--- /dev/null
+New: Added support for hessians to FE_NedelecSZ
+<br>
+(Sebastian Kinnewig, 2022/01/28)
*/
mutable std::vector<std::vector<DerivativeForm<1, dim, dim>>> shape_grads;
+ /**
+ * Storage for shape function hessians on the reference element. We only
+ * pre-compute cell-based DoFs, as the edge- and face-based DoFs depend on
+ * the cell.
+ *
+ * Due to the cell-dependent DoFs, this variable is declared mutable.
+ */
+ mutable std::vector<std::vector<DerivativeForm<2, dim, dim>>>
+ shape_hessians;
+
/**
* Storage for all possible edge parameterization between vertices. These
* are required in the computation of edge- and face-based DoFs, which are
std::vector<DerivativeForm<1, dim, dim>>(
n_q_points));
}
- // Not implementing second derivatives yet:
+
if ((flags & update_hessians) != 0u)
{
- Assert(false, ExcNotImplemented());
+ data.shape_hessians.resize(this->n_dofs_per_cell(),
+ std::vector<DerivativeForm<2, dim, dim>>(
+ n_q_points));
}
std::vector<Point<dim>> p_list(n_q_points);
cell_type2_offset + degree * degree;
const unsigned int cell_type3_offset2 = cell_type3_offset1 + degree;
- if ((flags & (update_values | update_gradients)) != 0u)
+ if ((flags & (update_values | update_gradients | update_hessians)) !=
+ 0u)
{
// compute all points we must evaluate the 1d polynomials at:
std::vector<Point<dim>> cell_points(n_q_points);
// We only need poly values and 1st derivative for
// update_values, but need the 2nd derivative too for
- // update_gradients.
- //
- // Note that this will need to be updated if we're supporting
- // update_hessians.
+ // update_gradients. For update_hessians we also need the 3rd
+ // derivatives.
const unsigned int poly_length(
- (flags & update_gradients) != 0u ? 3 : 2);
+ (flags & update_hessians) != 0u ?
+ 4 :
+ ((flags & update_gradients) != 0u ? 3 : 2));
std::vector<std::vector<double>> polyx(
degree, std::vector<double>(poly_length));
data.shape_grads[dof_index3_2][q][1][1] = 0.0;
}
}
+ if (flags & update_hessians)
+ {
+ for (unsigned int j = 0; j < degree; ++j)
+ {
+ const unsigned int shift_j(j * degree);
+ for (unsigned int i = 0; i < degree; ++i)
+ {
+ const unsigned int shift_ij(i + shift_j);
+
+ // Type 1:
+ const unsigned int dof_index1(cell_type1_offset +
+ shift_ij);
+ data.shape_hessians[dof_index1][q][0][0][0] =
+ 8.0 * polyx[i][3] * polyy[j][0];
+ data.shape_hessians[dof_index1][q][1][0][0] =
+ 8.0 * polyx[i][2] * polyy[j][1];
+
+ data.shape_hessians[dof_index1][q][0][1][0] =
+ data.shape_hessians[dof_index1][q][1][0][0];
+ data.shape_hessians[dof_index1][q][1][1][0] =
+ 8.0 * polyx[i][1] * polyy[j][2];
+
+ data.shape_hessians[dof_index1][q][0][0][1] =
+ data.shape_hessians[dof_index1][q][1][0][0];
+ data.shape_hessians[dof_index1][q][1][0][1] =
+ data.shape_hessians[dof_index1][q][1][1][0];
+
+ data.shape_hessians[dof_index1][q][0][1][1] =
+ data.shape_hessians[dof_index1][q][1][1][0];
+ data.shape_hessians[dof_index1][q][1][1][1] =
+ 8.0 * polyx[i][0] * polyy[j][3];
+
+
+
+ // Type 2:
+ const unsigned int dof_index2(cell_type2_offset +
+ shift_ij);
+ for (unsigned int d = 0; d < dim; ++d)
+ {
+ data.shape_hessians[dof_index2][q][0][0][d] =
+ data.shape_hessians[dof_index1][q][0][0][d];
+ data.shape_hessians[dof_index2][q][0][1][d] =
+ data.shape_hessians[dof_index1][q][0][1][d];
+ data.shape_hessians[dof_index2][q][1][0][d] =
+ -1.0 *
+ data.shape_hessians[dof_index1][q][1][0][d];
+ data.shape_hessians[dof_index2][q][1][1][d] =
+ -1.0 *
+ data.shape_hessians[dof_index1][q][1][1][d];
+ }
+ }
+ // Type 3:
+ const unsigned int dof_index3_1(cell_type3_offset1 +
+ j);
+ data.shape_hessians[dof_index3_1][q][0][0][0] = 0.0;
+ data.shape_hessians[dof_index3_1][q][0][0][1] = 0.0;
+ data.shape_hessians[dof_index3_1][q][0][1][0] = 0.0;
+ data.shape_hessians[dof_index3_1][q][0][1][1] =
+ 4.0 * polyy[j][2];
+ data.shape_hessians[dof_index3_1][q][1][0][0] = 0.0;
+ data.shape_hessians[dof_index3_1][q][1][0][1] = 0.0;
+ data.shape_hessians[dof_index3_1][q][1][1][0] = 0.0;
+ data.shape_hessians[dof_index3_1][q][1][1][1] = 0.0;
+
+ const unsigned int dof_index3_2(cell_type3_offset2 +
+ j);
+ data.shape_hessians[dof_index3_2][q][0][0][0] = 0.0;
+ data.shape_hessians[dof_index3_2][q][0][0][1] = 0.0;
+ data.shape_hessians[dof_index3_2][q][0][1][0] = 0.0;
+ data.shape_hessians[dof_index3_2][q][0][1][1] = 0.0;
+ data.shape_hessians[dof_index3_2][q][1][0][0] =
+ 4.0 * polyx[j][2];
+ data.shape_hessians[dof_index3_2][q][1][0][1] = 0.0;
+ data.shape_hessians[dof_index3_2][q][1][1][0] = 0.0;
+ data.shape_hessians[dof_index3_2][q][1][1][1] = 0.0;
+ }
+ }
}
}
break;
// for cell-based shape functions:
// these don't depend on the cell, so can precompute all here:
- if ((flags & (update_values | update_gradients)) != 0u)
+ if ((flags &
+ (update_values | update_gradients | update_hessians)) != 0u)
{
// Cell-based shape functions:
//
}
}
-
- // only need poly values and 1st derivative for update_values,
- // but need 2nd derivative too for update_gradients.
+ // We only need poly values and 1st derivative for
+ // update_values, but need the 2nd derivative too for
+ // update_gradients. For update_hessians we also need 3rd
+ // derivative.
const unsigned int poly_length(
- (flags & update_gradients) != 0u ? 3 : 2);
+ (flags & update_hessians) != 0u ?
+ 4 :
+ ((flags & update_gradients) != 0u ? 3 : 2));
+
// Loop through quad points:
for (unsigned int q = 0; q < n_q_points; ++q)
{
}
}
}
+ if (flags & update_hessians)
+ {
+ for (unsigned int k = 0; k < degree; ++k)
+ {
+ const unsigned int shift_k(k * degree * degree);
+ const unsigned int shift_j(
+ k * degree); // Used below when subbing k for j
+ // type 3
+
+ for (unsigned int j = 0; j < degree; ++j)
+ {
+ const unsigned int shift_jk(j * degree +
+ shift_k);
+ for (unsigned int i = 0; i < degree; ++i)
+ {
+ const unsigned int shift_ijk(shift_jk +
+ i);
+
+ // Type 1:
+ const unsigned int dof_index1(
+ cell_type1_offset + shift_ijk);
+
+ data.shape_hessians[dof_index1][q][0][0]
+ [0] =
+ 8.0 * polyx[i][3] * polyy[j][0] *
+ polyz[k][0];
+ data.shape_hessians[dof_index1][q][1][0]
+ [0] =
+ 8.0 * polyx[i][2] * polyy[j][1] *
+ polyz[k][0];
+ data.shape_hessians[dof_index1][q][2][0]
+ [0] =
+ 8.0 * polyx[i][2] * polyy[j][0] *
+ polyz[k][1];
+
+ data.shape_hessians[dof_index1][q][0][1]
+ [0] =
+ data.shape_hessians[dof_index1][q][1][0]
+ [0];
+ data.shape_hessians[dof_index1][q][1][1]
+ [0] =
+ 8.0 * polyx[i][1] * polyy[j][2] *
+ polyz[k][0];
+ data.shape_hessians[dof_index1][q][2][1]
+ [0] =
+ 8.0 * polyx[i][1] * polyy[j][1] *
+ polyz[k][1];
+
+ data.shape_hessians[dof_index1][q][0][2]
+ [0] =
+ data.shape_hessians[dof_index1][q][2][0]
+ [0];
+ data.shape_hessians[dof_index1][q][1][2]
+ [0] =
+ data.shape_hessians[dof_index1][q][2][1]
+ [0];
+ data.shape_hessians[dof_index1][q][2][2]
+ [0] =
+ 8.0 * polyx[i][1] * polyy[j][0] *
+ polyz[k][2];
+
+
+ data.shape_hessians[dof_index1][q][0][0]
+ [1] =
+ data.shape_hessians[dof_index1][q][1][0]
+ [0];
+ data.shape_hessians[dof_index1][q][1][0]
+ [1] =
+ data.shape_hessians[dof_index1][q][1][1]
+ [0];
+ data.shape_hessians[dof_index1][q][2][0]
+ [1] =
+ data.shape_hessians[dof_index1][q][2][1]
+ [0];
+
+ data.shape_hessians[dof_index1][q][0][1]
+ [1] =
+ data.shape_hessians[dof_index1][q][1][1]
