bool
BJacobiPreconditioner::solveSystem(
SAMRAIVectorReal<NDIM,double>& x,
SAMRAIVectorReal<NDIM,double>& b)
{
// Initialize the preconditioner, when necessary.
const bool deallocate_after_solve = !d_is_initialized;
if (deallocate_after_solve) initializeSolverState(x,b);
Pointer<PatchHierarchy<NDIM> > hierarchy = x.getPatchHierarchy();
const int coarsest_ln = x.getCoarsestLevelNumber();
const int finest_ln = x.getFinestLevelNumber() ;
#ifdef DEBUG_CHECK_ASSERTIONS
TBOX_ASSERT(x.getNumberOfComponents() == b.getNumberOfComponents());
TBOX_ASSERT(hierarchy == b.getPatchHierarchy());
TBOX_ASSERT(coarsest_ln == b.getCoarsestLevelNumber());
TBOX_ASSERT( finest_ln == b.getFinestLevelNumber() );
#endif
const std::string& x_name = x.getName();
const std::string& b_name = b.getName();
bool ret_val = true;
// Zero out the initial guess.
#ifdef DEBUG_CHECK_ASSERTIONS
TBOX_ASSERT(d_initial_guess_nonzero == false);
#endif
x.setToScalar(0.0, /*interior_only*/ false);
for (int comp = 0; comp < x.getNumberOfComponents(); ++comp)
{
// Setup a SAMRAIVectorReal to correspond to the individual vector
// component.
std::ostringstream str;
str << comp;
SAMRAIVectorReal<NDIM,double> x_comp(x_name+"_component_"+str.str(), hierarchy, coarsest_ln, finest_ln);
x_comp.addComponent(x.getComponentVariable(comp), x.getComponentDescriptorIndex(comp), x.getControlVolumeIndex(comp));
SAMRAIVectorReal<NDIM,double> b_comp(b_name+"_component_"+str.str(), hierarchy, coarsest_ln, finest_ln);
b_comp.addComponent(b.getComponentVariable(comp), b.getComponentDescriptorIndex(comp), b.getControlVolumeIndex(comp));
// Configure the component preconditioner.
Pointer<LinearSolver> pc_comp = d_pc_map[comp];
pc_comp->setInitialGuessNonzero(d_initial_guess_nonzero);
pc_comp->setMaxIterations(d_max_iterations);
pc_comp->setAbsoluteTolerance(d_abs_residual_tol);
pc_comp->setRelativeTolerance(d_rel_residual_tol);
// Apply the component preconditioner.
const bool ret_val_comp = pc_comp->solveSystem(x_comp, b_comp);
ret_val = ret_val && ret_val_comp;
}
// Deallocate the preconditioner, when necessary.
if (deallocate_after_solve) deallocateSolverState();
return ret_val;
}// solveSystem
bool
PETScKrylovLinearSolver::solveSystem(SAMRAIVectorReal<NDIM, double>& x, SAMRAIVectorReal<NDIM, double>& b)
{
IBTK_TIMER_START(t_solve_system);
#if !defined(NDEBUG)
TBOX_ASSERT(d_A);
#endif
int ierr;
// Initialize the solver, when necessary.
const bool deallocate_after_solve = !d_is_initialized;
if (deallocate_after_solve) initializeSolverState(x, b);
#if !defined(NDEBUG)
TBOX_ASSERT(d_petsc_ksp);
#endif
resetKSPOptions();
// Allocate scratch data.
d_b->allocateVectorData();
// Solve the system using a PETSc KSP object.
d_b->copyVector(Pointer<SAMRAIVectorReal<NDIM, double> >(&b, false));
d_A->setHomogeneousBc(d_homogeneous_bc);
d_A->modifyRhsForBcs(*d_b);
d_A->setHomogeneousBc(true);
PETScSAMRAIVectorReal::replaceSAMRAIVector(d_petsc_x, Pointer<SAMRAIVectorReal<NDIM, double> >(&x, false));
PETScSAMRAIVectorReal::replaceSAMRAIVector(d_petsc_b, d_b);
ierr = KSPSolve(d_petsc_ksp, d_petsc_b, d_petsc_x);
IBTK_CHKERRQ(ierr);
d_A->setHomogeneousBc(d_homogeneous_bc);
d_A->imposeSolBcs(x);
// Get iterations count and residual norm.
