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ElasticityDiamondAlgorithm.cpp
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Stéphane Del Pino authoredStéphane Del Pino authored
ElasticityDiamondAlgorithm.cpp 35.70 KiB
#include <language/algorithms/ElasticityDiamondAlgorithm.hpp>
#include <algebra/CRSMatrix.hpp>
#include <algebra/CRSMatrixDescriptor.hpp>
#include <algebra/LeastSquareSolver.hpp>
#include <algebra/LinearSolver.hpp>
#include <algebra/SmallMatrix.hpp>
#include <algebra/TinyVector.hpp>
#include <algebra/Vector.hpp>
#include <language/utils/InterpolateItemValue.hpp>
#include <mesh/Connectivity.hpp>
#include <mesh/DualConnectivityManager.hpp>
#include <mesh/DualMeshManager.hpp>
#include <mesh/Mesh.hpp>
#include <mesh/MeshData.hpp>
#include <mesh/MeshDataManager.hpp>
#include <mesh/MeshFaceBoundary.hpp>
#include <mesh/PrimalToDiamondDualConnectivityDataMapper.hpp>
#include <scheme/DirichletBoundaryConditionDescriptor.hpp>
#include <scheme/NeumannBoundaryConditionDescriptor.hpp>
#include <scheme/SymmetryBoundaryConditionDescriptor.hpp>
template <size_t Dimension>
ElasticityDiamondScheme<Dimension>::ElasticityDiamondScheme(
std::shared_ptr<const IMesh> i_mesh,
const std::vector<std::shared_ptr<const IBoundaryConditionDescriptor>>& bc_descriptor_list,
const FunctionSymbolId& lambda_id,
const FunctionSymbolId& mu_id,
const FunctionSymbolId& f_id,
const FunctionSymbolId& U_id)
{
using ConnectivityType = Connectivity<Dimension>;
using MeshType = Mesh<ConnectivityType>;
using MeshDataType = MeshData<Dimension>;
using BoundaryCondition =
std::variant<DirichletBoundaryCondition, NormalStrainBoundaryCondition, SymmetryBoundaryCondition>;
using BoundaryConditionList = std::vector<BoundaryCondition>;
BoundaryConditionList boundary_condition_list;
std::cout << "number of bc descr = " << bc_descriptor_list.size() << '\n';
std::shared_ptr mesh = std::dynamic_pointer_cast<const MeshType>(i_mesh);
NodeValue<bool> is_dirichlet{mesh->connectivity()};
is_dirichlet.fill(false);
NodeValue<TinyVector<Dimension>> dirichlet_value{mesh->connectivity()};
{
TinyVector<Dimension> nan_tiny_vector;
for (size_t i = 0; i < Dimension; ++i) {
nan_tiny_vector[i] = std::numeric_limits<double>::signaling_NaN();
}
dirichlet_value.fill(nan_tiny_vector);
}
for (const auto& bc_descriptor : bc_descriptor_list) {
bool is_valid_boundary_condition = true;
switch (bc_descriptor->type()) {
case IBoundaryConditionDescriptor::Type::symmetry: {
const SymmetryBoundaryConditionDescriptor& sym_bc_descriptor =
dynamic_cast<const SymmetryBoundaryConditionDescriptor&>(*bc_descriptor);
if constexpr (Dimension > 1) {
MeshFaceBoundary mesh_face_boundary = getMeshFaceBoundary(*mesh, sym_bc_descriptor.boundaryDescriptor());
boundary_condition_list.push_back(SymmetryBoundaryCondition{mesh_face_boundary.faceList()});
} else {
throw NotImplementedError("Symmetry conditions are not supported in 1d");
}
break;
}
case IBoundaryConditionDescriptor::Type::dirichlet: {
const DirichletBoundaryConditionDescriptor& dirichlet_bc_descriptor =
dynamic_cast<const DirichletBoundaryConditionDescriptor&>(*bc_descriptor);
if (dirichlet_bc_descriptor.name() == "dirichlet") {
if constexpr (Dimension > 1) {
MeshFaceBoundary mesh_face_boundary =
getMeshFaceBoundary(*mesh, dirichlet_bc_descriptor.boundaryDescriptor());
MeshDataType& mesh_data = MeshDataManager::instance().getMeshData(*mesh);
const FunctionSymbolId g_id = dirichlet_bc_descriptor.rhsSymbolId();
Array<const TinyVector<Dimension>> value_list = InterpolateItemValue<TinyVector<Dimension>(
TinyVector<Dimension>)>::template interpolate<ItemType::face>(g_id, mesh_data.xl(),
mesh_face_boundary.faceList());