+ [0];
+ data.shape_hessians[dof_index1][q][1][1]
+ [1] =
+ 8.0 * polyx[i][0] * polyy[j][3] *
+ polyz[k][0];
+ data.shape_hessians[dof_index1][q][2][1]
+ [1] =
+ 8.0 * polyx[i][0] * polyy[j][2] *
+ polyz[k][1];
+
+ data.shape_hessians[dof_index1][q][0][2]
+ [1] =
+ data.shape_hessians[dof_index1][q][2][1]
+ [0];
+ data.shape_hessians[dof_index1][q][1][2]
+ [1] =
+ data.shape_hessians[dof_index1][q][2][1]
+ [1];
+ data.shape_hessians[dof_index1][q][2][2]
+ [1] =
+ 8.0 * polyx[i][0] * polyy[j][1] *
+ polyz[k][2];
+
+
+ data.shape_hessians[dof_index1][q][0][0]
+ [2] =
+ data.shape_hessians[dof_index1][q][2][0]
+ [0];
+ data.shape_hessians[dof_index1][q][1][0]
+ [2] =
+ data.shape_hessians[dof_index1][q][2][1]
+ [0];
+ data.shape_hessians[dof_index1][q][2][0]
+ [2] =
+ data.shape_hessians[dof_index1][q][2][2]
+ [0];
+
+ data.shape_hessians[dof_index1][q][0][1]
+ [2] =
+ data.shape_hessians[dof_index1][q][2][1]
+ [0];
+ data.shape_hessians[dof_index1][q][1][1]
+ [2] =
+ data.shape_hessians[dof_index1][q][2][1]
+ [1];
+ data.shape_hessians[dof_index1][q][2][1]
+ [2] =
+ data.shape_hessians[dof_index1][q][2][2]
+ [1];
+
+ data.shape_hessians[dof_index1][q][0][2]
+ [2] =
+ data.shape_hessians[dof_index1][q][2][2]
+ [0];
+ data.shape_hessians[dof_index1][q][1][2]
+ [2] =
+ data.shape_hessians[dof_index1][q][2][2]
+ [1];
+ data.shape_hessians[dof_index1][q][2][2]
+ [2] =
+ 8.0 * polyx[i][0] * polyy[j][0] *
+ polyz[k][3];
+
+
+ // Type 2:
+ const unsigned int dof_index2_1(
+ cell_type2_offset1 + shift_ijk);
+ const unsigned int dof_index2_2(
+ cell_type2_offset2 + shift_ijk);
+
+ for (unsigned int d1 = 0; d1 < dim; ++d1)
+ {
+ for (unsigned int d2 = 0; d2 < dim;
+ ++d2)
+ {
+ data
+ .shape_hessians[dof_index2_1][q]
+ [0][d1][d2] =
+ data
+ .shape_hessians[dof_index1][q]
+ [0][d1][d2];
+ data
+ .shape_hessians[dof_index2_1][q]
+ [1][d1][d2] =
+ -1.0 *
+ data
+ .shape_hessians[dof_index1][q]
+ [1][d1][d2];
+ data
+ .shape_hessians[dof_index2_1][q]
+ [2][d1][d2] =
+ data
+ .shape_hessians[dof_index1][q]
+ [2][d1][d2];
+
+ data
+ .shape_hessians[dof_index2_2][q]
+ [0][d1][d2] =
+ data
+ .shape_hessians[dof_index1][q]
+ [0][d1][d2];
+ data
+ .shape_hessians[dof_index2_2][q]
+ [1][d1][d2] =
+ -1.0 *
+ data
+ .shape_hessians[dof_index1][q]
+ [1][d1][d2];
+ data
+ .shape_hessians[dof_index2_2][q]
+ [2][d1][d2] =
+ -1.0 *
+ data
+ .shape_hessians[dof_index1][q]
+ [2][d1][d2];
+ }
+ }
+ }
+ // Type 3: (note we re-use k and j for
+ // convenience):
+ const unsigned int shift_ij(
+ j + shift_j); // here we've subbed j for i,
+ // k for j.
+ const unsigned int dof_index3_1(
+ cell_type3_offset1 + shift_ij);
+ const unsigned int dof_index3_2(
+ cell_type3_offset2 + shift_ij);
+ const unsigned int dof_index3_3(
+ cell_type3_offset3 + shift_ij);
+ for (unsigned int d1 = 0; d1 < dim; ++d1)
+ {
+ for (unsigned int d2 = 0; d2 < dim; ++d2)
+ {
+ for (unsigned int d3 = 0; d3 < dim;
+ ++d3)
+ {
+ data
+ .shape_hessians[dof_index3_1][q]
+ [d1][d2][d3] =
+ 0.0;
+ data
+ .shape_hessians[dof_index3_2][q]
+ [d1][d2][d3] =
+ 0.0;
+ data
+ .shape_hessians[dof_index3_3][q]
+ [d1][d2][d3] =
+ 0.0;
+ }
+ }
+ }
+ data
+ .shape_hessians[dof_index3_1][q][0][1][1] =
+ 4.0 * polyy[j][2] * polyz[k][0];
+ data
+ .shape_hessians[dof_index3_1][q][0][1][2] =
+ 4.0 * polyy[j][1] * polyz[k][1];
+
+ data
+ .shape_hessians[dof_index3_1][q][0][2][1] =
+ data
+ .shape_hessians[dof_index3_1][q][0][1][2];
+ data
+ .shape_hessians[dof_index3_1][q][0][2][2] =
+ 4.0 * polyy[j][0] * polyz[k][2];
+
+
+ data
+ .shape_hessians[dof_index3_2][q][1][0][0] =
+ 4.0 * polyx[j][2] * polyz[k][0];
+ data
+ .shape_hessians[dof_index3_2][q][1][0][2] =
+ 4.0 * polyx[j][1] * polyz[k][1];
+
+ data
+ .shape_hessians[dof_index3_2][q][1][2][0] =
+ data
+ .shape_hessians[dof_index3_2][q][1][0][2];
+ data
+ .shape_hessians[dof_index3_2][q][1][2][2] =
+ 4.0 * polyx[j][0] * polyz[k][2];
+
+
+ data
+ .shape_hessians[dof_index3_3][q][2][0][0] =
+ 4.0 * polyx[j][2] * polyy[k][0];
+ data
+ .shape_hessians[dof_index3_3][q][2][0][1] =
+ 4.0 * polyx[j][1] * polyy[k][1];
+
+ data
+ .shape_hessians[dof_index3_3][q][2][1][0] =
+ data
+ .shape_hessians[dof_index3_3][q][2][0][1];
+ data
+ .shape_hessians[dof_index3_3][q][2][1][1] =
+ 4.0 * polyx[j][0] * polyy[k][2];
+ }
+ }
+ }
}
}
}
{
case 2:
{
- if ((flags & (update_values | update_gradients)) != 0u)
+ if ((flags & (update_values | update_gradients | update_hessians)) !=
+ 0u)
{
// Define an edge numbering so that each edge, E_{m} = [e^{m}_{1},
// e^{m}_{2}] e1 = higher global numbering of the two local
}
}
- // Define \sigma_{m} = sigma_{e^{m}_{2}} - sigma_{e^{m}_{2}}
+ // Define \sigma_{m} = sigma_{e^{m}_{2}} - sigma_{e^{m}_{1}}
// \lambda_{m} = \lambda_{e^{m}_{1}} + \lambda_{e^{m}_{2}}
//
// To help things, in fe_data, we have precomputed (sigma_{i} -
// derivatives of the 1d polynomials, but only first derivatives
// for the shape values.
const unsigned int poly_length(
- (flags & update_gradients) != 0u ? 3 : 2);
+ (flags & update_hessians) != 0u ?
+ 4 :
+ ((flags & update_gradients) != 0u ? 3 : 2));
for (unsigned int m = 0; m < lines_per_cell; ++m)
{
{
// Compute all required 1d polynomials and their
// derivatives, starting at degree 2. e.g. to access
- // L'_{3}(2x-1) use polyx[1][1].
+ // L'_{i+2}(edge_sigma) use polyx[i][1].
IntegratedLegendrePolynomials[i + 1].value(
edge_sigma_values[m][q], poly[i - 1]);
}
edge_lambda_values[m][q] * poly[poly_index][2];
}
}
+ if (flags & update_hessians)
+ {
+ // Lowest order edge shape function
+ for (unsigned int d1 = 0; d1 < dim; ++d1)
+ {
+ for (unsigned int d2 = 0; d2 < dim; ++d2)
+ {
+ for (unsigned int d3 = 0; d3 < dim; ++d3)
+ {
+ fe_data.shape_hessians[shift_m][q][d1][d2]
+ [d3] = 0;
+ }
+ }
+ }
+
+ // Higher order edge shape function
+ for (unsigned int i = 0; i < degree; ++i)
+ {
+ const unsigned int dof_index(i + 1 + shift_m);
+
+ for (unsigned int d1 = 0; d1 < dim; ++d1)
+ {
+ for (unsigned int d2 = 0; d2 < dim; ++d2)
+ {
+ for (unsigned int d3 = 0; d3 < dim; ++d3)
+ {
+ fe_data.shape_hessians[dof_index][q]
+ [d1][d2][d3] =
+ edge_sigma_grads[m][d1] *
+ edge_sigma_grads[m][d2] *
+ edge_sigma_grads[m][d3] *
+ poly[i][3] *
+ edge_lambda_values[m][q] +
+ poly[i][2] *
+ (edge_sigma_grads[m][d1] *
+ edge_sigma_grads[m][d2] *
+ edge_lambda_grads[m][d3] +
+ edge_sigma_grads[m][d3] *
+ edge_sigma_grads[m][d1] *
+ edge_lambda_grads[m][d2] +
+ edge_sigma_grads[m][d3] *
+ edge_sigma_grads[m][d2] *
+ edge_lambda_grads[m][d1]);
+ }
+ }
+ }
+ }
+ }
}
}
}
}
case 3:
{
- if ((flags & (update_values | update_gradients)) != 0u)
+ if ((flags & (update_values | update_gradients | update_hessians)) !=
+ 0u)
{
// Define an edge numbering so that each edge, E_{m} = [e^{m}_{1},
// e^{m}_{2}] e1 = higher global numbering of the two local
}
}
- // Define \sigma_{m} = sigma_{e^{m}_{2}} - sigma_{e^{m}_{2}}
+ // Define \sigma_{m} = sigma_{e^{m}_{1}} - sigma_{e^{m}_{2}}
// \lambda_{m} = \lambda_{e^{m}_{1}} + \lambda_{e^{m}_{2}}
//
// To help things, in fe_data, we have precomputed (sigma_{i} -
// derivatives of the 1d polynomials, but only first derivatives
// for the shape values.
const unsigned int poly_length(
- (flags & update_gradients) != 0u ? 3 : 2);
+ (flags & update_hessians) != 0u ?