ierr = KSPGetIterationNumber(d_petsc_ksp, &d_current_iterations);
IBTK_CHKERRQ(ierr);
ierr = KSPGetResidualNorm(d_petsc_ksp, &d_current_residual_norm);
IBTK_CHKERRQ(ierr);
d_A->setHomogeneousBc(d_homogeneous_bc);
// Determine the convergence reason.
KSPConvergedReason reason;
ierr = KSPGetConvergedReason(d_petsc_ksp, &reason);
IBTK_CHKERRQ(ierr);
const bool converged = (static_cast<int>(reason) > 0);
if (d_enable_logging) reportKSPConvergedReason(reason, plog);
// Dealocate scratch data.
d_b->deallocateVectorData();
// Deallocate the solver, when necessary.
if (deallocate_after_solve) deallocateSolverState();
IBTK_TIMER_STOP(t_solve_system);
return converged;
} // solveSystem
bool
IBImplicitModHelmholtzPETScLevelSolver::solveSystem(
SAMRAIVectorReal<NDIM,double>& x,
SAMRAIVectorReal<NDIM,double>& b)
{
IBAMR_TIMER_START(t_solve_system);
int ierr;
if (d_enable_logging) plog << d_object_name << "::solveSystem():" << std::endl;
// Initialize the solver, when necessary.
const bool deallocate_after_solve = !d_is_initialized;
if (deallocate_after_solve) initializeSolverState(x,b);
#if 0 // XXXX
// Configure solver.
ierr = KSPSetTolerances(d_petsc_ksp, d_rel_residual_tol, d_abs_residual_tol, PETSC_DEFAULT, d_max_iterations); IBTK_CHKERRQ(ierr);
ierr = KSPSetInitialGuessNonzero(d_petsc_ksp, d_initial_guess_nonzero ? PETSC_TRUE : PETSC_FALSE); IBTK_CHKERRQ(ierr);
#endif
// Solve the system.
Pointer<PatchLevel<NDIM> > patch_level = d_hierarchy->getPatchLevel(d_level_num);
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);
if (d_initial_guess_nonzero) PETScVecUtilities::copyToPatchLevelVec(d_petsc_x, x_idx, x_var, patch_level);
PETScVecUtilities::copyToPatchLevelVec(d_petsc_b, b_idx, b_var, patch_level);
PETScVecUtilities::constrainPatchLevelVec(d_petsc_b, d_dof_index_idx, d_dof_index_var, patch_level, d_dof_index_fill);
ierr = KSPSolve(d_petsc_ksp, d_petsc_b, d_petsc_x); IBTK_CHKERRQ(ierr);
PETScVecUtilities::copyFromPatchLevelVec(d_petsc_x, x_idx, x_var, patch_level);
typedef SideDataSynchronization::SynchronizationTransactionComponent SynchronizationTransactionComponent; // XXXX
SynchronizationTransactionComponent x_synch_transaction = SynchronizationTransactionComponent(x_idx, "CONSERVATIVE_COARSEN");
Pointer<SideDataSynchronization> side_synch_op = new SideDataSynchronization();
side_synch_op->initializeOperatorState(x_synch_transaction, x.getPatchHierarchy());
side_synch_op->synchronizeData(0.0);
// Log solver info.
