diff --git a/src/scheme/ScalarNodalScheme.cpp b/src/scheme/ScalarNodalScheme.cpp
index 8246e2121a55d8ddefde348b6dc2527a9a1b2668..c349f4b5e3e3516c10629f6f755c4e38a3e702b9 100644
--- a/src/scheme/ScalarNodalScheme.cpp
+++ b/src/scheme/ScalarNodalScheme.cpp
@@ -420,10 +420,10 @@ class ScalarNodalSchemeHandler::ScalarNodalScheme : public ScalarNodalSchemeHand
kappa[node_id] = zero;
const auto& node_to_cell = node_to_cell_matrix[node_id];
double weight = 0;
- for (size_t j = 0; j < node_to_cell.size(); ++j) {
- const CellId J = node_to_cell[j];
- double local_weight = 1. / l2Norm(xr[node_id] - xj[J]);
- kappa[node_id] += local_weight * cell_kappaj[J];
+ for (size_t i_cell = 0; i_cell < node_to_cell.size(); ++i_cell) {
+ const CellId cell_id = node_to_cell[i_cell];
+ double local_weight = 1. / l2Norm(xr[node_id] - xj[cell_id]);
+ kappa[node_id] += local_weight * cell_kappaj[cell_id];
weight += local_weight;
}
kappa[node_id] = 1. / weight * kappa[node_id];
@@ -438,10 +438,10 @@ class ScalarNodalSchemeHandler::ScalarNodalScheme : public ScalarNodalSchemeHand
kappa[node_id] = zero;
const auto& node_to_cell = node_to_cell_matrix[node_id];
double weight = 0;
- for (size_t j = 0; j < node_to_cell.size(); ++j) {
- const CellId J = node_to_cell[j];
- double local_weight = 1. / l2Norm(xr[node_id] - xj[J]);
- kappa[node_id] += local_weight * cell_kappajb[J];
+ for (size_t i_cell = 0; i_cell < node_to_cell.size(); ++i_cell) {
+ const CellId cell_id = node_to_cell[i_cell];
+ double local_weight = 1. / l2Norm(xr[node_id] - xj[cell_id]);
+ kappa[node_id] += local_weight * cell_kappajb[cell_id];
weight += local_weight;
}
kappa[node_id] = 1. / weight * kappa[node_id];
@@ -487,6 +487,71 @@ class ScalarNodalSchemeHandler::ScalarNodalScheme : public ScalarNodalSchemeHand
return kappa_invBeta;
}();
+ const NodeValue<const TinyMatrix<Dimension>> corner_betar = [&] {
+ NodeValue<TinyMatrix<Dimension>> beta{mesh->connectivity()};
+ parallel_for(
+ mesh->numberOfNodes(), PUGS_LAMBDA(NodeId node_id) {
+ if (node_is_corner[node_id]) {
+ const auto& node_local_number_in_its_cell = node_local_numbers_in_their_cells.itemArray(node_id);
+ const auto& node_to_cell = node_to_cell_matrix[node_id];
+
+ size_t i_cell = node_to_cell[0];
+ const CellId cell_id = node_to_cell[i_cell];
+ const unsigned int i_node = node_local_number_in_its_cell[i_cell];
+
+ const auto& cell_nodes = cell_to_node_matrix[cell_id];
+ const NodeId node_id_p1 = cell_to_node_matrix[cell_id][(i_node + 1) % cell_nodes.size()];
+ const NodeId node_id_p2 = cell_to_node_matrix[cell_id][(i_node + 2) % cell_nodes.size()];
+ const NodeId node_id_m1 = cell_to_node_matrix[cell_id][(i_node - 1) % cell_nodes.size()];
+
+ const TinyVector<Dimension> xj1 = 1. / 3. * (xr[node_id] + xr[node_id_m1] + xr[node_id_p2]);
+ const TinyVector<Dimension> xj2 = 1. / 3. * (xr[node_id] + xr[node_id_p2] + xr[node_id_p1]);
+
+ const TinyVector<Dimension> xrm1 = xr[node_id_m1];
+ const TinyVector<Dimension> xrp1 = xr[node_id_p1];
+ const TinyVector<Dimension> xrp2 = xr[node_id_p2];
+
+ TinyVector<Dimension> Cjr1;
+ TinyVector<Dimension> Cjr2;
+
+ if (Dimension == 2) {
+ Cjr1[0] = -0.5 * (xrm1[1] - xrp2[1]);
