From: Martin Kronbichler Date: Mon, 10 Aug 2015 09:23:14 +0000 (+0200) Subject: Also implement Jacobians for MappingFEField. X-Git-Tag: v8.4.0-rc2~630^2 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=43c0d2dde7b1ef2db8ca8eb4fc26da783efcd53f;p=dealii.git Also implement Jacobians for MappingFEField. --- diff --git a/include/deal.II/fe/mapping_fe_field.h b/include/deal.II/fe/mapping_fe_field.h index bc9e474b50..2086daf122 100644 --- a/include/deal.II/fe/mapping_fe_field.h +++ b/include/deal.II/fe/mapping_fe_field.h @@ -395,35 +395,6 @@ public: const Point &initial_p_unit, InternalData &mdata) const; - /** - * Do the computation for the fill_* functions. - */ - void compute_fill (const typename Triangulation::cell_iterator &cell, - const unsigned int npts, - const typename QProjector::DataSetDescriptor data_set, - const CellSimilarity::Similarity cell_similarity, - const InternalData &data, - std::vector > &quadrature_points) const; - - - /** - * Do the computation for the fill_* functions. - */ - void compute_fill_face (const typename Triangulation::cell_iterator &cell, - const unsigned int face_no, - const unsigned int subface_no, - const unsigned int npts, - const typename QProjector::DataSetDescriptor data_set, - const std::vector &weights, - const InternalData &mapping_data, - std::vector > &quadrature_points, - std::vector &JxW_values, - std::vector > &boundary_form, - std::vector > &normal_vectors, - std::vector > &jacobians, - std::vector > &inverse_jacobians) const; - - /** * Always returns @p false. */ diff --git a/source/fe/mapping_fe_field.cc b/source/fe/mapping_fe_field.cc index 6b5ab6bac0..47e2a6065c 100644 --- a/source/fe/mapping_fe_field.cc +++ b/source/fe/mapping_fe_field.cc @@ -370,6 +370,352 @@ MappingFEField::get_subface_data (const UpdateFlags upda } + +namespace internal +{ + namespace + { + /** + * Compute the locations of quadrature points on the object described by + * the first argument (and the cell for which the mapping support points + * have already been set), but only if the update_flags of the @p data + * argument indicate so. + */ + template + void + maybe_compute_q_points (const typename dealii::QProjector::DataSetDescriptor data_set, + const typename dealii::MappingFEField::InternalData &data, + const FiniteElement &fe, + const ComponentMask &fe_mask, + const std::vector &fe_to_real, + std::vector > &quadrature_points) + { + const UpdateFlags update_flags(data.current_update_flags()); + + if (update_flags & update_quadrature_points) + { + for (unsigned int point=0; point result; + const double *shape = &data.shape(point+data_set,0); + + for (unsigned int k=0; k + void + maybe_update_Jacobians (const CellSimilarity::Similarity cell_similarity, + const typename dealii::QProjector::DataSetDescriptor data_set, + const typename dealii::MappingFEField::InternalData &data, + const FiniteElement &fe, + const ComponentMask &fe_mask, + const std::vector &fe_to_real) + { + const UpdateFlags update_flags(data.current_update_flags()); + + // then Jacobians + if (update_flags & update_contravariant_transformation) + { + + // if the current cell is just a translation of the previous one, no + // need to recompute jacobians... + if (cell_similarity != CellSimilarity::translation) + { + const unsigned int n_q_points = data.contravariant.size(); + + Assert (data.n_shape_functions > 0, ExcInternalError()); + + for (unsigned int point=0; point *data_derv = + &data.derivative(point+data_set, 0); + + Tensor<1, dim> result[spacedim]; + + for (unsigned int k=0; k + void + maybe_update_jacobian_grads (const CellSimilarity::Similarity cell_similarity, + const typename dealii::QProjector::DataSetDescriptor data_set, + const typename dealii::MappingFEField::InternalData &data, + const FiniteElement &fe, + const ComponentMask &fe_mask, + const std::vector &fe_to_real, + std::vector > &jacobian_grads) + { + const UpdateFlags