+ 4 :
+ ((flags & update_gradients) != 0u ? 3 : 2));
+
std::vector<std::vector<double>> poly(
degree, std::vector<double>(poly_length));
for (unsigned int m = 0; m < lines_per_cell; ++m)
for (unsigned int q = 0; q < n_q_points; ++q)
{
// precompute values of all 1d polynomials required:
+ // for example poly[i][1] = L'_{i+2}(edge_sigma_values)
if (degree > 0)
{
for (unsigned int i = 0; i < degree; ++i)
}
if ((flags & update_values) != 0u)
{
- // Lowest order shape functions:
+ // Lowest order edge shape functions:
for (unsigned int d = 0; d < dim; ++d)
{
fe_data.shape_values[shift_m][q][d] =
0.5 * edge_sigma_grads[m][d] *
edge_lambda_values[m][q];
}
+ // Higher order edge shape functions
if (degree > 0)
{
for (unsigned int i = 0; i < degree; ++i)
}
if ((flags & update_gradients) != 0u)
{
- // Lowest order shape functions:
+ // Lowest order edge shape functions:
for (unsigned int d1 = 0; d1 < dim; ++d1)
{
for (unsigned int d2 = 0; d2 < dim; ++d2)
edge_lambda_grads[m][q][d2];
}
}
+ // Higher order edge shape functions
if (degree > 0)
{
for (unsigned int i = 0; i < degree; ++i)
}
}
}
+ if (flags & update_hessians)
+ {
+ // Lowest order edge shape functions:
+ for (unsigned int d1 = 0; d1 < dim; ++d1)
+ {
+ for (unsigned int d2 = 0; d2 < dim; ++d2)
+ {
+ for (unsigned int d3 = 0; d3 < dim; ++d3)
+ {
+ fe_data.shape_hessians[shift_m][q][d1][d2]
+ [d3] =
+ 0.5 * edge_sigma_grads[m][d1] *
+ edge_lambda_gradgrads_3d[m][d3][d2];
+ }
+ }
+ }
+
+ // Higher order edge shape functions
+ if (degree > 0)
+ {
+ for (unsigned int i = 0; i < degree; ++i)
+ {
+ const unsigned int dof_index(i + 1 + shift_m);
+
+ for (unsigned int d1 = 0; d1 < dim; ++d1)
+ {
+ for (unsigned int d2 = 0; d2 < dim; ++d2)
+ {
+ for (unsigned int d3 = 0; d3 < dim;
+ ++d3)
+ {
+ fe_data
+ .shape_hessians[dof_index][q]
+ [d1][d2][d3] =
+ edge_sigma_grads[m][d1] *
+ edge_sigma_grads[m][d2] *
+ edge_sigma_grads[m][d3] *
+ poly[i][3] *
+ edge_lambda_values[m][q] +
+ poly[i][2] *
+ (edge_sigma_grads[m][d1] *
+ edge_sigma_grads[m][d2] *
+ edge_lambda_grads[m][q]
+ [d3] +
+ edge_sigma_grads[m][d3] *
+ edge_sigma_grads[m][d1] *
+ edge_lambda_grads[m][q]
+ [d2] +
+ edge_sigma_grads[m][d3] *
+ edge_sigma_grads[m][d2] *
+ edge_lambda_grads[m][q]
+ [d1]) +
+ poly[i][1] *
+ (edge_sigma_grads[m][d1] *
+ edge_lambda_gradgrads_3d
+ [m][d3][d2] +
+ edge_sigma_grads[m][d2] *
+ edge_lambda_gradgrads_3d
+ [m][d3][d1] +
+ edge_sigma_grads[m][d3] *
+ edge_lambda_gradgrads_3d
+ [m][d2][d1]);
+ }
+ }
+ }
+ }
+ }
+ }
}
}
}
{
const UpdateFlags flags(fe_data.update_each);
- if ((flags & (update_values | update_gradients)) != 0u)
+ if ((flags & (update_values | update_gradients | update_hessians)) != 0u)
{
const unsigned int n_q_points = quadrature.size();
}
}
// Now can generate the basis
- const unsigned int poly_length((flags & update_gradients) != 0u ? 3 :
+ const unsigned int poly_length((flags & update_hessians) != 0u ? 4 :
+ (flags & update_gradients) != 0u ? 3 :
2);
+
std::vector<std::vector<double>> polyxi(
degree, std::vector<double>(poly_length));
std::vector<std::vector<double>> polyeta(
}
}
}
+ if ((flags & update_hessians) != 0u)
+ {
+ for (unsigned int j = 0; j < degree; ++j)
+ {
+ const unsigned int shift_j(j * degree);
+ for (unsigned int i = 0; i < degree; ++i)
+ {
+ const unsigned int shift_ij(shift_j + i);
+
+ // Type 1:
+ const unsigned int dof_index1(face_type1_offset +
+ shift_ij);
+ for (unsigned int d1 = 0; d1 < dim; ++d1)
+ {
+ for (unsigned int d2 = 0; d2 < dim; ++d2)
+ {
+ for (unsigned int d3 = 0; d3 < dim; ++d3)
+ {
+ fe_data.shape_hessians[dof_index1][q]
+ [d1][d2][d3] =
+ polyxi[i][1] *
+ face_xi_grads[m][d3] *
+ (face_eta_grads[m][d1] *
+ (polyeta[j][2] *
+ face_eta_grads[m][d2] *
+ face_lambda_values[m][q] +
+ polyeta[j][1] *
+ face_lambda_grads[m][d2]) +
+ polyeta[j][1] *
+ face_eta_grads[m][d2] *
+ face_lambda_grads[m][d1]) +
+ polyxi[i][0] *
+ (polyeta[j][3] *
+ face_eta_grads[m][d1] *
+ face_eta_grads[m][d2] *
+ face_eta_grads[m][d3] *
+ face_lambda_values[m][q] +
+ polyeta[j][2] *
+ (face_eta_grads[m][d1] *
+ face_eta_grads[m][d2] *
+ face_lambda_grads[m][d3] +
+ face_eta_grads[m][d3] *
+ (face_eta_grads[m][d1] *
+ face_lambda_grads[m]
+ [d2] +
+ face_eta_grads[m][d2] *
+ face_lambda_grads
+ [m][d1]))) +
+ (polyxi[i][1] * polyeta[j][1] *
+ face_eta_grads[m][d3] +
+ polyxi[i][2] * polyeta[j][0] *
+ face_xi_grads[m][d3]) *
+ (face_xi_grads[m][d1] *
+ face_lambda_grads[m][d2] +
+ face_xi_grads[m][d2] *
+ face_lambda_grads[m][d1]) +
+ face_lambda_grads[m][d3] *
+ (polyxi[i][2] * polyeta[j][0] *
+ face_xi_grads[m][d1] *
+ face_xi_grads[m][d2] +
+ polyxi[i][1] * polyeta[j][1] *
+ (face_xi_grads[m][d1] *
+ face_eta_grads[m][d2] +
+ face_xi_grads[m][d2] *
+ face_eta_grads[m][d1])) +
+ face_lambda_values[m][q] *
+ (polyxi[i][3] * polyeta[j][0] *
+ face_xi_grads[m][d1] *
+ face_xi_grads[m][d2] *
+ face_xi_grads[m][d3] +
+ polyxi[i][1] * polyeta[j][2] *
+ face_eta_grads[m][d3] *
+ (face_xi_grads[m][d1] *
+ face_eta_grads[m][d2] +
+ face_xi_grads[m][d2] *
+ face_eta_grads[m][d1]) +
+ polyxi[i][2] * polyeta[j][1] *
+ (face_xi_grads[m][d3] *
+ face_xi_grads[m][d2] *
+ face_eta_grads[m][d1] +
+ face_xi_grads[m][d1] *
+ (face_xi_grads[m][d2] *
+ face_eta_grads[m][d3] +
+ face_xi_grads[m][d3] *
+ face_eta_grads[m][d2])));
+ }
+ }
+ }
+
+ // Type 2:
+ const unsigned int dof_index2(face_type2_offset +
+ shift_ij);
+ for (unsigned int d1 = 0; d1 < dim; ++d1)
+ {
+ for (unsigned int d2 = 0; d2 < dim; ++d2)
+ {
+ for (unsigned int d3 = 0; d3 < dim; ++d3)
+ {
+ fe_data.shape_hessians[dof_index2][q]
+ [d1][d2][d3] =
+ face_xi_grads[m][d1] *
+ (polyxi[i][1] * polyeta[j][1] *
+ (face_eta_grads[m][d2] *
+ face_lambda_grads[m][d3] +
+ face_eta_grads[m][d3] *
+ face_lambda_grads[m][d2]) +
+ polyxi[i][2] * polyeta[j][0] *
+ (face_xi_grads[m][d2] *
+ face_lambda_grads[m][d3] +
+ face_xi_grads[m][d3] *
+ face_lambda_grads[m][d2]) +
+ face_lambda_values[m][q] *
+ (face_eta_grads[m][d2] *
+ (polyxi[i][1] *
+ polyeta[j][2] *
+ face_eta_grads[m][d3] +
+ polyxi[i][2] *
+ polyeta[j][1] *
+ face_xi_grads[m][d3]) +
+ face_xi_grads[m][d2] *
+ (polyxi[i][2] *
+ polyeta[j][1] *
+ face_eta_grads[m][d3] +
+ polyxi[i][3] *
+ polyeta[j][0] *
+ face_xi_grads[m][d3]))) -
+ polyxi[i][0] *
+ face_eta_grads[m][d1] *
+ (face_eta_grads[m][d2] *
+ (polyeta[j][3] *
+ face_eta_grads[m][d3] *
+ face_lambda_values[m][q] +
+ polyeta[j][2] *
+ face_lambda_grads[m][d3]) +
+ polyeta[j][2] *
+ face_eta_grads[m][d3] *
+ face_lambda_grads[m][d2]) -
+ face_eta_grads[m][d1] *
+ (polyxi[i][1] *
+ face_xi_grads[m][d3] *
+ (polyeta[j][2] *
+ face_eta_grads[m][d2] *
+ face_lambda_values[m][q] +
+ polyeta[j][1] *
+ face_lambda_grads[m][d2]) +
+ face_xi_grads[m][d2] *
+ (polyxi[i][1] *
+ (polyeta[j][2] *
+ face_eta_grads[m][d3] *
+ face_lambda_values[m]
+ [q] +
+ polyeta[j][1] *
+ face_lambda_grads[m]
+ [d3]) +
+ polyxi[i][2] * polyeta[j][1] *
+ face_xi_grads[m][d3] *
+ face_lambda_values[m][q]));
+ }
+ }
+ }
+ }
+ // Type 3:
+ const unsigned int dof_index3_1(face_type3_offset1 +
+ j);
+ const unsigned int dof_index3_2(face_type3_offset2 +
+ j);
+ for (unsigned int d1 = 0; d1 < dim; ++d1)
+ {
+ for (unsigned int d2 = 0; d2 < dim; ++d2)
+ {
+ for (unsigned int d3 = 0; d3 < dim; ++d3)
+ {
+ fe_data.shape_hessians[dof_index3_1][q]
+ [d1][d2][d3] =
+ face_xi_grads[m][d1] *
+ (face_eta_grads[m][d2] *
+ (polyeta[j][2] *
+ face_eta_grads[m][d3] *
+ face_lambda_values[m][q] +
+ polyeta[j][1] *
+ face_lambda_grads[m][d3]) +
+ face_lambda_grads[m][d2] *
+ polyeta[j][1] *
+ face_eta_grads[m][d3]);
+
+ fe_data.shape_hessians[dof_index3_2][q]
+ [d1][d2][d3] =
+ face_eta_grads[m][d1] *
+ (face_xi_grads[m][d2] *
+ (polyxi[j][2] *
+ face_xi_grads[m][d3] *
+ face_lambda_values[m][q] +
+ polyxi[j][1] *
+ face_lambda_grads[m][d3]) +
+ face_lambda_grads[m][d2] *
+ polyxi[j][1] * face_xi_grads[m][d3]);
+ }
+ }
+ }
+ }
+ }
}
}
}
- if ((flags & update_hessians) != 0u)
- {
- Assert(false, ExcNotImplemented());
- }
}
}
}
}
}
+
if ((flags & update_gradients) != 0u)
{
// Now have all shape_grads stored on the reference cell.