boundary_condition_list.push_back(DirichletBoundaryCondition{mesh_face_boundary.faceList(), value_list});
} else {
throw NotImplementedError("Dirichlet conditions are not supported in 1d");
}
} else if (dirichlet_bc_descriptor.name() == "normal_strain") {
if constexpr (Dimension > 1) {
MeshFaceBoundary mesh_face_boundary =
getMeshFaceBoundary(*mesh, dirichlet_bc_descriptor.boundaryDescriptor());
MeshDataType& mesh_data = MeshDataManager::instance().getMeshData(*mesh);
const FunctionSymbolId g_id = dirichlet_bc_descriptor.rhsSymbolId();
Array<const TinyVector<Dimension>> value_list = InterpolateItemValue<TinyVector<Dimension>(
TinyVector<Dimension>)>::template interpolate<ItemType::face>(g_id, mesh_data.xl(),
mesh_face_boundary.faceList());
boundary_condition_list.push_back(NormalStrainBoundaryCondition{mesh_face_boundary.faceList(), value_list});
} else {
throw NotImplementedError("Normal strain conditions are not supported in 1d");
}
} else {
is_valid_boundary_condition = false;
}
break;
}
default: {
is_valid_boundary_condition = false;
}
}
if (not is_valid_boundary_condition) {
std::ostringstream error_msg;
error_msg << *bc_descriptor << " is an invalid boundary condition for elasticity equation";
throw NormalError(error_msg.str());
}
}
if constexpr (Dimension > 1) {
const CellValue<const size_t> cell_dof_number = [&] {
CellValue<size_t> compute_cell_dof_number{mesh->connectivity()};
parallel_for(
mesh->numberOfCells(), PUGS_LAMBDA(CellId cell_id) { compute_cell_dof_number[cell_id] = cell_id; });
return compute_cell_dof_number;
}();
size_t number_of_dof = mesh->numberOfCells();
const FaceValue<const size_t> face_dof_number = [&] {
FaceValue<size_t> compute_face_dof_number{mesh->connectivity()};
compute_face_dof_number.fill(std::numeric_limits<size_t>::max());
for (const auto& boundary_condition : boundary_condition_list) {
std::visit(
[&](auto&& bc) {
using T = std::decay_t<decltype(bc)>; if constexpr ((std::is_same_v<T, NormalStrainBoundaryCondition>) or
(std::is_same_v<T, SymmetryBoundaryCondition>) or
(std::is_same_v<T, DirichletBoundaryCondition>)) {
const auto& face_list = bc.faceList();
for (size_t i_face = 0; i_face < face_list.size(); ++i_face) {
const FaceId face_id = face_list[i_face];
if (compute_face_dof_number[face_id] != std::numeric_limits<size_t>::max()) {
std::ostringstream os;
os << "The face " << face_id << " is used at least twice for boundary conditions";
throw NormalError(os.str());
} else {
compute_face_dof_number[face_id] = number_of_dof++;
}
}
}
},
boundary_condition);
}
return compute_face_dof_number;
}();
const auto& primal_face_to_node_matrix = mesh->connectivity().faceToNodeMatrix();
const auto& face_to_cell_matrix = mesh->connectivity().faceToCellMatrix();
const FaceValue<const bool> primal_face_is_neumann = [&] {
FaceValue<bool> face_is_neumann{mesh->connectivity()};
face_is_neumann.fill(false);
for (const auto& boundary_condition : boundary_condition_list) {
std::visit(
[&](auto&& bc) {
using T = std::decay_t<decltype(bc)>;
if constexpr ((std::is_same_v<T, NormalStrainBoundaryCondition>)) {
const auto& face_list = bc.faceList();
for (size_t i_face = 0; i_face < face_list.size(); ++i_face) {
const FaceId face_id = face_list[i_face];
face_is_neumann[face_id] = true;
}
}
},
boundary_condition);
}
return face_is_neumann;
}();
const FaceValue<const bool> primal_face_is_symmetry = [&] {
FaceValue<bool> face_is_symmetry{mesh->connectivity()};
face_is_symmetry.fill(false);
for (const auto& boundary_condition : boundary_condition_list) {
std::visit(
[&](auto&& bc) {
using T = std::decay_t<decltype(bc)>;
if constexpr ((std::is_same_v<T, SymmetryBoundaryCondition>)) {
