void VectorMatrixAssembler::assembleWithJacobian(
std::size_t const mesh_item_id, LocalAssemblerInterface& local_assembler,
std::vector<std::reference_wrapper<NumLib::LocalToGlobalIndexMap>> const&
dof_tables,
const double t, GlobalVector const& x, GlobalVector const& xdot,
const double dxdot_dx, const double dx_dx, GlobalMatrix& M, GlobalMatrix& K,
GlobalVector& b, GlobalMatrix& Jac,
CoupledSolutionsForStaggeredScheme const* const cpl_xs)
{
std::vector<std::vector<GlobalIndexType>> indices_of_processes;
indices_of_processes.reserve(dof_tables.size());
for (std::size_t i = 0; i < dof_tables.size(); i++)
{
indices_of_processes.emplace_back(
NumLib::getIndices(mesh_item_id, dof_tables[i].get()));
}
auto const& indices = (cpl_xs == nullptr)
? indices_of_processes[0]
: indices_of_processes[cpl_xs->process_id];
auto const local_xdot = xdot.get(indices);
_local_M_data.clear();
_local_K_data.clear();
_local_b_data.clear();
_local_Jac_data.clear();
if (cpl_xs == nullptr)
{
auto const local_x = x.get(indices);
_jacobian_assembler->assembleWithJacobian(
local_assembler, t, local_x, local_xdot, dxdot_dx, dx_dx,
_local_M_data, _local_K_data, _local_b_data, _local_Jac_data);
}
else
{
auto local_coupled_xs0 =
getPreviousLocalSolutions(*cpl_xs, indices_of_processes);
auto local_coupled_xs =
getCurrentLocalSolutions(*cpl_xs, indices_of_processes);
ProcessLib::LocalCoupledSolutions local_coupled_solutions(
cpl_xs->dt, cpl_xs->process_id, std::move(local_coupled_xs0),
std::move(local_coupled_xs));
_jacobian_assembler->assembleWithJacobianForStaggeredScheme(
local_assembler, t, local_xdot, dxdot_dx, dx_dx, _local_M_data,
_local_K_data, _local_b_data, _local_Jac_data,
local_coupled_solutions);
}
auto const num_r_c = indices.size();
auto const r_c_indices =
NumLib::LocalToGlobalIndexMap::RowColumnIndices(indices, indices);
if (!_local_M_data.empty())
{
auto const local_M = MathLib::toMatrix(_local_M_data, num_r_c, num_r_c);
M.add(r_c_indices, local_M);
}
if (!_local_K_data.empty())
{
auto const local_K = MathLib::toMatrix(_local_K_data, num_r_c, num_r_c);
K.add(r_c_indices, local_K);
}
if (!_local_b_data.empty())
{
assert(_local_b_data.size() == num_r_c);
b.add(indices, _local_b_data);
}
if (!_local_Jac_data.empty())
{
auto const local_Jac =
MathLib::toMatrix(_local_Jac_data, num_r_c, num_r_c);
Jac.add(r_c_indices, local_Jac);
}
else
{
OGS_FATAL(
"No Jacobian has been assembled! This might be due to programming "
"errors in the local assembler of the current process.");
}
}
void VectorMatrixAssembler::assemble(
const std::size_t mesh_item_id, LocalAssemblerInterface& local_assembler,
std::vector<std::reference_wrapper<NumLib::LocalToGlobalIndexMap>> const&
dof_tables,
const double t, const GlobalVector& x, GlobalMatrix& M, GlobalMatrix& K,
GlobalVector& b, CoupledSolutionsForStaggeredScheme const* const cpl_xs)
{
std::vector<std::vector<GlobalIndexType>> indices_of_processes;
indices_of_processes.reserve(dof_tables.size());
for (std::size_t i = 0; i < dof_tables.size(); i++)
{
indices_of_processes.emplace_back(
NumLib::getIndices(mesh_item_id, dof_tables[i].get()));
}
auto const& indices = (cpl_xs == nullptr)
? indices_of_processes[0]
: indices_of_processes[cpl_xs->process_id];
_local_M_data.clear();
_local_K_data.clear();
_local_b_data.clear();
if (cpl_xs == nullptr)
{
auto const local_x = x.get(indices);
local_assembler.assemble(t, local_x, _local_M_data, _local_K_data,
_local_b_data);
}
else
{
auto local_coupled_xs0 =
getPreviousLocalSolutions(*cpl_xs, indices_of_processes);
auto local_coupled_xs =
getCurrentLocalSolutions(*cpl_xs, indices_of_processes);
ProcessLib::LocalCoupledSolutions local_coupled_solutions(
cpl_xs->dt, cpl_xs->process_id, std::move(local_coupled_xs0),
std::move(local_coupled_xs));
local_assembler.assembleForStaggeredScheme(t, _local_M_data,
_local_K_data, _local_b_data,
local_coupled_solutions);
}
auto const num_r_c = indices.size();
auto const r_c_indices =
NumLib::LocalToGlobalIndexMap::RowColumnIndices(indices, indices);
if (!_local_M_data.empty())
{
auto const local_M = MathLib::toMatrix(_local_M_data, num_r_c, num_r_c);
M.add(r_c_indices, local_M);
}
if (!_local_K_data.empty())
{
auto const local_K = MathLib::toMatrix(_local_K_data, num_r_c, num_r_c);
K.add(r_c_indices, local_K);
}
if (!_local_b_data.empty())