}
}
}
+
+ if (flags & update_hessians)
+ {
+ // Now have all shape_grads stored on the reference cell.
+ // Must now transform to the physical cell.
+ std::vector<Tensor<3, dim>> input(n_q_points);
+ std::vector<Tensor<3, dim>> transformed_shape_hessians(n_q_points);
+ for (unsigned int dof = 0; dof < this->n_dofs_per_cell(); ++dof)
+ {
+ for (unsigned int q = 0; q < n_q_points; ++q)
+ {
+ input[q] = fe_data.shape_hessians[dof][q];
+ }
+ mapping.transform(make_array_view(input),
+ mapping_covariant_hessian,
+ mapping_internal,
+ make_array_view(transformed_shape_hessians));
+
+ const unsigned int first =
+ data.shape_function_to_row_table[dof * this->n_components() +
+ this->get_nonzero_components(dof)
+ .first_selected_component()];
+
+ for (unsigned int q = 0; q < n_q_points; ++q)
+ {
+ for (unsigned int d1 = 0; d1 < dim; ++d1)
+ {
+ for (unsigned int d2 = 0; d2 < dim; ++d2)
+ {
+ for (unsigned int d3 = 0; d3 < dim; ++d3)
+ {
+ for (unsigned int d4 = 0; d4 < dim; ++d4)
+ {
+ transformed_shape_hessians[q][d1][d3][d4] -=
+ (data.shape_values(first + d2, q) *
+ mapping_data
+ .jacobian_pushed_forward_2nd_derivatives
+ [q][d2][d1][d3][d4]) +
+ (data.shape_gradients[first + d1][q][d2] *
+ mapping_data
+ .jacobian_pushed_forward_grads[q][d2][d3]
+ [d4]) +
+ (data.shape_gradients[first + d2][q][d3] *
+ mapping_data
+ .jacobian_pushed_forward_grads[q][d2][d1]
+ [d4]) +
+ (data.shape_gradients[first + d2][q][d4] *
+ mapping_data
+ .jacobian_pushed_forward_grads[q][d2][d3]
+ [d1]);
+ }
+ }
+ }
+ }
+ }
+
+ for (unsigned int q = 0; q < n_q_points; ++q)
+ {
+ for (unsigned int d = 0; d < dim; ++d)
+ {
+ data.shape_hessians[first + d][q] =
+ transformed_shape_hessians[q][d];
+ }
+ }
+ }
+ }
}
}
}
}
+ if (flags & update_hessians)
+ {
+ // Now have all shape_grads stored on the reference cell.
+ // Must now transform to the physical cell.
+ std::vector<Tensor<3, dim>> input(n_q_points);
+ std::vector<Tensor<3, dim>> transformed_shape_hessians(n_q_points);
+ for (unsigned int dof = 0; dof < this->n_dofs_per_cell(); ++dof)
+ {
+ for (unsigned int q = 0; q < n_q_points; ++q)
+ input[q] = fe_data.shape_hessians[dof][offset + q];
+
+ mapping.transform(input,
+ mapping_covariant_hessian,
+ mapping_internal,
+ make_array_view(transformed_shape_hessians));
+
+ const unsigned int first =
+ data.shape_function_to_row_table[dof * this->n_components() +
+ this->get_nonzero_components(dof)
+ .first_selected_component()];
+
+ for (unsigned int q = 0; q < n_q_points; ++q)
+ {
+ for (unsigned int d1 = 0; d1 < dim; ++d1)
+ {
+ for (unsigned int d2 = 0; d2 < dim; ++d2)
+ {
+ for (unsigned int d3 = 0; d3 < dim; ++d3)
+ {
+ for (unsigned int d4 = 0; d4 < dim; ++d4)
+ {
+ transformed_shape_hessians[q][d1][d3][d4] -=
+ (data.shape_values(first + d2, q) *
+ mapping_data
+ .jacobian_pushed_forward_2nd_derivatives
+ [q][d2][d1][d3][d4]) +
+ (data.shape_gradients[first + d1][q][d2] *
+ mapping_data
+ .jacobian_pushed_forward_grads[q][d2][d3]
+ [d4]) +
+ (data.shape_gradients[first + d2][q][d3] *
+ mapping_data
+ .jacobian_pushed_forward_grads[q][d2][d1]
+ [d4]) +
+ (data.shape_gradients[first + d2][q][d4] *
+ mapping_data
+ .jacobian_pushed_forward_grads[q][d2][d3]
+ [d1]);
+ }
+ }
+ }
+ }
+ }
+
+ for (unsigned int q = 0; q < n_q_points; ++q)
+ {
+ for (unsigned int d = 0; d < dim; ++d)
+ {
+ data.shape_hessians[first + d][q] =
+ transformed_shape_hessians[q][d];
+ }
+ }
+ }
+ }
}
--- /dev/null
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2003 - 2020 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE.md at
+// the top level directory of deal.II.
+//
+// ---------------------------------------------------------------------
+
+
+// Observe how the values of the shape functions change as we make a
+// cell smaller and smaller.