update_flags(data.current_update_flags()); + if (update_flags & update_jacobian_grads) + { + const unsigned int n_q_points = jacobian_grads.size(); + + if (cell_similarity != CellSimilarity::translation) + { + for (unsigned int point=0; point *second = + &data.second_derivative(point+data_set, 0); + + DerivativeForm<2,dim,spacedim> result; + + for (unsigned int k=0; k + void + maybe_compute_face_data (const dealii::MappingFEField &mapping, + const typename dealii::Triangulation::cell_iterator &cell, + const unsigned int face_no, + const unsigned int subface_no, + const unsigned int n_q_points, + const std::vector &weights, + const typename dealii::MappingFEField::InternalData &data, + internal::FEValues::MappingRelatedData &output_data) + { + const UpdateFlags update_flags(data.current_update_flags()); + + if (update_flags & update_boundary_forms) + { + const unsigned int n_q_points = output_data.boundary_forms.size(); + if (update_flags & update_normal_vectors) + AssertDimension (output_data.normal_vectors.size(), n_q_points); + if (update_flags & update_JxW_values) + AssertDimension (output_data.JxW_values.size(), n_q_points); + + // map the unit tangentials to the real cell. checking for d!=dim-1 + // eliminates compiler warnings regarding unsigned int expressions < + // 0. + for (unsigned int d=0; d!=dim-1; ++d) + { + Assert (face_no+GeometryInfo::faces_per_cell*d < + data.unit_tangentials.size(), + ExcInternalError()); + Assert (data.aux[d].size() <= + data.unit_tangentials[face_no+GeometryInfo::faces_per_cell*d].size(), + ExcInternalError()); + + mapping.transform (data.unit_tangentials[face_no+GeometryInfo::faces_per_cell*d], + data.aux[d], + data, + mapping_contravariant); + } + + // if dim==spacedim, we can use the unit tangentials to compute the + // boundary form by simply taking the cross product + if (dim == spacedim) + { + for (unsigned int i=0; i cell_normal; + const DerivativeForm<1,spacedim,dim> DX_t = + data.contravariant[point].transpose(); + cross_product(cell_normal,DX_t[0],DX_t[1]); + cell_normal /= cell_normal.norm(); + + // then compute the face normal from the face tangent + // and the cell normal: + cross_product (output_data.boundary_forms[point], + data.aux[0][point], cell_normal); + + } + + } + } + + if (update_flags & (update_normal_vectors | update_JxW_values)) + for (unsigned int i=0; i::subface_ratio( + cell->subface_case(face_no), subface_no); + output_data.JxW_values[i] *= area_ratio; + } + } + + if (update_flags & update_normal_vectors) + output_data.normal_vectors[i] = Point(output_data.boundary_forms[i] / output_data.boundary_forms[i].norm()); + } + + if (update_flags & update_jacobians) + for (unsigned int point=0; point + void + do_fill_fe_face_values (const dealii::MappingFEField &mapping, + const typename dealii::Triangulation::cell_iterator &cell, + const unsigned int face_no, + const unsigned int subface_no, + const typename dealii::QProjector::DataSetDescriptor data_set, + const Quadrature &quadrature, + const typename dealii::MappingFEField::InternalData &data, + const FiniteElement &fe, + const ComponentMask &fe_mask, + const std::vector &fe_to_real, + internal::FEValues::MappingRelatedData &output_data) + { + maybe_compute_q_points (data_set, + data, + fe, fe_mask, fe_to_real, + output_data.quadrature_points); + maybe_update_Jacobians (CellSimilarity::none, + data_set, + data, + fe, fe_mask, fe_to_real); + maybe_update_jacobian_grads (CellSimilarity::none, + data_set, + data, + fe, fe_mask, fe_to_real, + output_data.jacobian_grads); + maybe_compute_face_data (mapping, + cell, face_no, subface_no, quadrature.size(), + quadrature.get_weights(), data, + output_data); + } + } +} + + + // Note that the CellSimilarity flag is modifiable, since MappingFEField can need to // recalculate data even when cells are similar. template @@ -394,10 +740,15 @@ fill_fe_values (const typename Triangulation::cell_iterator &cell, : CellSimilarity::invalid_next_cell); - compute_fill (cell, n_q_points, QProjector::DataSetDescriptor::cell (), - updated_cell_similarity, - data, - output_data.quadrature_points); + update_internal_dofs(cell, data); + + internal::maybe_compute_q_points(QProjector::DataSetDescriptor::cell (), + data, *fe, fe_mask, fe_to_real, + output_data.quadrature_points); + + internal::maybe_update_Jacobians(cell_similarity, + QProjector::DataSetDescriptor::cell (), + data, *fe, fe_mask, fe_to_real); const UpdateFlags update_flags(data.current_update_flags()); const std::vector &weights=quadrature.get_weights(); @@ -474,11 +825,9 @@ fill_fe_values (const typename Triangulation::cell_iterator &cell, } } //codim>0 case - } } - // copy values from InternalData to vector given by reference if (update_flags & update_jacobians) { @@ -488,49 +837,6 @@ fill_fe_values (const typename Triangulation::cell_iterator &cell, output_data.jacobians[point] = data.contravariant[point]; } - - // calculate values of the derivatives of the Jacobians. do it here, since - // we only do it for cells, not faces. - if (update_flags & update_jacobian_grads) - { - AssertDimension (output_data.jacobian_grads.size(), n_q_points); - - if (cell_similarity != CellSimilarity::translation) - { - std::fill(output_data.jacobian_grads.begin(), - output_data.jacobian_grads.end(), - DerivativeForm<2,dim,spacedim>()); - - const unsigned int data_set = QProjector::DataSetDescriptor::cell(); - - for (unsigned int point=0; point *second = - &data.second_derivative(point+data_set, 0); - - DerivativeForm<2,dim,spacedim> result; - - for (unsigned int k=0; ksystem_to_component_index(k).first; - if (fe_mask[comp_k]) - for (unsigned int j=0; j::cell_iterator &cell, output_data.inverse_jacobians[point] = data.covariant[point].transpose(); } + // calculate derivatives of the Jacobians + internal::maybe_update_jacobian_grads(cell_similarity, + QProjector::DataSetDescriptor::cell(), + data, *fe, fe_mask, fe_to_real, + output_data.jacobian_grads); + return updated_cell_similarity; } @@ -560,23 +872,20 @@ fill_fe_face_values (const typename Triangulation::cell_iterator & ExcInternalError()); const InternalData &data = static_cast (internal_data); - const unsigned int n_q_points=quadrature.size(); - this->compute_fill_face (cell, face_no, numbers::invalid_unsigned_int, - n_q_points, - QProjector::DataSetDescriptor:: - face (face_no, - cell->face_orientation(face_no), - cell->face_flip(face_no), - cell->face_rotation(face_no), - n_q_points), - quadrature.get_weights(), - data, - output_data.quadrature_points, - output_data.JxW_values, - output_data.boundary_forms, - output_data.normal_vectors, - output_data.jacobians, - output_data.inverse_jacobians); + update_internal_dofs(cell, data); + + internal::do_fill_fe_face_values (*this, + cell, face_no, numbers::invalid_unsigned_int, + QProjector::DataSetDescriptor:: + face (face_no, + cell->face_orientation(face_no), + cell->face_flip(face_no), + cell->face_rotation(face_no), + quadrature.size()), + quadrature, + data, + *fe, fe_mask, fe_to_real, + output_data); } @@ -596,24 +905,21 @@ fill_fe_subface_values (const typename Triangulation::cell_iterato ExcInternalError()); const InternalData &data = static_cast (internal_data); - const unsigned int n_q_points=quadrature.size(); - this->compute_fill_face (cell, face_no, subface_no, - n_q_points, - QProjector::DataSetDescriptor:: - subface (face_no, subface_no, - cell->face_orientation(face_no), - cell->face_flip(face_no), - cell->face_rotation(face_no), - n_q_points, - cell->subface_case(face_no)), - quadrature.get_weights(), - data, - output_data.quadrature_points, - output_data.JxW_values, - output_data.boundary_forms, - output_data.normal_vectors, - output_data.jacobians, - output_data.inverse_jacobians); + update_internal_dofs(cell, data); + + internal::do_fill_fe_face_values (*this, + cell, face_no, numbers::invalid_unsigned_int, + QProjector::DataSetDescriptor:: + subface (face_no, subface_no, + cell->face_orientation(face_no), + cell->face_flip(face_no), + cell->face_rotation(face_no), + quadrature.size(), + cell->subface_case(face_no)), + quadrature, + data, + *fe, fe_mask, fe_to_real, + output_data); } @@ -954,239 +1260,6 @@ failure: } -template -void -MappingFEField::compute_fill ( - const typename Triangulation::cell_iterator &cell, - const unsigned int n_q_points, - const typename QProjector::DataSetDescriptor data_set, - const CellSimilarity::Similarity cell_similarity, - const InternalData &data, - std::vector > &quadrature_points) const -{ - const UpdateFlags update_flags(data.current_update_flags()); - update_internal_dofs(cell, data); - - // first compute quadrature points - if (update_flags & update_quadrature_points) - { - AssertDimension (quadrature_points.size(), n_q_points); - - for (unsigned int point=0; point result; - const double *shape = &data.shape(point+data_set,0); - - for (unsigned int k=0; ksystem_to_component_index(k).first; - if (fe_mask[comp_k]) - result[fe_to_real[comp_k]] += data.local_dof_values[k] * shape[k]; - } - - quadrature_points[point] = result; - } - } - - - // then Jacobians - if (update_flags & update_contravariant_transformation) - { - AssertDimension (data.contravariant.size(), n_q_points); - - // if the current cell is just a - // translation of the previous one, no - // need to recompute jacobians... - if (cell_similarity != CellSimilarity::translation) - { - std::fill(data.contravariant.begin(), data.contravariant.end(), - DerivativeForm<1,dim,spacedim>()); - - Assert (data.n_shape_functions > 0, ExcInternalError()); - - for (unsigned int point=0; point *data_derv = - &data.derivative(point+data_set, 0); - - Tensor<1, dim> result[spacedim]; - - for (unsigned int k=0; ksystem_to_component_index(k).first; - if (fe_mask[comp_k]) - result[fe_to_real[comp_k]] += data.local_dof_values[k] * data_derv[k]; - } - - // write result into contravariant data. for - // j=dim in the case dim -void -MappingFEField::compute_fill_face ( - const typename Triangulation::cell_iterator &cell, - const unsigned int face_no, - const unsigned int subface_no, - const unsigned int n_q_points,//npts - const typename QProjector::DataSetDescriptor data_set, - const std::vector &weights, - const InternalData &data, - std::vector > &quadrature_points, - std::vector &JxW_values, - std::vector > &boundary_forms, - std::vector > &normal_vectors, - std::vector > &/*jacobians*/, - std::vector > &/*inverse_jacobians*/) const -{ - compute_fill (cell, n_q_points, data_set, CellSimilarity::none, - data, quadrature_points); - - - const UpdateFlags update_flags(data.current_update_flags()); - - if (update_flags & update_boundary_forms) - { - AssertDimension (boundary_forms.size(), n_q_points); - if (update_flags & update_normal_vectors) - AssertDimension (normal_vectors.size(), n_q_points); - if (update_flags & update_JxW_values) - AssertDimension (JxW_values.size(), n_q_points); - - // map the unit tangentials to the real cell. checking for d!=dim-1 - // eliminates compiler warnings regarding unsigned int expressions < - // 0. - for (unsigned int d=0; d!=dim-1; ++d) - { - Assert (face_no+GeometryInfo::faces_per_cell*d < - data.unit_tangentials.size(), - ExcInternalError()); - Assert (data.aux[d].size() <= - data.unit_tangentials[face_no+GeometryInfo::faces_per_cell*d].size(), - ExcInternalError()); - - transform (data.unit_tangentials[face_no+GeometryInfo::faces_per_cell*d], - data.aux[d], - data, - mapping_contravariant); - } - - // if dim==spacedim, we can use the unit tangentials to compute the - // boundary form by simply taking the cross product - if (dim == spacedim) - { - for (unsigned int i=0; i cell_normal; - const DerivativeForm<1,spacedim,dim> DX_t = - data.contravariant[point].transpose(); - cross_product(cell_normal,DX_t[0],DX_t[1]); - cell_normal /= cell_normal.norm(); - - // then compute the face normal from the face tangent - // and the cell normal: - cross_product (boundary_forms[point], - data.aux[0][point], cell_normal); - - } - - } - } - - - - if (update_flags & (update_normal_vectors - | update_JxW_values)) - for (unsigned int i=0; i::subface_ratio( - cell->subface_case(face_no), subface_no); - JxW_values[i] *= area_ratio; - } - } - - if (update_flags & update_normal_vectors) - normal_vectors[i] = Point(boundary_forms[i] / boundary_forms[i].norm()); - } - } - -} - template unsigned int diff --git a/tests/fe/jacobians.cc b/tests/fe/jacobians.cc index 696de23412..da90b03c37 100644 --- a/tests/fe/jacobians.cc +++ b/tests/fe/jacobians.cc @@ -15,26 +15,26 @@ // Show the Jacobians, inverse Jacobians, and Jacobian gradients on hyperball -// with one quadrature point +// with one quadrature point for MappingQ and MappingFEField #include "../tests.h" #include #include #include +#include +#include #include +#include #include #include #include +#include -template -void test() -{ - Triangulation tria; - GridGenerator::hyper_ball (tria); - static const HyperBallBoundary boundary; - tria.set_boundary (0, boundary); - MappingQ mapping(3); +template +void do_test(const Triangulation &tria, + const Mapping &mapping) +{ FE_Nothing dummy; // choose a point that is not right in the // middle of the cell so that the Jacobian @@ -91,6 +91,36 @@ void test() } + +template +void test() +{ + Triangulation tria; + GridGenerator::hyper_ball (tria); + static const HyperBallBoundary boundary; + tria.set_boundary (0, boundary); + + { + deallog << "========== MappingQ ==========" << std::endl; + MappingQ mapping(3); + do_test(tria, mapping); + } + + { + deallog << "========== MappingFEField ==========" << std::endl; + FESystem fe_euler(FE_Q (QGaussLobatto<1>(4)), dim); + DoFHandler map_dh(tria); + map_dh.distribute_dofs (fe_euler); + + Vector euler_vec(map_dh.n_dofs()); + VectorTools::get_position_vector(map_dh, euler_vec); + + MappingFEField mapping(map_dh, euler_vec); + do_test(tria, mapping); + } +} + + int main() { diff --git a/tests/fe/jacobians.output b/tests/fe/jacobians.output index a29f3a7cd3..a34d5b1017 100644 --- a/tests/fe/jacobians.output +++ b/tests/fe/jacobians.output @@ -1,4 +1,5 @@ +DEAL::========== MappingQ ========== DEAL::2d Jacobians: DEAL::0.97416533 0.06643545 -0.03128628 0.58141017 DEAL::0.67100687 0.01733694 -0.02724953 1.06933838 @@ -20,6 +21,57 @@ DEAL::0 0 0 0 0 0 0 0 DEAL::-0.39107846 -0.10981715 -0.10981715 0.63752903 -0.00204199 -0.83033717 -0.83033717 -0.04134342 DEAL::0.02659837 -0.90774034 -0.90774034 -0.00223032 0.90847214 0.06185307 0.06185307 -0.57789806 DEAL:: +DEAL::========== MappingFEField ========== +DEAL::2d Jacobians: +DEAL::0.97416533 0.06643545 -0.03128628 0.58141017 +DEAL::0.67100687 0.01733694 -0.02724953 1.06933838 +DEAL::0.58578644 0 0 0.58578644 +DEAL::0.03128628 -0.58141017 0.97416533 0.06643545 +DEAL::-0.02724953 1.06933838 -0.67100687 -0.01733694 +DEAL:: +DEAL::2d inverse Jacobians: +DEAL::1.02276649 -0.11686749 0.05503611 1.71366741 +DEAL::1.48931714 -0.02414596 0.03795168 0.93454238 +DEAL::1.70710678 0 0 1.70710678 +DEAL::0.11686749 1.02276649 -1.71366741 0.05503611 +DEAL::-0.02414596 -1.48931714 0.93454238 -0.03795168 +DEAL:: +DEAL::2d Jacobian gradients: +DEAL::-0.00204199 -0.83033717 -0.83033717 -0.04134342 0.39107846 0.10981715 0.10981715 -0.63752903 +DEAL::-0.90847214 -0.06185307 -0.06185307 0.57789806 0.02659837 -0.90774034 -0.90774034 -0.00223032 +DEAL::0 0 0 0 0 0 0 0 +DEAL::-0.39107846 -0.10981715 -0.10981715 0.63752903 -0.00204199 -0.83033717 -0.83033717 -0.04134342 +DEAL::0.02659837 -0.90774034 -0.90774034 -0.00223032 0.90847214 0.06185307 0.06185307 -0.57789806 +DEAL:: +DEAL::========== MappingQ ========== +DEAL::3d Jacobians: +DEAL::0.42264973 0 0 0 0.42264973 0 0 0 0.42264973 +DEAL::0.71650265 0.00057392 0.06336402 