+ Cjr1[1] = 0.5 * (xrm1[0] - xrp2[0]);
+ Cjr2[0] = -0.5 * (xrp2[1] - xrp1[1]);
+ Cjr2[1] = 0.5 * (xrp2[0] - xrp1[0]);
+ } else {
+ std::cout << "Dimension " << Dimension << " not implemented. \n";
+ throw NotImplementedError("The scheme is not implemented in this dimension.");
+ }
+
+ beta[node_id] = tensorProduct(Cjr1, (xr[node_id] - xj1)) + tensorProduct(Cjr2, (xr[node_id] - xj2));
+ }
+ });
+ return beta;
+ }();
+
+ const NodeValue<const TinyMatrix<Dimension>> corner_kappar_invBetar = [&] {
+ NodeValue<TinyMatrix<Dimension>> kappa_invBeta{mesh->connectivity()};
+ parallel_for(
+ mesh->numberOfNodes(), PUGS_LAMBDA(NodeId node_id) {
+ if (node_is_corner[node_id]) {
+ kappa_invBeta[node_id] = node_kappar[node_id] * inverse(corner_betar[node_id]);
+ }
+ });
+ return kappa_invBeta;
+ }();
+
+ const NodeValue<const TinyMatrix<Dimension>> corner_kapparb_invBetar = [&] {
+ NodeValue<TinyMatrix<Dimension>> kappa_invBeta{mesh->connectivity()};
+ parallel_for(
+ mesh->numberOfNodes(), PUGS_LAMBDA(NodeId node_id) {
+ if (node_is_corner[node_id]) {
+ kappa_invBeta[node_id] = node_kapparb[node_id] * inverse(corner_betar[node_id]);
+ }
+ });
+ return kappa_invBeta;
+ }();
+
const NodeValue<const TinyVector<Dimension>> sum_Cjr = [&] {
NodeValue<TinyVector<Dimension>> compute_sum_Cjr{mesh->connectivity()};
parallel_for(
@@ -564,7 +629,7 @@ class ScalarNodalSchemeHandler::ScalarNodalScheme : public ScalarNodalSchemeHand
dot(kappar_invBetar[node_id] * Cjr(cell_id_k, i_node_k), Cjr(cell_id_j, i_node_j));
}
}
- } else if ((node_is_neumann[node_id]) && (not node_is_corner[node_id])) {
+ } else if ((node_is_neumann[node_id]) && (not node_is_corner[node_id]) && (not node_is_dirichlet[node_id])) {
const TinyMatrix<Dimension> I = identity;
const TinyVector<Dimension> n = exterior_normal[node_id];
const TinyMatrix<Dimension> nxn = tensorProduct(n, n);
@@ -584,6 +649,32 @@ class ScalarNodalSchemeHandler::ScalarNodalScheme : public ScalarNodalSchemeHand
P * Cjr(cell_id_k, i_node_j));
}
}
+ } else if ((node_is_dirichlet[node_id]) && (not node_is_corner[node_id])) {
+ for (size_t i_cell_j = 0; i_cell_j < node_to_cell.size(); ++i_cell_j) {
+ const CellId cell_id_j = node_to_cell[i_cell_j];
+ const size_t i_node_j = node_local_number_in_its_cells[i_cell_j];
+
+ for (size_t i_cell_k = 0; i_cell_k < node_to_cell.size(); ++i_cell_k) {
+ const CellId cell_id_k = node_to_cell[i_cell_k];
+ const size_t i_node_k = node_local_number_in_its_cells[i_cell_k];
+
+ S(cell_id_j, cell_id_k) +=
+ dot(kappar_invBetar[node_id] * Cjr(cell_id_k, i_node_k), Cjr(cell_id_j, i_node_j));
+ }
+ }
+ } else if (node_is_dirichlet[node_id] && node_is_corner[node_id]) {
+ for (size_t i_cell_j = 0; i_cell_j < node_to_cell.size(); ++i_cell_j) {
+ const CellId cell_id_j = node_to_cell[i_cell_j];
+ const size_t i_node_j = node_local_number_in_its_cells[i_cell_j];
+
+ for (size_t i_cell_k = 0; i_cell_k < node_to_cell.size(); ++i_cell_k) {
+ const CellId cell_id_k = node_to_cell[i_cell_k];
+ const size_t i_node_k = node_local_number_in_its_cells[i_cell_k];
+
+ S(cell_id_j, cell_id_k) +=
+ dot(corner_kappar_invBetar[node_id] * Cjr(cell_id_k, i_node_k), Cjr(cell_id_j, i_node_j));
+ }
+ }
}
}