const auto& face_list = bc.faceList();
for (size_t i_face = 0; i_face < face_list.size(); ++i_face) {
const FaceId face_id = face_list[i_face];
face_is_symmetry[face_id] = true;
}
}
},
boundary_condition);
}
return face_is_symmetry;
}();
NodeValue<bool> primal_node_is_on_boundary(mesh->connectivity()); if (parallel::size() > 1) {
throw NotImplementedError("Calculation of node_is_on_boundary is incorrect");
}
primal_node_is_on_boundary.fill(false);
for (FaceId face_id = 0; face_id < mesh->numberOfFaces(); ++face_id) {
if (face_to_cell_matrix[face_id].size() == 1) {
for (size_t i_node = 0; i_node < primal_face_to_node_matrix[face_id].size(); ++i_node) {
NodeId node_id = primal_face_to_node_matrix[face_id][i_node];
primal_node_is_on_boundary[node_id] = true;
}
}
}
FaceValue<bool> primal_face_is_on_boundary(mesh->connectivity());
if (parallel::size() > 1) {
throw NotImplementedError("Calculation of face_is_on_boundary is incorrect");
}
primal_face_is_on_boundary.fill(false);
for (FaceId face_id = 0; face_id < mesh->numberOfFaces(); ++face_id) {
if (face_to_cell_matrix[face_id].size() == 1) {
primal_face_is_on_boundary[face_id] = true;
}
}
FaceValue<bool> primal_face_is_dirichlet(mesh->connectivity());
if (parallel::size() > 1) {
throw NotImplementedError("Calculation of face_is_neumann is incorrect");
}
primal_face_is_dirichlet.fill(false);
for (FaceId face_id = 0; face_id < mesh->numberOfFaces(); ++face_id) {
primal_face_is_dirichlet[face_id] = (primal_face_is_on_boundary[face_id] && (!primal_face_is_neumann[face_id]) &&
(!primal_face_is_symmetry[face_id]));
}
MeshDataType& mesh_data = MeshDataManager::instance().getMeshData(*mesh);
const NodeValue<const TinyVector<Dimension>>& xr = mesh->xr();
const FaceValue<const TinyVector<Dimension>>& xl = mesh_data.xl();
const CellValue<const TinyVector<Dimension>>& xj = mesh_data.xj();
const auto& node_to_cell_matrix = mesh->connectivity().nodeToCellMatrix();
const auto& node_to_face_matrix = mesh->connectivity().nodeToFaceMatrix();
CellValuePerNode<double> w_rj{mesh->connectivity()};
FaceValuePerNode<double> w_rl{mesh->connectivity()};
const NodeValuePerFace<const TinyVector<Dimension>> primal_nlr = mesh_data.nlr();
auto project_to_face = [&](const TinyVector<Dimension>& x, const FaceId face_id) -> const TinyVector<Dimension> {
TinyVector<Dimension> proj;
const TinyVector<Dimension> nil = primal_nlr(face_id, 0);
proj = x - dot((x - xl[face_id]), nil) * nil;
return proj;
};
for (size_t i = 0; i < w_rl.numberOfValues(); ++i) {
w_rl[i] = std::numeric_limits<double>::signaling_NaN();
}
for (NodeId i_node = 0; i_node < mesh->numberOfNodes(); ++i_node) {
SmallVector<double> b{Dimension + 1};
b[0] = 1;
for (size_t i = 1; i < Dimension + 1; i++) {
b[i] = xr[i_node][i - 1];
}
const auto& node_to_cell = node_to_cell_matrix[i_node];
if (not primal_node_is_on_boundary[i_node]) {
SmallMatrix<double> A{Dimension + 1, node_to_cell.size()};
for (size_t j = 0; j < node_to_cell.size(); j++) {
A(0, j) = 1; }
for (size_t i = 1; i < Dimension + 1; i++) {
for (size_t j = 0; j < node_to_cell.size(); j++) {
const CellId J = node_to_cell[j];
A(i, j) = xj[J][i - 1];
}
}
SmallVector<double> x{node_to_cell.size()};
x = zero;
LeastSquareSolver ls_solver;
ls_solver.solveLocalSystem(A, x, b);
for (size_t j = 0; j < node_to_cell.size(); j++) {
w_rj(i_node, j) = x[j];
}
} else {
int nb_face_used = 0;
for (size_t i_face = 0; i_face < node_to_face_matrix[i_node].size(); ++i_face) {
FaceId face_id = node_to_face_matrix[i_node][i_face];
if (primal_face_is_on_boundary[face_id]) {
nb_face_used++;
}
}
SmallMatrix<double> A{Dimension + 1, node_to_cell.size() + nb_face_used};
for (size_t j = 0; j < node_to_cell.size() + nb_face_used; j++) {