+
+#include <deal.II/base/function.h>
+#include <deal.II/base/quadrature_lib.h>
+
+#include <deal.II/dofs/dof_handler.h>
+
+#include <deal.II/fe/fe_dgq.h>
+#include <deal.II/fe/fe_nedelec_sz.h>
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/fe/fe_raviart_thomas.h>
+#include <deal.II/fe/fe_system.h>
+#include <deal.II/fe/fe_values.h>
+#include <deal.II/fe/mapping_q1.h>
+
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/manifold_lib.h>
+
+#include <deal.II/lac/vector.h>
+
+#include <sstream>
+
+#include "../tests.h"
+
+template <int dim>
+Tensor<1, dim>
+ones()
+{
+ Tensor<1, dim> result;
+ for (unsigned int i = 0; i < dim; ++i)
+ result[i] = 1.0;
+ return result;
+}
+
+template <int dim>
+void
+test(const Triangulation<dim> &tr,
+ const FiniteElement<dim> &fe,
+ const double tolerance)
+{
+ DoFHandler<dim> dof(tr);
+ dof.distribute_dofs(fe);
+
+ std::stringstream ss;
+
+ deallog << "FE=" << fe.get_name() << std::endl;
+
+ const QGauss<dim> quadrature(4);
+ FEValues<dim> fe_values(fe,
+ quadrature,
+ update_hessians | update_quadrature_points |
+ update_JxW_values);
+
+ const QGauss<dim - 1> face_quadrature(4);
+ FEFaceValues<dim> fe_face_values(fe,
+ face_quadrature,
+ update_gradients | update_quadrature_points |
+ update_normal_vectors | update_JxW_values);
+
+ for (const auto &cell : dof.active_cell_iterators())
+ {
+ fe_values.reinit(cell);
+
+ deallog << "Cell nodes:" << std::endl;
+ for (const unsigned int i : GeometryInfo<dim>::vertex_indices())
+ deallog << i << ": ( " << cell->vertex(i) << " )" << std::endl;
+
+ bool cell_ok = true;
+
+ for (unsigned int c = 0; c < fe.n_components(); ++c)
+ {
+ FEValuesExtractors::Scalar single_component(c);
+
+ for (unsigned int i = 0; i < fe_values.dofs_per_cell; ++i)
+ {
+ ss << "component=" << c << ", dof=" << i << std::endl;
+
+ Tensor<2, dim> bulk_integral;
+ for (const auto q : fe_values.quadrature_point_indices())
+ {
+ bulk_integral += fe_values[single_component].hessian(i, q) *
+ fe_values.JxW(q);
+ }
+
+ Tensor<2, dim> boundary_integral;
+ for (const unsigned int face : GeometryInfo<dim>::face_indices())
+ {
+ fe_face_values.reinit(cell, face);
+ for (const auto q : fe_face_values.quadrature_point_indices())
+ {
+ Tensor<1, dim> gradient =
+ fe_face_values[single_component].gradient(i, q);
+ Tensor<2, dim> gradient_normal_outer_prod =
+ outer_product(gradient,
+ fe_face_values.normal_vector(q));
+ boundary_integral +=
+ gradient_normal_outer_prod * fe_face_values.JxW(q);
+ }
+ }
+
+ if ((bulk_integral - boundary_integral).norm_square() >
+ tolerance * (bulk_integral.norm() + boundary_integral.norm()))
+ {
+ deallog << "Failed:" << std::endl;
+ deallog << ss.str() << std::endl;
+ deallog << " bulk integral=" << bulk_integral << std::endl;
+ deallog << "boundary integral=" << boundary_integral
+ << std::endl;
+ deallog
+ << "Error! difference between bulk and surface integrals is greater than "
+ << tolerance << "!\n\n"
+ << std::endl;
+ cell_ok = false;
+ }
+
+ ss.str("");
+ }
+ }
+
+ deallog << (cell_ok ? "OK: cell bulk and boundary integrals match...\n" :
+ "Failed divergence test...\n")
+ << std::endl;
+ }
+}
+
+
+
+template <int dim>
+void
+test_hyper_ball(const double tolerance)
+{
+ Triangulation<dim> tr;
+ GridGenerator::hyper_ball(tr);
+
+ static const SphericalManifold<dim> boundary;
+ tr.set_manifold(0, boundary);
+
+ tr.refine_global(1);
+
+ FE_NedelecSZ<dim> fe(1);
+ test(tr, fe, tolerance);
+}
+
+
+int
+main()
+{
+ initlog();
+ deallog << std::setprecision(8);
+
+ test_hyper_ball<2>(1e-6);
+ test_hyper_ball<3>(1e-6);
+
+ deallog << "done..." << std::endl;
+}
--- /dev/null
+
+DEAL::FE=FE_NedelecSZ<2>(1)
+DEAL::Cell nodes:
+DEAL::0: ( -0.70710678 -0.70710678 )
+DEAL::1: ( -1.1102230e-16 -1.0000000 )
+DEAL::2: ( -0.50000000 -0.50000000 )
+DEAL::3: ( -5.5511151e-17 -0.64644661 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -1.1102230e-16 -1.0000000 )
+DEAL::1: ( 0.70710678 -0.70710678 )
+DEAL::2: ( -5.5511151e-17 -0.64644661 )
+DEAL::3: ( 0.50000000 -0.50000000 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.50000000 -0.50000000 )
+DEAL::1: ( -5.5511151e-17 -0.64644661 )
+DEAL::2: ( -0.29289322 -0.29289322 )
+DEAL::3: ( 0.0000000 -0.29289322 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -5.5511151e-17 -0.64644661 )
+DEAL::1: ( 0.50000000 -0.50000000 )
+DEAL::2: ( 0.0000000 -0.29289322 )
+DEAL::3: ( 0.29289322 -0.29289322 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.70710678 -0.70710678 )
+DEAL::1: ( -0.50000000 -0.50000000 )
+DEAL::2: ( -1.0000000 -1.1102230e-16 )
+DEAL::3: ( -0.64644661 -5.5511151e-17 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.50000000 -0.50000000 )
+DEAL::1: ( -0.29289322 -0.29289322 )
+DEAL::2: ( -0.64644661 -5.5511151e-17 )
+DEAL::3: ( -0.29289322 0.0000000 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -1.0000000 -1.1102230e-16 )
+DEAL::1: ( -0.64644661 -5.5511151e-17 )
+DEAL::2: ( -0.70710678 0.70710678 )
+DEAL::3: ( -0.50000000 0.50000000 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.64644661 -5.5511151e-17 )
+DEAL::1: ( -0.29289322 0.0000000 )
+DEAL::2: ( -0.50000000 0.50000000 )
+DEAL::3: ( -0.29289322 0.29289322 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.29289322 -0.29289322 )
+DEAL::1: ( 0.0000000 -0.29289322 )
+DEAL::2: ( -0.29289322 0.0000000 )
+DEAL::3: ( 0.0000000 0.0000000 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.0000000 -0.29289322 )
+DEAL::1: ( 0.29289322 -0.29289322 )
+DEAL::2: ( 0.0000000 0.0000000 )
+DEAL::3: ( 0.29289322 0.0000000 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.29289322 0.0000000 )
+DEAL::1: ( 0.0000000 0.0000000 )
+DEAL::2: ( -0.29289322 0.29289322 )
+DEAL::3: ( 0.0000000 0.29289322 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.0000000 0.0000000 )
+DEAL::1: ( 0.29289322 0.0000000 )
+DEAL::2: ( 0.0000000 0.29289322 )
+DEAL::3: ( 0.29289322 0.29289322 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.70710678 -0.70710678 )
+DEAL::1: ( 1.0000000 -1.1102230e-16 )
+DEAL::2: ( 0.50000000 -0.50000000 )
+DEAL::3: ( 0.64644661 -5.5511151e-17 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 1.0000000 -1.1102230e-16 )
+DEAL::1: ( 0.70710678 0.70710678 )
+DEAL::2: ( 0.64644661 -5.5511151e-17 )
+DEAL::3: ( 0.50000000 0.50000000 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.50000000 -0.50000000 )
+DEAL::1: ( 0.64644661 -5.5511151e-17 )
+DEAL::2: ( 0.29289322 -0.29289322 )
+DEAL::3: ( 0.29289322 0.0000000 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.64644661 -5.5511151e-17 )
+DEAL::1: ( 0.50000000 0.50000000 )
+DEAL::2: ( 0.29289322 0.0000000 )
+DEAL::3: ( 0.29289322 0.29289322 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.70710678 0.70710678 )
+DEAL::1: ( -0.50000000 0.50000000 )
+DEAL::2: ( -1.1102230e-16 1.0000000 )
+DEAL::3: ( -5.5511151e-17 0.64644661 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.50000000 0.50000000 )
+DEAL::1: ( -0.29289322 0.29289322 )
+DEAL::2: ( -5.5511151e-17 0.64644661 )
+DEAL::3: ( 0.0000000 0.29289322 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -1.1102230e-16 1.0000000 )
+DEAL::1: ( -5.5511151e-17 0.64644661 )
+DEAL::2: ( 0.70710678 0.70710678 )
+DEAL::3: ( 0.50000000 0.50000000 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -5.5511151e-17 0.64644661 )
+DEAL::1: ( 0.0000000 0.29289322 )
+DEAL::2: ( 0.50000000 0.50000000 )
+DEAL::3: ( 0.29289322 0.29289322 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::FE=FE_NedelecSZ<3>(1)
+DEAL::Cell nodes:
+DEAL::0: ( -0.21132487 -0.21132487 -0.21132487 )
+DEAL::1: ( 0.0000000 -0.21132487 -0.21132487 )
+DEAL::2: ( -0.21132487 0.0000000 -0.21132487 )
+DEAL::3: ( 0.0000000 0.0000000 -0.21132487 )
+DEAL::4: ( -0.21132487 -0.21132487 0.0000000 )
