idx, P_out_cc_var,
-1.0, U_scratch_idx, U_scratch_sc_var, d_no_fill_op, d_new_time,
cf_bdry_synch);
IBAMR_TIMER_STOP(t_apply);
return;
}// apply
bool
StaggeredStokesProjectionPreconditioner::solveSystem(SAMRAIVectorReal<NDIM, double>& x,
SAMRAIVectorReal<NDIM, double>& b)
{
IBAMR_TIMER_START(t_solve_system);
// Initialize the solver (if necessary).
const bool deallocate_at_completion = !d_is_initialized;
if (!d_is_initialized) initializeSolverState(x, b);
// Determine whether we are solving a steady-state problem.
const bool steady_state =
d_U_problem_coefs.cIsZero() ||
(d_U_problem_coefs.cIsConstant() && MathUtilities<double>::equalEps(d_U_problem_coefs.getCConstant(), 0.0));
// Get the vector components.
const int F_U_idx = b.getComponentDescriptorIndex(0);
const int F_P_idx = b.getComponentDescriptorIndex(1);
const Pointer<Variable<NDIM> >& F_U_var = b.getComponentVariable(0);
const Pointer<Variable<NDIM> >& F_P_var = b.getComponentVariable(1);
Pointer<SideVariable<NDIM, double> > F_U_sc_var = F_U_var;
Pointer<CellVariable<NDIM, double> > F_P_cc_var = F_P_var;
const int U_idx = x.getComponentDescriptorIndex(0);
const int P_idx = x.getComponentDescriptorIndex(1);
const Pointer<Variable<NDIM> >& U_var = x.getComponentVariable(0);
const Pointer<Variable<NDIM> >& P_var = x.getComponentVariable(1);
Pointer<SideVariable<NDIM, double> > U_sc_var = U_var;
Pointer<CellVariable<NDIM, double> > P_cc_var = P_var;
// Setup the component solver vectors.
Pointer<SAMRAIVectorReal<NDIM, double> > F_U_vec;
F_U_vec = new SAMRAIVectorReal<NDIM, double>(d_object_name + "::F_U", d_hierarchy, d_coarsest_ln, d_finest_ln);
F_U_vec->addComponent(F_U_sc_var, F_U_idx, d_velocity_wgt_idx, d_velocity_data_ops);
Pointer<SAMRAIVectorReal<NDIM, double> > U_vec;
U_vec = new SAMRAIVectorReal<NDIM, double>(d_object_name + "::U", d_hierarchy, d_coarsest_ln, d_finest_ln);
U_vec->addComponent(U_sc_var, U_idx, d_velocity_wgt_idx, d_velocity_data_ops);
Pointer<SAMRAIVectorReal<NDIM, double> > Phi_scratch_vec;
Phi_scratch_vec =
new SAMRAIVectorReal<NDIM, double>(d_object_name + "::Phi_scratch", d_hierarchy, d_coarsest_ln, d_finest_ln);
Phi_scratch_vec->addComponent(d_Phi_var, d_Phi_scratch_idx, d_pressure_wgt_idx, d_pressure_data_ops);
Pointer<SAMRAIVectorReal<NDIM, double> > F_Phi_vec;
F_Phi_vec = new SAMRAIVectorReal<NDIM, double>(d_object_name + "::F_Phi", d_hierarchy, d_coarsest_ln, d_finest_ln);
F_Phi_vec->addComponent(d_F_Phi_var, d_F_Phi_idx, d_pressure_wgt_idx, d_pressure_data_ops);
Pointer<SAMRAIVectorReal<NDIM, double> > P_vec;
P_vec = new SAMRAIVectorReal<NDIM, double>(d_object_name + "::P", d_hierarchy, d_coarsest_ln, d_finest_ln);
P_vec->addComponent(P_cc_var, P_idx, d_pressure_wgt_idx, d_pressure_data_ops);
// Allocate scratch data.
for (int ln = d_coarsest_ln; ln <= d_finest_ln; ++ln)
{
Pointer<PatchLevel<NDIM> > level = d_hierarchy->getPatchLevel(ln);
level->allocatePatchData(d_Phi_scratch_idx);
level->allocatePatchData(d_F_Phi_idx);
}
// (1) Solve the velocity sub-problem for an initial approximation to U.