A(0, j) = 1;
}
for (size_t i = 1; i < Dimension + 1; i++) {
for (size_t j = 0; j < node_to_cell.size(); j++) {
const CellId J = node_to_cell[j];
A(i, j) = xj[J][i - 1];
}
}
for (size_t i = 1; i < Dimension + 1; i++) {
int cpt_face = 0;
for (size_t i_face = 0; i_face < node_to_face_matrix[i_node].size(); ++i_face) {
FaceId face_id = node_to_face_matrix[i_node][i_face];
if (primal_face_is_on_boundary[face_id]) {
if (primal_face_is_symmetry[face_id]) {
for (size_t j = 0; j < face_to_cell_matrix[face_id].size(); ++j) {
const CellId cell_id = face_to_cell_matrix[face_id][j];
TinyVector<Dimension> xproj = project_to_face(xj[cell_id], face_id);
A(i, node_to_cell.size() + cpt_face) = xproj[i - 1];
}
} else {
A(i, node_to_cell.size() + cpt_face) = xl[face_id][i - 1];
}
cpt_face++;
}
}
}
SmallVector<double> x{node_to_cell.size() + nb_face_used};
x = zero;
LeastSquareSolver ls_solver;
ls_solver.solveLocalSystem(A, x, b);
for (size_t j = 0; j < node_to_cell.size(); j++) {
w_rj(i_node, j) = x[j];
}
int cpt_face = node_to_cell.size();
for (size_t i_face = 0; i_face < node_to_face_matrix[i_node].size(); ++i_face) {
FaceId face_id = node_to_face_matrix[i_node][i_face];
if (primal_face_is_on_boundary[face_id]) {
w_rl(i_node, i_face) = x[cpt_face++];
}
} }
}
{
std::shared_ptr diamond_mesh = DualMeshManager::instance().getDiamondDualMesh(*mesh);
MeshDataType& diamond_mesh_data = MeshDataManager::instance().getMeshData(*diamond_mesh);
std::shared_ptr mapper =
DualConnectivityManager::instance().getPrimalToDiamondDualConnectivityDataMapper(mesh->connectivity());
CellValue<double> dual_muj =
InterpolateItemValue<double(TinyVector<Dimension>)>::template interpolate<ItemType::cell>(mu_id,
diamond_mesh_data
.xj());
CellValue<double> dual_lambdaj =
InterpolateItemValue<double(TinyVector<Dimension>)>::template interpolate<ItemType::cell>(lambda_id,
diamond_mesh_data
.xj());
CellValue<TinyVector<Dimension>> Uj = InterpolateItemValue<TinyVector<Dimension>(
TinyVector<Dimension>)>::template interpolate<ItemType::cell>(U_id, mesh_data.xj());
CellValue<TinyVector<Dimension>> fj = InterpolateItemValue<TinyVector<Dimension>(
TinyVector<Dimension>)>::template interpolate<ItemType::cell>(f_id, mesh_data.xj());
const CellValue<const double> dual_Vj = diamond_mesh_data.Vj();
const FaceValue<const double> mes_l = [&] {
if constexpr (Dimension == 1) {
FaceValue<double> compute_mes_l{mesh->connectivity()};
compute_mes_l.fill(1);
return compute_mes_l;
} else {
return mesh_data.ll();
}
}();
const CellValue<const double> dual_mes_l_j = [=] {
CellValue<double> compute_mes_j{diamond_mesh->connectivity()};
mapper->toDualCell(mes_l, compute_mes_j);
return compute_mes_j;
}();
const CellValue<const double> primal_Vj = mesh_data.Vj();
FaceValue<const CellId> face_dual_cell_id = [=]() {
FaceValue<CellId> computed_face_dual_cell_id{mesh->connectivity()};
CellValue<CellId> dual_cell_id{diamond_mesh->connectivity()};
parallel_for(
diamond_mesh->numberOfCells(), PUGS_LAMBDA(CellId cell_id) { dual_cell_id[cell_id] = cell_id; });
mapper->fromDualCell(dual_cell_id, computed_face_dual_cell_id);
return computed_face_dual_cell_id;
}();
NodeValue<const NodeId> dual_node_primal_node_id = [=]() {
CellValue<NodeId> cell_ignored_id{mesh->connectivity()};
cell_ignored_id.fill(NodeId{std::numeric_limits<unsigned int>::max()});
NodeValue<NodeId> node_primal_id{mesh->connectivity()};
parallel_for(
mesh->numberOfNodes(), PUGS_LAMBDA(NodeId node_id) { node_primal_id[node_id] = node_id; });
NodeValue<NodeId> computed_dual_node_primal_node_id{diamond_mesh->connectivity()};
mapper->toDualNode(node_primal_id, cell_ignored_id, computed_dual_node_primal_node_id);