+DEAL::5: ( 0.0000000 -0.21132487 0.0000000 )
+DEAL::6: ( -0.21132487 0.0000000 0.0000000 )
+DEAL::7: ( 0.0000000 0.0000000 -1.3877788e-17 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.0000000 -0.21132487 -0.21132487 )
+DEAL::1: ( 0.21132487 -0.21132487 -0.21132487 )
+DEAL::2: ( 0.0000000 0.0000000 -0.21132487 )
+DEAL::3: ( 0.21132487 0.0000000 -0.21132487 )
+DEAL::4: ( 0.0000000 -0.21132487 0.0000000 )
+DEAL::5: ( 0.21132487 -0.21132487 0.0000000 )
+DEAL::6: ( 0.0000000 0.0000000 -1.3877788e-17 )
+DEAL::7: ( 0.21132487 0.0000000 0.0000000 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.21132487 0.0000000 -0.21132487 )
+DEAL::1: ( 0.0000000 0.0000000 -0.21132487 )
+DEAL::2: ( -0.21132487 0.21132487 -0.21132487 )
+DEAL::3: ( 0.0000000 0.21132487 -0.21132487 )
+DEAL::4: ( -0.21132487 0.0000000 0.0000000 )
+DEAL::5: ( 0.0000000 0.0000000 -1.3877788e-17 )
+DEAL::6: ( -0.21132487 0.21132487 0.0000000 )
+DEAL::7: ( 0.0000000 0.21132487 0.0000000 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.0000000 0.0000000 -0.21132487 )
+DEAL::1: ( 0.21132487 0.0000000 -0.21132487 )
+DEAL::2: ( 0.0000000 0.21132487 -0.21132487 )
+DEAL::3: ( 0.21132487 0.21132487 -0.21132487 )
+DEAL::4: ( 0.0000000 0.0000000 -1.3877788e-17 )
+DEAL::5: ( 0.21132487 0.0000000 0.0000000 )
+DEAL::6: ( 0.0000000 0.21132487 0.0000000 )
+DEAL::7: ( 0.21132487 0.21132487 0.0000000 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.21132487 -0.21132487 0.0000000 )
+DEAL::1: ( 0.0000000 -0.21132487 0.0000000 )
+DEAL::2: ( -0.21132487 0.0000000 0.0000000 )
+DEAL::3: ( 0.0000000 0.0000000 -1.3877788e-17 )
+DEAL::4: ( -0.21132487 -0.21132487 0.21132487 )
+DEAL::5: ( 0.0000000 -0.21132487 0.21132487 )
+DEAL::6: ( -0.21132487 0.0000000 0.21132487 )
+DEAL::7: ( 0.0000000 0.0000000 0.21132487 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.0000000 -0.21132487 0.0000000 )
+DEAL::1: ( 0.21132487 -0.21132487 0.0000000 )
+DEAL::2: ( 0.0000000 0.0000000 -1.3877788e-17 )
+DEAL::3: ( 0.21132487 0.0000000 0.0000000 )
+DEAL::4: ( 0.0000000 -0.21132487 0.21132487 )
+DEAL::5: ( 0.21132487 -0.21132487 0.21132487 )
+DEAL::6: ( 0.0000000 0.0000000 0.21132487 )
+DEAL::7: ( 0.21132487 0.0000000 0.21132487 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.21132487 0.0000000 0.0000000 )
+DEAL::1: ( 0.0000000 0.0000000 -1.3877788e-17 )
+DEAL::2: ( -0.21132487 0.21132487 0.0000000 )
+DEAL::3: ( 0.0000000 0.21132487 0.0000000 )
+DEAL::4: ( -0.21132487 0.0000000 0.21132487 )
+DEAL::5: ( 0.0000000 0.0000000 0.21132487 )
+DEAL::6: ( -0.21132487 0.21132487 0.21132487 )
+DEAL::7: ( 0.0000000 0.21132487 0.21132487 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.0000000 0.0000000 -1.3877788e-17 )
+DEAL::1: ( 0.21132487 0.0000000 0.0000000 )
+DEAL::2: ( 0.0000000 0.21132487 0.0000000 )
+DEAL::3: ( 0.21132487 0.21132487 0.0000000 )
+DEAL::4: ( 0.0000000 0.0000000 0.21132487 )
+DEAL::5: ( 0.21132487 0.0000000 0.21132487 )
+DEAL::6: ( 0.0000000 0.21132487 0.21132487 )
+DEAL::7: ( 0.21132487 0.21132487 0.21132487 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.57735027 -0.57735027 -0.57735027 )
+DEAL::1: ( 0.0000000 -0.70710678 -0.70710678 )
+DEAL::2: ( -0.70710678 0.0000000 -0.70710678 )
+DEAL::3: ( 0.0000000 0.0000000 -1.0000000 )
+DEAL::4: ( -0.39433757 -0.39433757 -0.39433757 )
+DEAL::5: ( 0.0000000 -0.45921582 -0.45921582 )
+DEAL::6: ( -0.45921582 0.0000000 -0.45921582 )
+DEAL::7: ( 0.0000000 0.0000000 -0.60566243 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.0000000 -0.70710678 -0.70710678 )
+DEAL::1: ( 0.57735027 -0.57735027 -0.57735027 )
+DEAL::2: ( 0.0000000 0.0000000 -1.0000000 )
+DEAL::3: ( 0.70710678 0.0000000 -0.70710678 )
+DEAL::4: ( 0.0000000 -0.45921582 -0.45921582 )
+DEAL::5: ( 0.39433757 -0.39433757 -0.39433757 )
+DEAL::6: ( 0.0000000 0.0000000 -0.60566243 )
+DEAL::7: ( 0.45921582 0.0000000 -0.45921582 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.70710678 0.0000000 -0.70710678 )
+DEAL::1: ( 0.0000000 0.0000000 -1.0000000 )
+DEAL::2: ( -0.57735027 0.57735027 -0.57735027 )
+DEAL::3: ( 0.0000000 0.70710678 -0.70710678 )
+DEAL::4: ( -0.45921582 0.0000000 -0.45921582 )
+DEAL::5: ( 0.0000000 0.0000000 -0.60566243 )
+DEAL::6: ( -0.39433757 0.39433757 -0.39433757 )
+DEAL::7: ( 0.0000000 0.45921582 -0.45921582 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.0000000 0.0000000 -1.0000000 )
+DEAL::1: ( 0.70710678 0.0000000 -0.70710678 )
+DEAL::2: ( 0.0000000 0.70710678 -0.70710678 )
+DEAL::3: ( 0.57735027 0.57735027 -0.57735027 )
+DEAL::4: ( 0.0000000 0.0000000 -0.60566243 )
+DEAL::5: ( 0.45921582 0.0000000 -0.45921582 )
+DEAL::6: ( 0.0000000 0.45921582 -0.45921582 )
+DEAL::7: ( 0.39433757 0.39433757 -0.39433757 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.39433757 -0.39433757 -0.39433757 )
+DEAL::1: ( 0.0000000 -0.45921582 -0.45921582 )
+DEAL::2: ( -0.45921582 0.0000000 -0.45921582 )
+DEAL::3: ( 0.0000000 0.0000000 -0.60566243 )
+DEAL::4: ( -0.21132487 -0.21132487 -0.21132487 )
+DEAL::5: ( 0.0000000 -0.21132487 -0.21132487 )
+DEAL::6: ( -0.21132487 0.0000000 -0.21132487 )
+DEAL::7: ( 0.0000000 0.0000000 -0.21132487 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.0000000 -0.45921582 -0.45921582 )
+DEAL::1: ( 0.39433757 -0.39433757 -0.39433757 )
+DEAL::2: ( 0.0000000 0.0000000 -0.60566243 )
+DEAL::3: ( 0.45921582 0.0000000 -0.45921582 )
+DEAL::4: ( 0.0000000 -0.21132487 -0.21132487 )
+DEAL::5: ( 0.21132487 -0.21132487 -0.21132487 )
+DEAL::6: ( 0.0000000 0.0000000 -0.21132487 )
+DEAL::7: ( 0.21132487 0.0000000 -0.21132487 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.45921582 0.0000000 -0.45921582 )
+DEAL::1: ( 0.0000000 0.0000000 -0.60566243 )
+DEAL::2: ( -0.39433757 0.39433757 -0.39433757 )
+DEAL::3: ( 0.0000000 0.45921582 -0.45921582 )
+DEAL::4: ( -0.21132487 0.0000000 -0.21132487 )
+DEAL::5: ( 0.0000000 0.0000000 -0.21132487 )
+DEAL::6: ( -0.21132487 0.21132487 -0.21132487 )
+DEAL::7: ( 0.0000000 0.21132487 -0.21132487 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.0000000 0.0000000 -0.60566243 )
+DEAL::1: ( 0.45921582 0.0000000 -0.45921582 )
+DEAL::2: ( 0.0000000 0.45921582 -0.45921582 )
+DEAL::3: ( 0.39433757 0.39433757 -0.39433757 )
+DEAL::4: ( 0.0000000 0.0000000 -0.21132487 )
+DEAL::5: ( 0.21132487 0.0000000 -0.21132487 )
+DEAL::6: ( 0.0000000 0.21132487 -0.21132487 )
+DEAL::7: ( 0.21132487 0.21132487 -0.21132487 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.57735027 -0.57735027 -0.57735027 )
+DEAL::1: ( 0.70710678 0.0000000 -0.70710678 )
+DEAL::2: ( 0.39433757 -0.39433757 -0.39433757 )
+DEAL::3: ( 0.45921582 0.0000000 -0.45921582 )
+DEAL::4: ( 0.70710678 -0.70710678 0.0000000 )
+DEAL::5: ( 1.0000000 0.0000000 0.0000000 )
+DEAL::6: ( 0.45921582 -0.45921582 0.0000000 )
+DEAL::7: ( 0.60566243 0.0000000 -2.7755576e-17 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.70710678 0.0000000 -0.70710678 )
+DEAL::1: ( 0.57735027 0.57735027 -0.57735027 )
+DEAL::2: ( 0.45921582 0.0000000 -0.45921582 )
+DEAL::3: ( 0.39433757 0.39433757 -0.39433757 )
+DEAL::4: ( 1.0000000 0.0000000 0.0000000 )
+DEAL::5: ( 0.70710678 0.70710678 0.0000000 )
+DEAL::6: ( 0.60566243 0.0000000 -2.7755576e-17 )
+DEAL::7: ( 0.45921582 0.45921582 0.0000000 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.39433757 -0.39433757 -0.39433757 )
+DEAL::1: ( 0.45921582 0.0000000 -0.45921582 )
+DEAL::2: ( 0.21132487 -0.21132487 -0.21132487 )
+DEAL::3: ( 0.21132487 0.0000000 -0.21132487 )
+DEAL::4: ( 0.45921582 -0.45921582 0.0000000 )
+DEAL::5: ( 0.60566243 0.0000000 -2.7755576e-17 )
+DEAL::6: ( 0.21132487 -0.21132487 0.0000000 )
+DEAL::7: ( 0.21132487 0.0000000 0.0000000 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.45921582 0.0000000 -0.45921582 )
+DEAL::1: ( 0.39433757 0.39433757 -0.39433757 )