KSPConvergedReason reason;
ierr = KSPGetConvergedReason(d_petsc_ksp, &reason); IBTK_CHKERRQ(ierr);
const bool converged = reason > 0;
if (d_enable_logging)
{
plog << d_object_name << "::solveSystem(): solver " << (converged ? "converged" : "diverged") << "\n"
<< "iterations = " << d_current_its << "\n"
<< "residual norm = " << d_current_residual_norm << std::endl;
}
// Deallocate the solver, when necessary.
if (deallocate_after_solve) deallocateSolverState();
IBAMR_TIMER_STOP(t_solve_system);
return converged;
}// solveSystem
bool
FACPreconditioner::solveSystem(
SAMRAIVectorReal<NDIM,double>& u,
SAMRAIVectorReal<NDIM,double>& f)
{
// Initialize the solver, when necessary.
const bool deallocate_after_solve = !d_is_initialized;
if (deallocate_after_solve) initializeSolverState(u,f);
// Set the initial guess to equal zero.
u.setToScalar(0.0, /*interior_only*/ false);
// Keep track of whether we need to (re-)compute the residual. Because u is
// initialized to equal zero, the initial residual is precisely the
// right-hand-side vector f. We only need to recompute the residual once we
// start modifying the solution vector u.
d_recompute_residual = false;
// Apply a single FAC cycle.
if (d_cycle_type == V_CYCLE && d_num_pre_sweeps == 0)
{
// V-cycle MG without presmoothing keeps the residual equal to the
// initial right-hand-side vector f, so we can simply use that vector
// for the residual in the FAC algorithm.
FACVCycleNoPreSmoothing(u, f, d_finest_ln);
}
else
{
d_f->copyVector(Pointer<SAMRAIVectorReal<NDIM,double> >(&f, false), false);
d_r->copyVector(Pointer<SAMRAIVectorReal<NDIM,double> >(&f, false), false);
switch (d_cycle_type)
{
case V_CYCLE:
FACVCycle(u, *d_f, d_finest_ln);
break;
case W_CYCLE:
FACWCycle(u, *d_f, d_finest_ln);
break;
case F_CYCLE:
FACFCycle(u, *d_f, d_finest_ln);
break;
default:
TBOX_ERROR(d_object_name << "::solveSystem():\n"
<< " unrecognized FAC cycle type: " << enum_to_string<MGCycleType>(d_cycle_type) << "." << std::endl);
}
}
// Deallocate the solver, when necessary.
if (deallocate_after_solve) deallocateSolverState();
return true;
}// solveSystem
bool
PETScPCLSWrapper::solveSystem(SAMRAIVectorReal<NDIM, double>& x, SAMRAIVectorReal<NDIM, double>& b)
{
if (!d_is_initialized) initializeSolverState(x, b);
// Update the PETSc Vec wrappers.
PETScSAMRAIVectorReal::replaceSAMRAIVector(d_petsc_x, Pointer<SAMRAIVectorReal<NDIM, double> >(&x, false));
PETScSAMRAIVectorReal::replaceSAMRAIVector(d_petsc_b, Pointer<SAMRAIVectorReal<NDIM, double> >(&b, false));
// Apply the preconditioner.
int ierr = PCApply(d_petsc_pc, d_petsc_x, d_petsc_b);
IBTK_CHKERRQ(ierr);
return true;
} // solveSystem
bool
CCDivGradHypreLevelSolver::solveSystem(
SAMRAIVectorReal<NDIM,double>& x,
SAMRAIVectorReal<NDIM,double>& b)
{
IBTK_TIMER_START(t_solve_system);
if (d_enable_logging) plog << d_object_name << "::solveSystem():" << std::endl;
// Initialize the solver, when necessary.
const bool deallocate_after_solve = !d_is_initialized;
if (deallocate_after_solve) initializeSolverState(x,b);
// Solve the system using the hypre solver.
static const int comp = 0;
const int x_idx = x.getComponentDescriptorIndex(comp);
const int b_idx = b.getComponentDescriptorIndex(comp);
bool converged = true;
IntVector<NDIM> chkbrd_mode_id;
#if (NDIM > 2)
for (chkbrd_mode_id(2) = 0; chkbrd_mode_id(2) < 2; ++chkbrd_mode_id(2))
{
#endif
for (chkbrd_mode_id(1) = 0; chkbrd_mode_id(1) < 2; ++chkbrd_mode_id(1))
{
for (chkbrd_mode_id(0) = 0; chkbrd_mode_id(0) < 2; ++chkbrd_mode_id(0))
{
bool converged_mode = solveSystem(x_idx, b_idx, chkbrd_mode_id);
if (d_enable_logging)
{
plog << d_object_name << "::solveSystem(): solver " << (converged_mode ? "converged" : "diverged") << "\n"
<< "chkbrd_mode_id = " << chkbrd_mode_id << "\n"
<< "iterations = " << d_current_its << "\n"
<< "residual norm = " << d_current_residual_norm << std::endl;
}
converged = converged && converged_mode;
}
}
#if (NDIM > 2)
}
#endif
// Deallocate the solver, when necessary.