return computed_dual_node_primal_node_id;
}();
CellValue<NodeId> primal_cell_dual_node_id = [=]() {
CellValue<NodeId> cell_id{mesh->connectivity()};
NodeValue<NodeId> node_ignored_id{mesh->connectivity()};
node_ignored_id.fill(NodeId{std::numeric_limits<unsigned int>::max()});
NodeValue<NodeId> dual_node_id{diamond_mesh->connectivity()};
parallel_for(
diamond_mesh->numberOfNodes(), PUGS_LAMBDA(NodeId node_id) { dual_node_id[node_id] = node_id; });
CellValue<NodeId> computed_primal_cell_dual_node_id{mesh->connectivity()};
mapper->fromDualNode(dual_node_id, node_ignored_id, cell_id);
return cell_id;
}();
const auto& dual_Cjr = diamond_mesh_data.Cjr();
FaceValue<TinyVector<Dimension>> dualClj = [&] {
FaceValue<TinyVector<Dimension>> computedClj{mesh->connectivity()};
const auto& dual_node_to_cell_matrix = diamond_mesh->connectivity().nodeToCellMatrix();
const auto& dual_cell_to_node_matrix = diamond_mesh->connectivity().cellToNodeMatrix();
parallel_for(
mesh->numberOfFaces(), PUGS_LAMBDA(FaceId face_id) {
const auto& primal_face_to_cell = face_to_cell_matrix[face_id];
for (size_t i = 0; i < primal_face_to_cell.size(); i++) {
CellId cell_id = primal_face_to_cell[i];
const NodeId dual_node_id = primal_cell_dual_node_id[cell_id];
for (size_t i_dual_cell = 0; i_dual_cell < dual_node_to_cell_matrix[dual_node_id].size(); i_dual_cell++) {
const CellId dual_cell_id = dual_node_to_cell_matrix[dual_node_id][i_dual_cell];
if (face_dual_cell_id[face_id] == dual_cell_id) {
for (size_t i_dual_node = 0; i_dual_node < dual_cell_to_node_matrix[dual_cell_id].size();
i_dual_node++) {
const NodeId final_dual_node_id = dual_cell_to_node_matrix[dual_cell_id][i_dual_node];
if (final_dual_node_id == dual_node_id) {
computedClj[face_id] = dual_Cjr(dual_cell_id, i_dual_node);
}
}
}
}
}
});
return computedClj;
}();
FaceValue<TinyVector<Dimension>> nlj = [&] {
FaceValue<TinyVector<Dimension>> computedNlj{mesh->connectivity()};
parallel_for(
mesh->numberOfFaces(),
PUGS_LAMBDA(FaceId face_id) { computedNlj[face_id] = 1. / l2Norm(dualClj[face_id]) * dualClj[face_id]; });
return computedNlj;
}();
FaceValue<const double> alpha_lambda_l = [&] {
CellValue<double> alpha_j{diamond_mesh->connectivity()};
parallel_for(
diamond_mesh->numberOfCells(), PUGS_LAMBDA(CellId diamond_cell_id) {
alpha_j[diamond_cell_id] = dual_lambdaj[diamond_cell_id] / dual_Vj[diamond_cell_id];
});
FaceValue<double> computed_alpha_l{mesh->connectivity()};
mapper->fromDualCell(alpha_j, computed_alpha_l);
return computed_alpha_l;
}();
FaceValue<const double> alpha_mu_l = [&] { CellValue<double> alpha_j{diamond_mesh->connectivity()};
parallel_for(
diamond_mesh->numberOfCells(), PUGS_LAMBDA(CellId diamond_cell_id) {
alpha_j[diamond_cell_id] = dual_muj[diamond_cell_id] / dual_Vj[diamond_cell_id];
});
FaceValue<double> computed_alpha_l{mesh->connectivity()};
mapper->fromDualCell(alpha_j, computed_alpha_l);
return computed_alpha_l;
}();
const TinyMatrix<Dimension> I = identity;
const Array<int> non_zeros{number_of_dof * Dimension};
non_zeros.fill(Dimension * Dimension);
CRSMatrixDescriptor<double> S(number_of_dof * Dimension, number_of_dof * Dimension, non_zeros);
for (FaceId face_id = 0; face_id < mesh->numberOfFaces(); ++face_id) {
const double beta_mu_l = l2Norm(dualClj[face_id]) * alpha_mu_l[face_id] * mes_l[face_id];
const double beta_lambda_l = l2Norm(dualClj[face_id]) * alpha_lambda_l[face_id] * mes_l[face_id];
const auto& primal_face_to_cell = face_to_cell_matrix[face_id];
for (size_t i_cell = 0; i_cell < primal_face_to_cell.size(); ++i_cell) {
const CellId i_id = primal_face_to_cell[i_cell];
const bool is_face_reversed_for_cell_i = (dot(dualClj[face_id], xl[face_id] - xj[i_id]) < 0);