+DEAL::2: ( 0.21132487 0.0000000 -0.21132487 )
+DEAL::3: ( 0.21132487 0.21132487 -0.21132487 )
+DEAL::4: ( 0.60566243 0.0000000 -2.7755576e-17 )
+DEAL::5: ( 0.45921582 0.45921582 0.0000000 )
+DEAL::6: ( 0.21132487 0.0000000 0.0000000 )
+DEAL::7: ( 0.21132487 0.21132487 0.0000000 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.70710678 -0.70710678 0.0000000 )
+DEAL::1: ( 1.0000000 0.0000000 0.0000000 )
+DEAL::2: ( 0.45921582 -0.45921582 0.0000000 )
+DEAL::3: ( 0.60566243 0.0000000 -2.7755576e-17 )
+DEAL::4: ( 0.57735027 -0.57735027 0.57735027 )
+DEAL::5: ( 0.70710678 0.0000000 0.70710678 )
+DEAL::6: ( 0.39433757 -0.39433757 0.39433757 )
+DEAL::7: ( 0.45921582 0.0000000 0.45921582 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 1.0000000 0.0000000 0.0000000 )
+DEAL::1: ( 0.70710678 0.70710678 0.0000000 )
+DEAL::2: ( 0.60566243 0.0000000 -2.7755576e-17 )
+DEAL::3: ( 0.45921582 0.45921582 0.0000000 )
+DEAL::4: ( 0.70710678 0.0000000 0.70710678 )
+DEAL::5: ( 0.57735027 0.57735027 0.57735027 )
+DEAL::6: ( 0.45921582 0.0000000 0.45921582 )
+DEAL::7: ( 0.39433757 0.39433757 0.39433757 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.45921582 -0.45921582 0.0000000 )
+DEAL::1: ( 0.60566243 0.0000000 -2.7755576e-17 )
+DEAL::2: ( 0.21132487 -0.21132487 0.0000000 )
+DEAL::3: ( 0.21132487 0.0000000 0.0000000 )
+DEAL::4: ( 0.39433757 -0.39433757 0.39433757 )
+DEAL::5: ( 0.45921582 0.0000000 0.45921582 )
+DEAL::6: ( 0.21132487 -0.21132487 0.21132487 )
+DEAL::7: ( 0.21132487 0.0000000 0.21132487 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.60566243 0.0000000 -2.7755576e-17 )
+DEAL::1: ( 0.45921582 0.45921582 0.0000000 )
+DEAL::2: ( 0.21132487 0.0000000 0.0000000 )
+DEAL::3: ( 0.21132487 0.21132487 0.0000000 )
+DEAL::4: ( 0.45921582 0.0000000 0.45921582 )
+DEAL::5: ( 0.39433757 0.39433757 0.39433757 )
+DEAL::6: ( 0.21132487 0.0000000 0.21132487 )
+DEAL::7: ( 0.21132487 0.21132487 0.21132487 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.57735027 -0.57735027 0.57735027 )
+DEAL::1: ( 0.0000000 -0.70710678 0.70710678 )
+DEAL::2: ( -0.39433757 -0.39433757 0.39433757 )
+DEAL::3: ( 0.0000000 -0.45921582 0.45921582 )
+DEAL::4: ( -0.70710678 0.0000000 0.70710678 )
+DEAL::5: ( 0.0000000 0.0000000 1.0000000 )
+DEAL::6: ( -0.45921582 0.0000000 0.45921582 )
+DEAL::7: ( -2.7755576e-17 -2.7755576e-17 0.60566243 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.0000000 -0.70710678 0.70710678 )
+DEAL::1: ( 0.57735027 -0.57735027 0.57735027 )
+DEAL::2: ( 0.0000000 -0.45921582 0.45921582 )
+DEAL::3: ( 0.39433757 -0.39433757 0.39433757 )
+DEAL::4: ( 0.0000000 0.0000000 1.0000000 )
+DEAL::5: ( 0.70710678 0.0000000 0.70710678 )
+DEAL::6: ( -2.7755576e-17 -2.7755576e-17 0.60566243 )
+DEAL::7: ( 0.45921582 0.0000000 0.45921582 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.39433757 -0.39433757 0.39433757 )
+DEAL::1: ( 0.0000000 -0.45921582 0.45921582 )
+DEAL::2: ( -0.21132487 -0.21132487 0.21132487 )
+DEAL::3: ( 0.0000000 -0.21132487 0.21132487 )
+DEAL::4: ( -0.45921582 0.0000000 0.45921582 )
+DEAL::5: ( -2.7755576e-17 -2.7755576e-17 0.60566243 )
+DEAL::6: ( -0.21132487 0.0000000 0.21132487 )
+DEAL::7: ( 0.0000000 0.0000000 0.21132487 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.0000000 -0.45921582 0.45921582 )
+DEAL::1: ( 0.39433757 -0.39433757 0.39433757 )
+DEAL::2: ( 0.0000000 -0.21132487 0.21132487 )
+DEAL::3: ( 0.21132487 -0.21132487 0.21132487 )
+DEAL::4: ( -2.7755576e-17 -2.7755576e-17 0.60566243 )
+DEAL::5: ( 0.45921582 0.0000000 0.45921582 )
+DEAL::6: ( 0.0000000 0.0000000 0.21132487 )
+DEAL::7: ( 0.21132487 0.0000000 0.21132487 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.70710678 0.0000000 0.70710678 )
+DEAL::1: ( 0.0000000 0.0000000 1.0000000 )
+DEAL::2: ( -0.45921582 0.0000000 0.45921582 )
+DEAL::3: ( -2.7755576e-17 -2.7755576e-17 0.60566243 )
+DEAL::4: ( -0.57735027 0.57735027 0.57735027 )
+DEAL::5: ( 0.0000000 0.70710678 0.70710678 )
+DEAL::6: ( -0.39433757 0.39433757 0.39433757 )
+DEAL::7: ( 0.0000000 0.45921582 0.45921582 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.0000000 0.0000000 1.0000000 )
+DEAL::1: ( 0.70710678 0.0000000 0.70710678 )
+DEAL::2: ( -2.7755576e-17 -2.7755576e-17 0.60566243 )
+DEAL::3: ( 0.45921582 0.0000000 0.45921582 )
+DEAL::4: ( 0.0000000 0.70710678 0.70710678 )
+DEAL::5: ( 0.57735027 0.57735027 0.57735027 )
+DEAL::6: ( 0.0000000 0.45921582 0.45921582 )
+DEAL::7: ( 0.39433757 0.39433757 0.39433757 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.45921582 0.0000000 0.45921582 )
+DEAL::1: ( -2.7755576e-17 -2.7755576e-17 0.60566243 )
+DEAL::2: ( -0.21132487 0.0000000 0.21132487 )
+DEAL::3: ( 0.0000000 0.0000000 0.21132487 )
+DEAL::4: ( -0.39433757 0.39433757 0.39433757 )
+DEAL::5: ( 0.0000000 0.45921582 0.45921582 )
+DEAL::6: ( -0.21132487 0.21132487 0.21132487 )
+DEAL::7: ( 0.0000000 0.21132487 0.21132487 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -2.7755576e-17 -2.7755576e-17 0.60566243 )
+DEAL::1: ( 0.45921582 0.0000000 0.45921582 )
+DEAL::2: ( 0.0000000 0.0000000 0.21132487 )
+DEAL::3: ( 0.21132487 0.0000000 0.21132487 )
+DEAL::4: ( 0.0000000 0.45921582 0.45921582 )
+DEAL::5: ( 0.39433757 0.39433757 0.39433757 )
+DEAL::6: ( 0.0000000 0.21132487 0.21132487 )
+DEAL::7: ( 0.21132487 0.21132487 0.21132487 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.57735027 -0.57735027 -0.57735027 )
+DEAL::1: ( -0.39433757 -0.39433757 -0.39433757 )
+DEAL::2: ( -0.70710678 0.0000000 -0.70710678 )
+DEAL::3: ( -0.45921582 0.0000000 -0.45921582 )
+DEAL::4: ( -0.70710678 -0.70710678 0.0000000 )
+DEAL::5: ( -0.45921582 -0.45921582 0.0000000 )
+DEAL::6: ( -1.0000000 0.0000000 0.0000000 )
+DEAL::7: ( -0.60566243 0.0000000 1.1102230e-16 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.39433757 -0.39433757 -0.39433757 )
+DEAL::1: ( -0.21132487 -0.21132487 -0.21132487 )
+DEAL::2: ( -0.45921582 0.0000000 -0.45921582 )
+DEAL::3: ( -0.21132487 0.0000000 -0.21132487 )
+DEAL::4: ( -0.45921582 -0.45921582 0.0000000 )
+DEAL::5: ( -0.21132487 -0.21132487 0.0000000 )
+DEAL::6: ( -0.60566243 0.0000000 1.1102230e-16 )
+DEAL::7: ( -0.21132487 0.0000000 0.0000000 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.70710678 0.0000000 -0.70710678 )
+DEAL::1: ( -0.45921582 0.0000000 -0.45921582 )
+DEAL::2: ( -0.57735027 0.57735027 -0.57735027 )
+DEAL::3: ( -0.39433757 0.39433757 -0.39433757 )
+DEAL::4: ( -1.0000000 0.0000000 0.0000000 )
+DEAL::5: ( -0.60566243 0.0000000 1.1102230e-16 )
+DEAL::6: ( -0.70710678 0.70710678 0.0000000 )
+DEAL::7: ( -0.45921582 0.45921582 0.0000000 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.45921582 0.0000000 -0.45921582 )
+DEAL::1: ( -0.21132487 0.0000000 -0.21132487 )
+DEAL::2: ( -0.39433757 0.39433757 -0.39433757 )
+DEAL::3: ( -0.21132487 0.21132487 -0.21132487 )
+DEAL::4: ( -0.60566243 0.0000000 1.1102230e-16 )
+DEAL::5: ( -0.21132487 0.0000000 0.0000000 )
+DEAL::6: ( -0.45921582 0.45921582 0.0000000 )
+DEAL::7: ( -0.21132487 0.21132487 0.0000000 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.70710678 -0.70710678 0.0000000 )
+DEAL::1: ( -0.45921582 -0.45921582 0.0000000 )
+DEAL::2: ( -1.0000000 0.0000000 0.0000000 )
+DEAL::3: ( -0.60566243 0.0000000 1.1102230e-16 )
+DEAL::4: ( -0.57735027 -0.57735027 0.57735027 )
+DEAL::5: ( -0.39433757 -0.39433757 0.39433757 )
+DEAL::6: ( -0.70710678 0.0000000 0.70710678 )
+DEAL::7: ( -0.45921582 0.0000000 0.45921582 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.45921582 -0.45921582 0.0000000 )
+DEAL::1: ( -0.21132487 -0.21132487 0.0000000 )
+DEAL::2: ( -0.60566243 0.0000000 1.1102230e-16 )
+DEAL::3: ( -0.21132487 0.0000000 0.0000000 )
+DEAL::4: ( -0.39433757 -0.39433757 0.39433757 )
+DEAL::5: ( -0.21132487 -0.21132487 0.21132487 )
+DEAL::6: ( -0.45921582 0.0000000 0.45921582 )