if (deallocate_after_solve) deallocateSolverState();
IBTK_TIMER_STOP(t_solve_system);
return converged;
}// solveSystem
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;
}
bool PETScNewtonKrylovSolver::solveSystem(SAMRAIVectorReal<NDIM, double>& x,
SAMRAIVectorReal<NDIM, double>& b)
{
IBTK_TIMER_START(t_solve_system);
int ierr;
// Initialize the solver, when necessary.
const bool deallocate_after_solve = !d_is_initialized;
if (deallocate_after_solve) initializeSolverState(x, b);
#if !defined(NDEBUG)
TBOX_ASSERT(d_petsc_snes);
#endif
resetSNESOptions();
Pointer<PETScKrylovLinearSolver> p_krylov_solver = d_krylov_solver;
if (p_krylov_solver) p_krylov_solver->resetKSPOptions();
// Allocate scratch data.
if (d_b) d_b->allocateVectorData();
if (d_r) d_r->allocateVectorData();
// Solve the system using a PETSc SNES object.
PETScSAMRAIVectorReal::replaceSAMRAIVector(
d_petsc_x, Pointer<SAMRAIVectorReal<NDIM, double> >(&x, false));
Pointer<LinearOperator> A = d_F;
if (A)
{
d_b->copyVector(Pointer<SAMRAIVectorReal<NDIM, double> >(&b, false));
A->modifyRhsForInhomogeneousBc(*d_b);
ierr = PetscObjectStateIncrease(reinterpret_cast<PetscObject>(d_petsc_b));
IBTK_CHKERRQ(ierr);
PETScSAMRAIVectorReal::replaceSAMRAIVector(d_petsc_b, d_b);
}
else
{
PETScSAMRAIVectorReal::replaceSAMRAIVector(
d_petsc_b, Pointer<SAMRAIVectorReal<NDIM, double> >(&b, false));
}
ierr = SNESSolve(d_petsc_snes, d_petsc_b, d_petsc_x);
IBTK_CHKERRQ(ierr);
ierr = SNESGetIterationNumber(d_petsc_snes, &d_current_iterations);
IBTK_CHKERRQ(ierr);
ierr = SNESGetLinearSolveIterations(d_petsc_snes, &d_current_linear_iterations);
IBTK_CHKERRQ(ierr);
ierr = SNESGetFunctionNorm(d_petsc_snes, &d_current_residual_norm);
IBTK_CHKERRQ(ierr);
// Determine the convergence reason.
SNESConvergedReason reason;
ierr = SNESGetConvergedReason(d_petsc_snes, &reason);
IBTK_CHKERRQ(ierr);
const bool converged = (static_cast<int>(reason) > 0);
if (d_enable_logging) reportSNESConvergedReason(reason, plog);
// Deallocate scratch data.
if (d_b) d_b->deallocateVectorData();
if (d_r) d_r->deallocateVectorData();
// Deallocate the solver, when necessary.
if (deallocate_after_solve) deallocateSolverState();
IBTK_TIMER_STOP(t_solve_system);
return converged;
} // solveSystem
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
bool BGaussSeidelPreconditioner::solveSystem(SAMRAIVectorReal<NDIM, double>& x, SAMRAIVectorReal<NDIM, double>& b)
{
// Initialize the preconditioner, when necessary.
const bool deallocate_after_solve = !d_is_initialized;
if (deallocate_after_solve) initializeSolverState(x, b);
#if !defined(NDEBUG)
Pointer<PatchHierarchy<NDIM> > hierarchy = x.getPatchHierarchy();
const int coarsest_ln = x.getCoarsestLevelNumber();
const int finest_ln = x.getFinestLevelNumber();
TBOX_ASSERT(x.getNumberOfComponents() == b.getNumberOfComponents());
TBOX_ASSERT(hierarchy == b.getPatchHierarchy());
TBOX_ASSERT(coarsest_ln == b.getCoarsestLevelNumber());
TBOX_ASSERT(finest_ln == b.getFinestLevelNumber());
#endif
bool ret_val = true;
// Zero out the initial guess.