const TinyVector<Dimension> nil = [&] {
if (is_face_reversed_for_cell_i) {
return -nlj[face_id];
} else {
return nlj[face_id];
}
}();
for (size_t j_cell = 0; j_cell < primal_face_to_cell.size(); ++j_cell) {
const CellId j_id = primal_face_to_cell[j_cell];
TinyMatrix<Dimension> M =
beta_mu_l * I + beta_mu_l * tensorProduct(nil, nil) + beta_lambda_l * tensorProduct(nil, nil);
TinyMatrix<Dimension> N = tensorProduct(nil, nil);
if (i_cell == j_cell) {
for (size_t i = 0; i < Dimension; ++i) {
for (size_t j = 0; j < Dimension; ++j) {
S((cell_dof_number[i_id] * Dimension) + i, (cell_dof_number[j_id] * Dimension) + j) += M(i, j);
if (primal_face_is_neumann[face_id]) {
S(face_dof_number[face_id] * Dimension + i, cell_dof_number[j_id] * Dimension + j) -= M(i, j);
}
if (primal_face_is_symmetry[face_id]) {
S(face_dof_number[face_id] * Dimension + i, cell_dof_number[j_id] * Dimension + j) +=
-((i == j) ? 1 : 0) + N(i, j);
S(face_dof_number[face_id] * Dimension + i, face_dof_number[face_id] * Dimension + j) +=
(i == j) ? 1 : 0;
}
}
}
} else {
for (size_t i = 0; i < Dimension; ++i) {
for (size_t j = 0; j < Dimension; ++j) {
S((cell_dof_number[i_id] * Dimension) + i, (cell_dof_number[j_id] * Dimension) + j) -= M(i, j);
}
}
}
}
}
}
const auto& dual_cell_to_node_matrix = diamond_mesh->connectivity().cellToNodeMatrix();
const auto& primal_node_to_cell_matrix = mesh->connectivity().nodeToCellMatrix();
for (FaceId face_id = 0; face_id < mesh->numberOfFaces(); ++face_id) {
const double alpha_mu_face_id = mes_l[face_id] * alpha_mu_l[face_id];
const double alpha_lambda_face_id = mes_l[face_id] * alpha_lambda_l[face_id];
for (size_t i_face_cell = 0; i_face_cell < face_to_cell_matrix[face_id].size(); ++i_face_cell) {
CellId i_id = face_to_cell_matrix[face_id][i_face_cell];
const bool is_face_reversed_for_cell_i = (dot(dualClj[face_id], xl[face_id] - xj[i_id]) < 0);
for (size_t i_node = 0; i_node < primal_face_to_node_matrix[face_id].size(); ++i_node) {
NodeId node_id = primal_face_to_node_matrix[face_id][i_node];
const TinyVector<Dimension> nil = [&] {
if (is_face_reversed_for_cell_i) {
return -nlj[face_id];
} else {
return nlj[face_id];
}
}();
CellId dual_cell_id = face_dual_cell_id[face_id];
for (size_t i_dual_node = 0; i_dual_node < dual_cell_to_node_matrix[dual_cell_id].size(); ++i_dual_node) {
const NodeId dual_node_id = dual_cell_to_node_matrix[dual_cell_id][i_dual_node];
if (dual_node_primal_node_id[dual_node_id] == node_id) {
const TinyVector<Dimension> Clr = dual_Cjr(dual_cell_id, i_dual_node);
TinyMatrix<Dimension> M = alpha_mu_face_id * dot(Clr, nil) * I +
alpha_mu_face_id * tensorProduct(Clr, nil) +
alpha_lambda_face_id * tensorProduct(nil, Clr);
for (size_t j_cell = 0; j_cell < primal_node_to_cell_matrix[node_id].size(); ++j_cell) {
CellId j_id = primal_node_to_cell_matrix[node_id][j_cell];
for (size_t i = 0; i < Dimension; ++i) {
for (size_t j = 0; j < Dimension; ++j) {
S((cell_dof_number[i_id] * Dimension) + i, (cell_dof_number[j_id] * Dimension) + j) -=
w_rj(node_id, j_cell) * M(i, j);
if (primal_face_is_neumann[face_id]) {
S(face_dof_number[face_id] * Dimension + i, cell_dof_number[j_id] * Dimension + j) +=
w_rj(node_id, j_cell) * M(i, j);
}
}
}
}
if (primal_node_is_on_boundary[node_id]) {
for (size_t l_face = 0; l_face < node_to_face_matrix[node_id].size(); ++l_face) {
FaceId l_id = node_to_face_matrix[node_id][l_face];
if (primal_face_is_on_boundary[l_id]) {
for (size_t i = 0; i < Dimension; ++i) {
for (size_t j = 0; j < Dimension; ++j) {
S(cell_dof_number[i_id] * Dimension + i, face_dof_number[l_id] * Dimension + j) -=
w_rl(node_id, l_face) * M(i, j);
}
}
if (primal_face_is_neumann[face_id]) {