//
// U^* := inv(rho/dt - K*mu*L) F_U
//
// An approximate Helmholtz solver is used.
d_velocity_solver->setHomogeneousBc(true);
LinearSolver* p_velocity_solver = dynamic_cast<LinearSolver*>(d_velocity_solver.getPointer());
if (p_velocity_solver) p_velocity_solver->setInitialGuessNonzero(false);
d_velocity_solver->solveSystem(*U_vec, *F_U_vec);
// (2) Solve the pressure sub-problem.
//
// We treat two cases:
//
// (i) rho/dt = 0.
//
// In this case,
//
// U - U^* + G Phi = 0
// -D U = F_P
//
// so that
//
// Phi := inv(-L_p) * F_Phi = inv(-L_p) * (-F_P - D U^*)
// P := -K*mu*F_Phi
//
// in which L_p = D*G.
//
// (ii) rho/dt != 0.
//
// In this case,
//
// rho (U - U^*) + G Phi = 0
// -D U = F_P
//
// so that
//
// Phi := inv(-L_rho) * F_phi = inv(-L_rho) * (-F_P - D U^*)
// P := (1/dt - K*mu*L_rho)*Phi = (1/dt) Phi - K*mu*F_phi
//
// in which L_rho = D*(1/rho)*G.
//
// Approximate Poisson solvers are used in both cases.
d_hier_math_ops->div(d_F_Phi_idx,
d_F_Phi_var,
-1.0,
U_idx,
U_sc_var,
d_no_fill_op,
d_new_time,
/*cf_bdry_synch*/ true,
-1.0,
F_P_idx,
F_P_cc_var);
d_pressure_solver->setHomogeneousBc(true);
LinearSolver* p_pressure_solver = dynamic_cast<LinearSolver*>(d_pressure_solver.getPointer());
p_pressure_solver->setInitialGuessNonzero(false);
d_pressure_solver->solveSystem(*Phi_scratch_vec, *F_Phi_vec);
if (steady_state)
{
d_pressure_data_ops->scale(P_idx, -d_U_problem_coefs.getDConstant(), d_F_Phi_idx);
}
else
{
d_pressure_data_ops->linearSum(
P_idx, 1.0 / getDt(), d_Phi_scratch_idx, -d_U_problem_coefs.getDConstant(), d_F_Phi_idx);
}
// (3) Evaluate U in terms of U^* and Phi.
//
// We treat two cases:
//
// (i) rho = 0. In this case,
//
// U = U^* - G Phi
//
// (ii) rho != 0. In this case,
//
// U = U^* - (1.0/rho) G Phi
double coef;
if (steady_state)
{
coef = -1.0;
}
else
{
coef = d_P_problem_coefs.getDConstant();
}
d_hier_math_ops->grad(U_idx,
U_sc_var,
/*cf_bdry_synch*/ true,
coef,
d_Phi_scratch_idx,
d_Phi_var,
d_Phi_bdry_fill_op,
d_pressure_solver->getSolutionTime(),
1.0,
U_idx,
U_sc_var);
// Account for nullspace vectors.
correctNullspace(U_vec, P_vec);
// Deallocate scratch data.
for (int ln = d_coarsest_ln; ln <= d_finest_ln; ++ln)
{
Pointer<PatchLevel<NDIM> > level = d_hierarchy->getPatchLevel(ln);
level->deallocatePatchData(d_Phi_scratch_idx);
level->deallocatePatchData(d_F_Phi_idx);
}
// Deallocate the solver (if necessary).
if (deallocate_at_completion) deallocateSolverState();
IBAMR_TIMER_STOP(t_solve_system);
return true;
} // solveSystem