+DEAL::7: ( -0.21132487 0.0000000 0.21132487 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -1.0000000 0.0000000 0.0000000 )
+DEAL::1: ( -0.60566243 0.0000000 1.1102230e-16 )
+DEAL::2: ( -0.70710678 0.70710678 0.0000000 )
+DEAL::3: ( -0.45921582 0.45921582 0.0000000 )
+DEAL::4: ( -0.70710678 0.0000000 0.70710678 )
+DEAL::5: ( -0.45921582 0.0000000 0.45921582 )
+DEAL::6: ( -0.57735027 0.57735027 0.57735027 )
+DEAL::7: ( -0.39433757 0.39433757 0.39433757 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.60566243 0.0000000 1.1102230e-16 )
+DEAL::1: ( -0.21132487 0.0000000 0.0000000 )
+DEAL::2: ( -0.45921582 0.45921582 0.0000000 )
+DEAL::3: ( -0.21132487 0.21132487 0.0000000 )
+DEAL::4: ( -0.45921582 0.0000000 0.45921582 )
+DEAL::5: ( -0.21132487 0.0000000 0.21132487 )
+DEAL::6: ( -0.39433757 0.39433757 0.39433757 )
+DEAL::7: ( -0.21132487 0.21132487 0.21132487 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.57735027 -0.57735027 -0.57735027 )
+DEAL::1: ( 0.0000000 -0.70710678 -0.70710678 )
+DEAL::2: ( -0.39433757 -0.39433757 -0.39433757 )
+DEAL::3: ( 0.0000000 -0.45921582 -0.45921582 )
+DEAL::4: ( -0.70710678 -0.70710678 0.0000000 )
+DEAL::5: ( 0.0000000 -1.0000000 0.0000000 )
+DEAL::6: ( -0.45921582 -0.45921582 0.0000000 )
+DEAL::7: ( 2.7755576e-17 -0.60566243 -5.5511151e-17 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.0000000 -0.70710678 -0.70710678 )
+DEAL::1: ( 0.57735027 -0.57735027 -0.57735027 )
+DEAL::2: ( 0.0000000 -0.45921582 -0.45921582 )
+DEAL::3: ( 0.39433757 -0.39433757 -0.39433757 )
+DEAL::4: ( 0.0000000 -1.0000000 0.0000000 )
+DEAL::5: ( 0.70710678 -0.70710678 0.0000000 )
+DEAL::6: ( 2.7755576e-17 -0.60566243 -5.5511151e-17 )
+DEAL::7: ( 0.45921582 -0.45921582 0.0000000 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.39433757 -0.39433757 -0.39433757 )
+DEAL::1: ( 0.0000000 -0.45921582 -0.45921582 )
+DEAL::2: ( -0.21132487 -0.21132487 -0.21132487 )
+DEAL::3: ( 0.0000000 -0.21132487 -0.21132487 )
+DEAL::4: ( -0.45921582 -0.45921582 0.0000000 )
+DEAL::5: ( 2.7755576e-17 -0.60566243 -5.5511151e-17 )
+DEAL::6: ( -0.21132487 -0.21132487 0.0000000 )
+DEAL::7: ( 0.0000000 -0.21132487 0.0000000 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.0000000 -0.45921582 -0.45921582 )
+DEAL::1: ( 0.39433757 -0.39433757 -0.39433757 )
+DEAL::2: ( 0.0000000 -0.21132487 -0.21132487 )
+DEAL::3: ( 0.21132487 -0.21132487 -0.21132487 )
+DEAL::4: ( 2.7755576e-17 -0.60566243 -5.5511151e-17 )
+DEAL::5: ( 0.45921582 -0.45921582 0.0000000 )
+DEAL::6: ( 0.0000000 -0.21132487 0.0000000 )
+DEAL::7: ( 0.21132487 -0.21132487 0.0000000 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.70710678 -0.70710678 0.0000000 )
+DEAL::1: ( 0.0000000 -1.0000000 0.0000000 )
+DEAL::2: ( -0.45921582 -0.45921582 0.0000000 )
+DEAL::3: ( 2.7755576e-17 -0.60566243 -5.5511151e-17 )
+DEAL::4: ( -0.57735027 -0.57735027 0.57735027 )
+DEAL::5: ( 0.0000000 -0.70710678 0.70710678 )
+DEAL::6: ( -0.39433757 -0.39433757 0.39433757 )
+DEAL::7: ( 0.0000000 -0.45921582 0.45921582 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.0000000 -1.0000000 0.0000000 )
+DEAL::1: ( 0.70710678 -0.70710678 0.0000000 )
+DEAL::2: ( 2.7755576e-17 -0.60566243 -5.5511151e-17 )
+DEAL::3: ( 0.45921582 -0.45921582 0.0000000 )
+DEAL::4: ( 0.0000000 -0.70710678 0.70710678 )
+DEAL::5: ( 0.57735027 -0.57735027 0.57735027 )
+DEAL::6: ( 0.0000000 -0.45921582 0.45921582 )
+DEAL::7: ( 0.39433757 -0.39433757 0.39433757 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.45921582 -0.45921582 0.0000000 )
+DEAL::1: ( 2.7755576e-17 -0.60566243 -5.5511151e-17 )
+DEAL::2: ( -0.21132487 -0.21132487 0.0000000 )
+DEAL::3: ( 0.0000000 -0.21132487 0.0000000 )
+DEAL::4: ( -0.39433757 -0.39433757 0.39433757 )
+DEAL::5: ( 0.0000000 -0.45921582 0.45921582 )
+DEAL::6: ( -0.21132487 -0.21132487 0.21132487 )
+DEAL::7: ( 0.0000000 -0.21132487 0.21132487 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 2.7755576e-17 -0.60566243 -5.5511151e-17 )
+DEAL::1: ( 0.45921582 -0.45921582 0.0000000 )
+DEAL::2: ( 0.0000000 -0.21132487 0.0000000 )
+DEAL::3: ( 0.21132487 -0.21132487 0.0000000 )
+DEAL::4: ( 0.0000000 -0.45921582 0.45921582 )
+DEAL::5: ( 0.39433757 -0.39433757 0.39433757 )
+DEAL::6: ( 0.0000000 -0.21132487 0.21132487 )
+DEAL::7: ( 0.21132487 -0.21132487 0.21132487 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.57735027 0.57735027 -0.57735027 )
+DEAL::1: ( -0.39433757 0.39433757 -0.39433757 )
+DEAL::2: ( 0.0000000 0.70710678 -0.70710678 )
+DEAL::3: ( 0.0000000 0.45921582 -0.45921582 )
+DEAL::4: ( -0.70710678 0.70710678 0.0000000 )
+DEAL::5: ( -0.45921582 0.45921582 0.0000000 )
+DEAL::6: ( 0.0000000 1.0000000 0.0000000 )
+DEAL::7: ( 2.7755576e-17 0.60566243 5.5511151e-17 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.39433757 0.39433757 -0.39433757 )
+DEAL::1: ( -0.21132487 0.21132487 -0.21132487 )
+DEAL::2: ( 0.0000000 0.45921582 -0.45921582 )
+DEAL::3: ( 0.0000000 0.21132487 -0.21132487 )
+DEAL::4: ( -0.45921582 0.45921582 0.0000000 )
+DEAL::5: ( -0.21132487 0.21132487 0.0000000 )
+DEAL::6: ( 2.7755576e-17 0.60566243 5.5511151e-17 )
+DEAL::7: ( 0.0000000 0.21132487 0.0000000 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.0000000 0.70710678 -0.70710678 )
+DEAL::1: ( 0.0000000 0.45921582 -0.45921582 )
+DEAL::2: ( 0.57735027 0.57735027 -0.57735027 )
+DEAL::3: ( 0.39433757 0.39433757 -0.39433757 )
+DEAL::4: ( 0.0000000 1.0000000 0.0000000 )
+DEAL::5: ( 2.7755576e-17 0.60566243 5.5511151e-17 )
+DEAL::6: ( 0.70710678 0.70710678 0.0000000 )
+DEAL::7: ( 0.45921582 0.45921582 0.0000000 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.0000000 0.45921582 -0.45921582 )
+DEAL::1: ( 0.0000000 0.21132487 -0.21132487 )
+DEAL::2: ( 0.39433757 0.39433757 -0.39433757 )
+DEAL::3: ( 0.21132487 0.21132487 -0.21132487 )
+DEAL::4: ( 2.7755576e-17 0.60566243 5.5511151e-17 )
+DEAL::5: ( 0.0000000 0.21132487 0.0000000 )
+DEAL::6: ( 0.45921582 0.45921582 0.0000000 )
+DEAL::7: ( 0.21132487 0.21132487 0.0000000 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.70710678 0.70710678 0.0000000 )
+DEAL::1: ( -0.45921582 0.45921582 0.0000000 )
+DEAL::2: ( 0.0000000 1.0000000 0.0000000 )
+DEAL::3: ( 2.7755576e-17 0.60566243 5.5511151e-17 )
+DEAL::4: ( -0.57735027 0.57735027 0.57735027 )
+DEAL::5: ( -0.39433757 0.39433757 0.39433757 )
+DEAL::6: ( 0.0000000 0.70710678 0.70710678 )
+DEAL::7: ( 0.0000000 0.45921582 0.45921582 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.45921582 0.45921582 0.0000000 )
+DEAL::1: ( -0.21132487 0.21132487 0.0000000 )
+DEAL::2: ( 2.7755576e-17 0.60566243 5.5511151e-17 )
+DEAL::3: ( 0.0000000 0.21132487 0.0000000 )
+DEAL::4: ( -0.39433757 0.39433757 0.39433757 )
+DEAL::5: ( -0.21132487 0.21132487 0.21132487 )
+DEAL::6: ( 0.0000000 0.45921582 0.45921582 )
+DEAL::7: ( 0.0000000 0.21132487 0.21132487 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.0000000 1.0000000 0.0000000 )
+DEAL::1: ( 2.7755576e-17 0.60566243 5.5511151e-17 )
+DEAL::2: ( 0.70710678 0.70710678 0.0000000 )
+DEAL::3: ( 0.45921582 0.45921582 0.0000000 )
+DEAL::4: ( 0.0000000 0.70710678 0.70710678 )
+DEAL::5: ( 0.0000000 0.45921582 0.45921582 )
+DEAL::6: ( 0.57735027 0.57735027 0.57735027 )
+DEAL::7: ( 0.39433757 0.39433757 0.39433757 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 2.7755576e-17 0.60566243 5.5511151e-17 )
+DEAL::1: ( 0.0000000 0.21132487 0.0000000 )
+DEAL::2: ( 0.45921582 0.45921582 0.0000000 )
+DEAL::3: ( 0.21132487 0.21132487 0.0000000 )
+DEAL::4: ( 0.0000000 0.45921582 0.45921582 )
+DEAL::5: ( 0.0000000 0.21132487 0.21132487 )
+DEAL::6: ( 0.39433757 0.39433757 0.39433757 )
+DEAL::7: ( 0.21132487 0.21132487 0.21132487 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::done...
projects / dealii.git / commitdiff