for (size_t i = 0; i < Dimension; ++i) {
for (size_t j = 0; j < Dimension; ++j) {
S(face_dof_number[face_id] * Dimension + i, face_dof_number[l_id] * Dimension + j) +=
w_rl(node_id, l_face) * M(i, j);
}
}
}
}
}
}
}
}
// }
}
}
}
for (FaceId face_id = 0; face_id < mesh->numberOfFaces(); ++face_id) {
if (primal_face_is_dirichlet[face_id]) {
for (size_t i = 0; i < Dimension; ++i) {
S(face_dof_number[face_id] * Dimension + i, face_dof_number[face_id] * Dimension + i) += 1; }
}
}
CRSMatrix A{S.getCRSMatrix()};
Vector<double> b{number_of_dof * Dimension};
b = zero;
for (CellId cell_id = 0; cell_id < mesh->numberOfCells(); ++cell_id) {
for (size_t i = 0; i < Dimension; ++i) {
b[(cell_dof_number[cell_id] * Dimension) + i] = primal_Vj[cell_id] * fj[cell_id][i];
}
}
// Dirichlet
NodeValue<bool> node_tag{mesh->connectivity()};
node_tag.fill(false);
for (const auto& boundary_condition : boundary_condition_list) {
std::visit(
[&](auto&& bc) {
using T = std::decay_t<decltype(bc)>;
if constexpr (std::is_same_v<T, DirichletBoundaryCondition>) {
const auto& face_list = bc.faceList();
const auto& value_list = bc.valueList();
for (size_t i_face = 0; i_face < face_list.size(); ++i_face) {
const FaceId face_id = face_list[i_face];
for (size_t i = 0; i < Dimension; ++i) {
b[(face_dof_number[face_id] * Dimension) + i] += value_list[i_face][i];
}
}
}
},
boundary_condition);
}
for (const auto& boundary_condition : boundary_condition_list) {
std::visit(
[&](auto&& bc) {
using T = std::decay_t<decltype(bc)>;
if constexpr ((std::is_same_v<T, NormalStrainBoundaryCondition>)) {
const auto& face_list = bc.faceList();
const auto& value_list = bc.valueList();
for (size_t i_face = 0; i_face < face_list.size(); ++i_face) {
FaceId face_id = face_list[i_face];
for (size_t i = 0; i < Dimension; ++i) {
b[face_dof_number[face_id] * Dimension + i] += mes_l[face_id] * value_list[i_face][i]; // sign
}
}
}
},
boundary_condition);
}
Vector<double> U{number_of_dof * Dimension};
U = zero;
CellValue<TinyVector<Dimension>> Speed{mesh->connectivity()};
FaceValue<TinyVector<Dimension>> Ul = InterpolateItemValue<TinyVector<Dimension>(
TinyVector<Dimension>)>::template interpolate<ItemType::face>(U_id, mesh_data.xl());
FaceValue<TinyVector<Dimension>> Speed_face{mesh->connectivity()};
Vector r = A * U - b;
std::cout << "initial (real) residu = " << std::sqrt(dot(r, r)) << '\n';
LinearSolver solver;
solver.solveLocalSystem(A, U, b);
r = A * U - b;
std::cout << "final (real) residu = " << std::sqrt(dot(r, r)) << '\n';
for (CellId cell_id = 0; cell_id < mesh->numberOfCells(); ++cell_id) {
for (size_t i = 0; i < Dimension; ++i) {
Speed[cell_id][i] = U[(cell_dof_number[cell_id] * Dimension) + i];
}
}
for (FaceId face_id = 0; face_id < mesh->numberOfFaces(); ++face_id) {
for (size_t i = 0; i < Dimension; ++i) {
if (primal_face_is_on_boundary[face_id]) {
Speed_face[face_id][i] = U[(face_dof_number[face_id] * Dimension) + i];
} else {
Speed_face[face_id][i] = Ul[face_id][i];
}
}
}
Vector<double> Uexacte{mesh->numberOfCells() * Dimension};
for (CellId j = 0; j < mesh->numberOfCells(); ++j) {
for (size_t l = 0; l < Dimension; ++l) {
Uexacte[(cell_dof_number[j] * Dimension) + l] = Uj[j][l];
}
}
Vector<double> error{mesh->numberOfCells() * Dimension};
for (CellId cell_id = 0; cell_id < mesh->numberOfCells(); ++cell_id) {
for (size_t i = 0; i < Dimension; ++i) {
error[(cell_id * Dimension) + i] = (Speed[cell_id][i] - Uj[cell_id][i]) * sqrt(primal_Vj[cell_id]);
}
}
Vector<double> error_face{mesh->numberOfFaces() * Dimension};
parallel_for(
mesh->numberOfFaces(), PUGS_LAMBDA(FaceId face_id) {
if (primal_face_is_on_boundary[face_id]) {
for (size_t i = 0; i < Dimension; ++i) {