{
assert(_local_b_data.size() == num_r_c);
b.add(indices, _local_b_data);
}
}
void LocalLinearLeastSquaresExtrapolator::extrapolateElement(
std::size_t const element_index,
const unsigned num_components,
ExtrapolatableElementCollection const& extrapolatables,
const double t,
GlobalVector const& current_solution,
LocalToGlobalIndexMap const& dof_table,
GlobalVector& counts)
{
auto const& integration_point_values =
extrapolatables.getIntegrationPointValues(
element_index, t, current_solution, dof_table,
_integration_point_values_cache);
auto const& N_0 = extrapolatables.getShapeMatrix(element_index, 0);
auto const num_nodes = static_cast<unsigned>(N_0.cols());
auto const num_values =
static_cast<unsigned>(integration_point_values.size());
if (num_values % num_components != 0)
OGS_FATAL(
"The number of computed integration point values is not divisable "
"by the number of num_components. Maybe the computed property is "
"not a %d-component vector for each integration point.",
num_components);
// number of integration points in the element
const auto num_int_pts = num_values / num_components;
if (num_int_pts < num_nodes)
OGS_FATAL(
"Least squares is not possible if there are more nodes than"
"integration points.");
auto const pair_it_inserted = _qr_decomposition_cache.emplace(
std::make_pair(num_nodes, num_int_pts), CachedData{});
auto& cached_data = pair_it_inserted.first->second;
if (pair_it_inserted.second)
{
DBUG("Computing new singular value decomposition");
// interpolation_matrix * nodal_values = integration_point_values
// We are going to pseudo-invert this relation now using singular value
// decomposition.
auto& interpolation_matrix = cached_data.A;
interpolation_matrix.resize(num_int_pts, num_nodes);
interpolation_matrix.row(0) = N_0;
for (unsigned int_pt = 1; int_pt < num_int_pts; ++int_pt)
{
auto const& shp_mat =
extrapolatables.getShapeMatrix(element_index, int_pt);
assert(shp_mat.cols() == num_nodes);
// copy shape matrix to extrapolation matrix row-wise
interpolation_matrix.row(int_pt) = shp_mat;
}
// JacobiSVD is extremely reliable, but fast only for small matrices.
// But we usually have small matrices and we don't compute very often.
// Cf.
// http://eigen.tuxfamily.org/dox/group__TopicLinearAlgebraDecompositions.html
//
// Decomposes interpolation_matrix = U S V^T.
Eigen::JacobiSVD<Eigen::MatrixXd> svd(
interpolation_matrix, Eigen::ComputeThinU | Eigen::ComputeThinV);
auto const& S = svd.singularValues();
auto const& U = svd.matrixU();
auto const& V = svd.matrixV();
// Compute and save the pseudo inverse V * S^{-1} * U^T.
auto const rank = svd.rank();
assert(rank == num_nodes);
// cf. http://eigen.tuxfamily.org/dox/JacobiSVD_8h_source.html
cached_data.A_pinv.noalias() = V.leftCols(rank) *
S.head(rank).asDiagonal().inverse() *
U.leftCols(rank).transpose();
}
else if (cached_data.A.row(0) != N_0)
{
OGS_FATAL("The cached and the passed shapematrices differ.");
}
auto const& global_indices =
_dof_table_single_component(element_index, 0).rows;
if (num_components == 1)
{
auto const integration_point_values_vec =
MathLib::toVector(integration_point_values);
// Apply the pre-computed pseudo-inverse.
Eigen::VectorXd const nodal_values =
cached_data.A_pinv * integration_point_values_vec;
// TODO does that give rise to PETSc problems? E.g., writing to ghost
// nodes? Furthermore: Is ghost nodes communication necessary for PETSc?
_nodal_values->add(global_indices, nodal_values);
counts.add(global_indices,
std::vector<double>(global_indices.size(), 1.0));
}
else
{
auto const integration_point_values_mat = MathLib::toMatrix(
integration_point_values, num_components, num_int_pts);
// Apply the pre-computed pseudo-inverse.
Eigen::MatrixXd const nodal_values =
cached_data.A_pinv * integration_point_values_mat.transpose();
std::vector<GlobalIndexType> indices;
indices.reserve(num_components * global_indices.size());
// _nodal_values is ordered location-wise
for (unsigned comp = 0; comp < num_components; ++comp)
{
for (auto i : global_indices)
{
indices.push_back(num_components * i + comp);
}
}
// Nodal_values are passed as a raw pointer, because PETScVector and
// EigenVector implementations differ slightly.
_nodal_values->add(indices, nodal_values.data());
counts.add(indices, std::vector<double>(indices.size(), 1.0));
}
}