#if !defined(NDEBUG)
TBOX_ASSERT(d_initial_guess_nonzero == false);
#endif
x.setToScalar(0.0, /*interior_only*/ false);
// Setup SAMRAIVectorReal objects to correspond to the individual vector
// components.
std::vector<Pointer<SAMRAIVectorReal<NDIM, double> > > x_comps =
getComponentVectors(Pointer<SAMRAIVectorReal<NDIM, double> >(&x, false));
std::vector<Pointer<SAMRAIVectorReal<NDIM, double> > > b_comps =
getComponentVectors(Pointer<SAMRAIVectorReal<NDIM, double> >(&b, false));
// Clone the right-hand-side vector to avoid modifying it during the
// preconditioning operation.
Pointer<SAMRAIVectorReal<NDIM, double> > f = b.cloneVector(b.getName());
f->allocateVectorData();
f->copyVector(Pointer<SAMRAIVectorReal<NDIM, double> >(&b, false), false);
std::vector<Pointer<SAMRAIVectorReal<NDIM, double> > > f_comps = getComponentVectors(f);
// Setup the order in which the component preconditioner are to be applied.
const int ncomps = x.getNumberOfComponents();
std::vector<int> comps;
comps.reserve(2 * ncomps - 1);
if (!d_reverse_order)
{
// Standard order: Run from comp = 0 to comp = ncomp-1.
for (int comp = 0; comp < ncomps; ++comp)
{
comps.push_back(comp);
}
if (d_symmetric_preconditioner)
{
for (int comp = ncomps - 2; comp >= 0; --comp)
{
comps.push_back(comp);
}
}
}
else
{
// Reversed order: Run from comp = ncomp-1 to comp = 0.
for (int comp = ncomps - 1; comp >= 0; --comp)
{
comps.push_back(comp);
}
if (d_symmetric_preconditioner)
{
for (int comp = 1; comp < ncomps; ++comp)
{
comps.push_back(comp);
}
}
}
// Apply the component preconditioners.
int count = 0;
for (std::vector<int>::const_iterator it = comps.begin(); it != comps.end(); ++it, ++count)
{
const int comp = (*it);
Pointer<SAMRAIVectorReal<NDIM, double> > x_comp = x_comps[comp];
Pointer<SAMRAIVectorReal<NDIM, double> > b_comp = b_comps[comp];
Pointer<SAMRAIVectorReal<NDIM, double> > f_comp = f_comps[comp];
// Update the right-hand-side vector.
f_comp->setToScalar(0.0);
for (int c = 0; c < ncomps; ++c)
{
if (c == comp) continue;
d_linear_ops_map[comp][c]->applyAdd(*x_comps[c], *f_comp, *f_comp);
}
f_comp->subtract(b_comp, f_comp);
// Configure the component preconditioner.
Pointer<LinearSolver> pc_comp = d_pc_map[comp];
pc_comp->setInitialGuessNonzero(count >= ncomps);
pc_comp->setMaxIterations(d_max_iterations);
pc_comp->setAbsoluteTolerance(d_abs_residual_tol);
pc_comp->setRelativeTolerance(d_rel_residual_tol);
// Apply the component preconditioner.
const bool ret_val_comp = pc_comp->solveSystem(*x_comp, *f_comp);
ret_val = ret_val && ret_val_comp;
}
// Free the copied right-hand-side vector data.
f->deallocateVectorData();
f->freeVectorComponents();
// Deallocate the preconditioner, when necessary.
if (deallocate_after_solve) deallocateSolverState();
return ret_val;
} // solveSystem