error_face[face_id * Dimension + i] = (Speed_face[face_id][i] - Ul[face_id][i]) * sqrt(mes_l[face_id]);
}
} else {
error_face[face_id] = 0;
}
});
std::cout << "||Error||_2 (cell)= " << std::sqrt(dot(error, error)) << "\n";
std::cout << "||Error||_2 (face)= " << std::sqrt(dot(error_face, error_face)) << "\n";
std::cout << "||Error||_2 (total)= " << std::sqrt(dot(error, error)) + std::sqrt(dot(error_face, error_face))
<< "\n";
NodeValue<TinyVector<3>> ur3d{mesh->connectivity()};
ur3d.fill(zero);
parallel_for(
mesh->numberOfNodes(), PUGS_LAMBDA(NodeId node_id) {
TinyVector<Dimension> x = zero;
const auto node_cells = node_to_cell_matrix[node_id];
for (size_t i_cell = 0; i_cell < node_cells.size(); ++i_cell) {
CellId cell_id = node_cells[i_cell];
x += w_rj(node_id, i_cell) * Speed[cell_id];
}
const auto node_faces = node_to_face_matrix[node_id];
for (size_t i_face = 0; i_face < node_faces.size(); ++i_face) {
FaceId face_id = node_faces[i_face];
if (primal_face_is_on_boundary[face_id]) {
x += w_rl(node_id, i_face) * Speed_face[face_id];
}
}
for (size_t i = 0; i < Dimension; ++i) {
ur3d[node_id][i] = x[i];
}
});
}
} else {
throw NotImplementedError("not done in 1d");
}}
template <size_t Dimension>
class ElasticityDiamondScheme<Dimension>::DirichletBoundaryCondition
{
private:
const Array<const TinyVector<Dimension>> m_value_list;
const Array<const FaceId> m_face_list;
public:
const Array<const FaceId>&
faceList() const
{
return m_face_list;
}
const Array<const TinyVector<Dimension>>&
valueList() const
{
return m_value_list;
}
DirichletBoundaryCondition(const Array<const FaceId>& face_list, const Array<const TinyVector<Dimension>>& value_list)
: m_value_list{value_list}, m_face_list{face_list}
{
Assert(m_value_list.size() == m_face_list.size());
}
~DirichletBoundaryCondition() = default;
};
template <size_t Dimension>
class ElasticityDiamondScheme<Dimension>::NormalStrainBoundaryCondition
{
private:
const Array<const TinyVector<Dimension>> m_value_list;
const Array<const FaceId> m_face_list;
public:
const Array<const FaceId>&
faceList() const
{
return m_face_list;
}
const Array<const TinyVector<Dimension>>&
valueList() const
{
return m_value_list;
}
NormalStrainBoundaryCondition(const Array<const FaceId>& face_list,
const Array<const TinyVector<Dimension>>& value_list)
: m_value_list{value_list}, m_face_list{face_list}
{
Assert(m_value_list.size() == m_face_list.size());
}
~NormalStrainBoundaryCondition() = default;
};
template <size_t Dimension>
class ElasticityDiamondScheme<Dimension>::SymmetryBoundaryCondition
{
private:
const Array<const TinyVector<Dimension>> m_value_list;
const Array<const FaceId> m_face_list;
public:
const Array<const FaceId>& faceList() const
{
return m_face_list;
}
public:
SymmetryBoundaryCondition(const Array<const FaceId>& face_list) : m_face_list{face_list} {}
~SymmetryBoundaryCondition() = default;
};
template ElasticityDiamondScheme<1>::ElasticityDiamondScheme(
std::shared_ptr<const IMesh>,
const std::vector<std::shared_ptr<const IBoundaryConditionDescriptor>>&,
const FunctionSymbolId&,
const FunctionSymbolId&,
const FunctionSymbolId&,
const FunctionSymbolId&);
template ElasticityDiamondScheme<2>::ElasticityDiamondScheme(
std::shared_ptr<const IMesh>,
const std::vector<std::shared_ptr<const IBoundaryConditionDescriptor>>&,
const FunctionSymbolId&,
const FunctionSymbolId&,
const FunctionSymbolId&,
const FunctionSymbolId&);
template ElasticityDiamondScheme<3>::ElasticityDiamondScheme(
std::shared_ptr<const IMesh>,
const std::vector<std::shared_ptr<const IBoundaryConditionDescriptor>>&,
const FunctionSymbolId&,
const FunctionSymbolId&,
const FunctionSymbolId&,
const FunctionSymbolId&);