//-----------------------------------------------------------------------------
Graph GraphBuilder::local_graph(const Mesh& mesh, const GenericDofMap& dofmap0,
const GenericDofMap& dofmap1)
{
Timer timer("Build local sparsity graph from dofmaps");
// Create empty graph
const std::size_t n = dofmap0.global_dimension();
Graph graph(n);
// Build graph
for (CellIterator cell(mesh); !cell.end(); ++cell)
{
const ArrayView<const dolfin::la_index> dofs0
= dofmap0.cell_dofs(cell->index());
const ArrayView<const dolfin::la_index> dofs1
= dofmap1.cell_dofs(cell->index());
//std::vector<dolfin::la_index>::const_iterator node0, node1;
for (auto node0 = dofs0.begin(); node0 != dofs0.end(); ++node0)
for (auto node1 = dofs1.begin(); node1 != dofs1.end(); ++node1)
if (*node0 != *node1)
graph[*node0].insert(*node1);
}
return graph;
}
//----------------------------------------------------------------------------
void LocalSolver::solve_local(GenericVector& x, const GenericVector& b,
const GenericDofMap& dofmap_b) const
{
dolfin_assert(_a);
dolfin_assert(_a->rank() == 2);
// Extract mesh
dolfin_assert(_a->function_space(0)->mesh());
const Mesh& mesh = *_a->function_space(0)->mesh();
// Check whether to use cache for factorizations
const bool use_cache
= _cholesky_cache.empty() and _lu_cache.empty() ? false : true;
// Create UFC object
UFC ufc_a(*_a);
// Get cell integral
std::shared_ptr<ufc::cell_integral> integral_a = ufc_a.default_cell_integral;
dolfin_assert(integral_a);
// Get dofmaps
std::array<std::shared_ptr<const GenericDofMap>, 2> dofmaps_a
= {{_a->function_space(0)->dofmap(), _a->function_space(1)->dofmap()}};
dolfin_assert(dofmaps_a[0] and dofmaps_a[1]);
// Check dimensions
dolfin_assert(dofmaps_a[0]->global_dimension()
== dofmaps_a[1]->global_dimension());
dolfin_assert(dofmaps_a[0]->global_dimension()
== dofmap_b.global_dimension());
// Eigen data structures for local tensors
Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor> A_e;
Eigen::VectorXd b_e, x_e;
// Eigen factorizations
Eigen::PartialPivLU<Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic,
Eigen::RowMajor>> lu;
Eigen::LLT<Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic,
Eigen::RowMajor>> cholesky;
// Assemble LHS over cells and solve
Progress p("Performing local (cell-wise) solve", mesh.num_cells());
ufc::cell ufc_cell;
std::vector<double> vertex_coordinates;
for (CellIterator cell(mesh); !cell.end(); ++cell)
{
// Get cell dofmaps
const ArrayView<const dolfin::la_index> dofs_L
= dofmap_b.cell_dofs(cell->index());
const ArrayView<const dolfin::la_index> dofs_a0
= dofmaps_a[0]->cell_dofs(cell->index());
// Check dimensions
dolfin_assert(dofs_L.size() == dofs_a0.size());
// Copy global RHS data into local RHS
b_e.resize(dofs_L.size());
b.get_local(b_e.data(), dofs_L.size(), dofs_L.data());
// Solve local problem
if (!use_cache)
{
// Update to current cell
cell->get_vertex_coordinates(vertex_coordinates);
cell->get_cell_data(ufc_cell);
// Update LHS UFC object
ufc_a.update(*cell, vertex_coordinates, ufc_cell,
integral_a->enabled_coefficients());
// Resize A_e and tabulate on for cell
const std::size_t dim = dofmaps_a[0]->num_element_dofs(cell->index());
dolfin_assert(dim == dofmaps_a[1]->num_element_dofs(cell->index()));
A_e.resize(dim, dim);
integral_a->tabulate_tensor(A_e.data(), ufc_a.w(),
vertex_coordinates.data(),
ufc_cell.orientation);
// Solve local problem
if (_solver_type == SolverType::Cholesky)
{
cholesky.compute(A_e);
x_e = cholesky.solve(b_e);
}
else
{
lu.compute(A_e);
x_e = lu.solve(b_e);
}
}
else
{
if (_solver_type == SolverType::Cholesky)
x_e = _cholesky_cache[cell->index()].solve(b_e);
else
x_e = _lu_cache[cell->index()].solve(b_e);
}
// Set solution in global vector
x.set_local(x_e.data(), dofs_a0.size(), dofs_a0.data());
p++;
}
// Finalise vector
x.apply("insert");
}