0.00057925 0.71615833 -0.02222757 -0.01407354 0.00523990 0.48019279 +DEAL::0.02009773 -0.55557232 -0.03579057 0.80181573 0.06854119 0.00343503 0.00375449 -0.12266862 0.80741050 +DEAL::0.80181573 0.06854119 0.00343503 0.00375449 -0.12266862 0.80741050 0.02009773 -0.55557232 -0.03579057 +DEAL::0.68594812 0.01191353 0.05718759 -0.03037115 0.90754836 -0.00214412 -0.15238827 -0.00211580 0.91136026 +DEAL::0.80181573 0.06854119 0.00343503 -0.02009773 0.55557232 0.03579057 0.00375449 -0.12266862 0.80741050 +DEAL::-0.03037115 0.90754836 -0.00214412 -0.68594812 -0.01191353 -0.05718759 -0.15238827 -0.00211580 0.91136026 +DEAL:: +DEAL::3d inverse Jacobians: +DEAL::2.36602540 0 0 0 2.36602540 0 0 0 2.36602540 +DEAL::1.39206023 0.00022835 -0.18367925 0.00014028 1.39586654 0.06459453 0.04079711 -0.01522512 2.07640876 +DEAL::0.15305951 1.24332587 0.00149519 -1.77697103 0.04490999 -0.07895994 -0.27068418 0.00104160 1.22652416 +DEAL::1.24332587 0.00149519 0.15305951 0.04490999 -0.07895994 -1.77697103 0.00104160 1.22652416 -0.27068418 +DEAL::1.43695022 -0.01907339 -0.09021307 0.04865553 1.10122987 -0.00046230 0.24038497 -0.00063265 1.08217535 +DEAL::1.24332587 -0.15305951 0.00149519 0.04490999 1.77697103 -0.07895994 0.00104160 0.27068418 1.22652416 +DEAL::-0.01907339 -1.43695022 -0.09021307 1.10122987 -0.04865553 -0.00046230 -0.00063265 -0.24038497 1.08217535 +DEAL:: +DEAL::3d Jacobian gradients: +DEAL::0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +DEAL::0.00137395 -0.00717231 -0.79419777 -0.00717231 0.01913055 -0.00149076 -0.79419777 -0.00149076 -0.04004959 -0.00724068 0.01930659 -0.00052463 0.01930659 -0.00070680 -0.74156764 -0.00052463 -0.74156764 0.01902151 0.17591921 0.00109594 0.04186023 0.00109594 0.17466345 -0.01561922 0.04186023 -0.01561922 -0.55167180 +DEAL::-0.25122164 -0.07828991 -0.00750963 -0.07828991 0.93587546 0.13995856 -0.00750963 0.13995856 -0.25564696 -0.01036284 -0.85760495 -0.04324137 -0.85760495 -0.12000055 -0.01202929 -0.04324137 -0.01202929 0.02453591 -0.04693108 -0.01316991 0.02699113 -0.01316991 0.14532022 -0.87698852 0.02699113 -0.87698852 0.00740082 +DEAL::-0.01036284 -0.85760495 -0.04324137 -0.85760495 -0.12000055 -0.01202929 -0.04324137 -0.01202929 0.02453591 -0.04693108 -0.01316991 0.02699113 -0.01316991 0.14532022 -0.87698852 0.02699113 -0.87698852 0.00740082 -0.25122164 -0.07828991 -0.00750963 -0.07828991 0.93587546 0.13995856 -0.00750963 0.13995856 -0.25564696 +DEAL::-1.37058893 -0.05160788 -0.24996159 -0.05160788 0.39711769 -0.00510516 -0.24996159 -0.00510516 0.40848276 0.04774078 -1.01187322 0.00879803 -1.01187322 -0.00078284 -0.07147435 0.00879803 -0.07147435 -0.01531514 0.34545125 0.01080303 -1.06671725 0.01080303 -0.07052681 -0.01516606 -1.06671725 -0.01516606 -0.00035074 +DEAL::-0.01036284 -0.85760495 -0.04324137 -0.85760495 -0.12000055 -0.01202929 -0.04324137 -0.01202929 0.02453591 0.25122164 0.07828991 0.00750963 0.07828991 -0.93587546 -0.13995856 0.00750963 -0.13995856 0.25564696 -0.04693108 -0.01316991 0.02699113 -0.01316991 0.14532022 -0.87698852 0.02699113 -0.87698852 0.00740082 +DEAL::0.04774078 -1.01187322 0.00879803 -1.01187322 -0.00078284 -0.07147435 0.00879803 -0.07147435 -0.01531514 1.37058893 0.05160788 0.24996159 0.05160788 -0.39711769 0.00510516 0.24996159 0.00510516 -0.40848276 0.34545125 0.01080303 -1.06671725 0.01080303 -0.07052681 -0.01516606 -1.06671725 -0.01516606 -0.00035074 +DEAL:: +DEAL::========== MappingFEField ========== DEAL::3d Jacobians: DEAL::0.42264973 0 0 0 0.42264973 0 0 0 0.42264973 DEAL::0.71650265 0.00057392 0.06336402 0.00057925 0.71615833 -0.02222757 -0.01407354 0.00523990 0.48019279 diff --git a/tests/fe/jacobians_face_fe_field.cc b/tests/fe/jacobians_face_fe_field.cc new file mode 100644 index 0000000000..e5ae45626d --- /dev/null +++ b/tests/fe/jacobians_face_fe_field.cc @@ -0,0 +1,171 @@ +// --------------------------------------------------------------------- +// +// Copyright (C) 2012 - 2015 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 at +// the top level of the deal.II distribution. +// +// --------------------------------------------------------------------- + + +// Show the Jacobians and inverse Jacobians of FEFaceValues and +// FESubfaceValues on a hyperball mesh with one quadrature point for +// MappingFEField. Note that the output needs to be identical to the test +// jacobian_face that uses an underlying MappingQ. + +#include "../tests.h" +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include + +template +void test() +{ + Triangulation tria; + GridGenerator::hyper_ball (tria); + static const HyperBallBoundary boundary; + tria.set_boundary (0, boundary); + tria.begin_active()->set_refine_flag(); + tria.execute_coarsening_and_refinement(); + + // create Euler vector field and MappingFEField + FESystem fe_euler(FE_Q (QGaussLobatto<1>(4)), dim); + DoFHandler map_dh(tria); + map_dh.distribute_dofs (fe_euler); + + Vector euler_vec(map_dh.n_dofs()); + VectorTools::get_position_vector(map_dh, euler_vec); + + MappingFEField mapping(map_dh, euler_vec); + + FE_Nothing dummy; + // choose a point that is not right in the middle of the cell so that the + // Jacobian contains many nonzero entries + Point quad_p; + for (int d=0; d quad(quad_p); + FEFaceValues fe_val (mapping, dummy, quad, + update_jacobians | update_inverse_jacobians | + update_jacobian_grads); + FESubfaceValues fe_sub_val (mapping, dummy, quad, + update_jacobians | update_inverse_jacobians | + update_jacobian_grads); + deallog << dim << "d Jacobians:" << std::endl; + typename Triangulation::active_cell_iterator + cell = tria.begin_active(), endc = tria.end(); + for ( ; cell != endc; ++cell) + for (unsigned int f=0; f::faces_per_cell; ++f) + { + fe_val.reinit (cell, f); + + for (unsigned int d=0; dat_boundary(f) == false && + cell->neighbor(f)->level() < cell->level()) + { + fe_sub_val.reinit(cell->neighbor(f), cell->neighbor_face_no(f), + cell->neighbor_of_coarser_neighbor(f).second); + + for (unsigned int d=0; d::faces_per_cell; ++f) + { + fe_val.reinit (cell, f); + + for (unsigned int d=0; dat_boundary(f) == false && + cell->neighbor(f)->level() < cell->level()) + { + fe_sub_val.reinit(cell->neighbor(f), cell->neighbor_face_no(f), + cell->neighbor_of_coarser_neighbor(f).second); + + for (unsigned int d=0; d::faces_per_cell; ++f) + { + fe_val.reinit (cell, f); + + for (unsigned int d=0; dat_boundary(f) == false && + cell->neighbor(f)->level() < cell->level()) + { + fe_sub_val.reinit(cell->neighbor(f), cell->neighbor_face_no(f), + cell->neighbor_of_coarser_neighbor(f).second); + + for (unsigned int d=0; d(); + test<3>(); + + return 0; +} diff --git a/tests/fe/jacobians_face_fe_field.output b/tests/fe/jacobians_face_fe_field.output new file mode 100644 index 0000000000..6846c5b81b --- /dev/null +++ b/tests/fe/jacobians_face_fe_field.output @@ -0,0 +1,451 @@ + +DEAL::2d Jacobians: +DEAL::1.23963445 -0.18547181 0.12412324 1.55786718 +DEAL::0.53368238 0 0.07513814 0.58578644 +DEAL::0.41421356 -0.28894903 0.41421356 1.06007883 +DEAL::0.41421356 0.28894903 -0.41421356 1.06007883 +DEAL::0.58578644 0 0 0.58578644 +DEAL::0.58578644 0 0 0.58578644 +DEAL::0.58578644 0 0 0.58578644 +DEAL::0.58578644 0 0 0.58578644 +DEAL::0.28894903 -0.41421356 1.06007883 0.41421356 +DEAL::-0.28894903 -0.41421356 1.06007883 -0.41421356 +DEAL::0.18547181 -1.23963445 1.55786718 0.12412324 +DEAL::0 -0.53368238 0.58578644 0.07513814 +DEAL::0.12412324 1.55786718 -1.23963445 0.18547181 +DEAL::0.07513814 0.58578644 -0.53368238 0 +DEAL::0.41421356 1.06007883 -0.41421356 0.28894903 +DEAL::-0.41421356 1.06007883 -0.41421356 -0.28894903 +DEAL::0.59041686 0.20710678 -0.30101918 0.20710678 +DEAL::0.41421356 -0.60030292 0.41421356 1.15104508 +DEAL::0.64835562 0 -0.16114263 0.35355339 +DEAL::0.70557057 0.20974632 -0.34485147 0.46555678 +DEAL::0.50000000 0.13315220 -0.14644661 0.29709503 +DEAL::0.64835562 0 0.16114263 0.35355339 +DEAL::0.59041686 -0.20710678 0.30101918 0.20710678 +DEAL::0.60030292 -0.41421356 1.15104508 0.41421356 +DEAL::0.74276054 -0.16287016 0.25506692 0.49467915 +DEAL::0.50000000 -0.09790993 0.14644661 0.32139848 +DEAL::0.41301515 0.20710678 -0.08493903 0.20710678 +DEAL::0.41421356 -0.10529159 0.41421356 0.81807057 +DEAL::0.41301515 0 -0.08493903 0.35355339 +DEAL::0.50000000 0.12012193 -0.14644661 0.26861436 +DEAL::0.29289322 0.12012193 0 0.26861436 +DEAL::0.58578644 0 0 0.58578644 +DEAL::0.41301515 0 0.08493903 0.35355339 +DEAL::0.41301515 -0.20710678 0.08493903 0.20710678 +DEAL::0.10529159 -0.41421356 0.81807057 0.41421356 +DEAL::0.50000000 -0.08698485 0.14644661 0.29204581 +DEAL::0.29289322 -0.08698485 0 0.29204581 +DEAL::0.58578644 0 0 0.58578644 +DEAL:: +DEAL::2d inverse Jacobians: +DEAL::0.79718629 0.09490898 -0.06351591 0.63434136 +DEAL::1.87377370 0 -0.24034676 1.70710678 +DEAL::1.89711181 0.51710175 -0.74127453 0.74127453 +DEAL::1.89711181 -0.51710175 0.74127453 0.74127453 +DEAL::1.70710678 0 0 1.70710678 +DEAL::1.70710678 0 0 1.70710678 +DEAL::1.70710678 0 0 1.70710678 +DEAL::1.70710678 0 0 1.70710678 +DEAL::0.74127453 0.74127453 -1.89711181 0.51710175 +DEAL::-0.74127453 0.74127453 -1.89711181 -0.51710175 +DEAL::0.06351591 0.63434136 -0.79718629 0.09490898 +DEAL::0.24034676 1.70710678 -1.87377370 0 +DEAL::0.09490898 -0.79718629 0.63434136 0.06351591 +DEAL::0 -1.87377370 1.70710678 0.24034676 +DEAL::0.51710175 -1.89711181 0.74127453 0.74127453 +DEAL::-0.51710175 -1.89711181 0.74127453 -0.74127453 +DEAL::1.12178547 -1.12178547 1.63045818 3.19796894 +DEAL::1.58670272 0.82751084 -0.57098875 0.57098875 +DEAL::1.54236343 0 0.70297871 2.82842712 +DEAL::1.16152683 -0.52330025 0.86037676 1.76034199 +DEAL::1.76792606 -0.79235000 0.87146116 2.97535453 +DEAL::1.54236343 0 -0.70297871 2.82842712 +DEAL::1.12178547 1.12178547 -1.63045818 3.19796894 +DEAL::0.57098875 0.57098875 -1.58670272 0.82751084 +DEAL::1.20957041 0.39824384 -0.62367982 1.81616949 +DEAL::1.83616594 0.55936445 -0.83665697 2.85652558 +DEAL::2.00821688 -2.00821688 0.82361379 4.00481334 +DEAL::2.13891922 0.27529435 -1.08299868 1.08299868 +DEAL::2.42121868 0 0.58168294 2.82842712 +DEAL::1.76837908 -0.79080328 0.96410752 3.29166896 +DEAL::3.41421356 -1.52680571 0 3.72280920 +DEAL::1.70710678 0 0 1.70710678 +DEAL::2.42121868 0 -0.58168294 2.82842712 +DEAL::2.00821688 2.00821688 -0.82361379 4.00481334 +DEAL::1.08299868 1.08299868 -2.13891922 0.27529435 +DEAL::1.83952492 0.54789621 -0.92243125 3.14937729 +DEAL::3.41421356 1.01691184 0 3.42412029 +DEAL::1.70710678 0 0 1.70710678 +DEAL:: +DEAL::2d Jacobian gradients: +DEAL::-1.84633620 0.54214837 0.54214837 2.31839763 -0.17634636 -1.51354439 -1.51354439 0.29875970 +DEAL::0.43443205 0.07846884 0.07846884 0 0.07837616 -0.93340477 -0.93340477 0 +DEAL::0 1.03088442 1.03088442 0.57789806 0 -0.66806882 -0.66806882 0.03717203 +DEAL::0 -1.03088442 -1.03088442 0.57789806 0 -0.66806882 -0.66806882 -0.03717203 +DEAL::0 0 0 0 0 0 0 0 +DEAL::0 0 0 0 0 0 0 0 +DEAL::0 0 0 0 0 0 0 0 +DEAL::0 0 0 0 0 0 0 0 +DEAL::-0.57789806 -1.03088442 -1.03088442 0 0.03717203 -0.66806882 -0.66806882 0 +DEAL::-0.57789806 1.03088442 1.03088442 0 -0.03717203 -0.66806882 -0.66806882 0 +DEAL::-2.31839763 -0.54214837 -0.54214837 1.84633620 0.29875970 -1.51354439 -1.51354439 -0.17634636 +DEAL::0 -0.07846884 -0.07846884 -0.43443205 0 -0.93340477 -0.93340477 0.07837616 +DEAL::-0.17634636 -1.51354439 -1.51354439 0.29875970 1.84633620 -0.54214837 -0.54214837 -2.31839763 +DEAL::0.07837616 -0.93340477 -0.93340477 0 -0.43443205 -0.07846884 -0.07846884 0 +DEAL::0 -0.66806882 -0.66806882 0.03717203 0 -1.03088442 -1.03088442 -0.57789806 +DEAL::0 -0.66806882 -0.66806882 -0.03717203 0 1.03088442 1.03088442 -0.57789806 +DEAL::0.06235292 -0.08471018 -0.08471018 0 0.13804815 0.38807799 0.38807799 0 +DEAL::0 2.00320701 2.00320701 1.20060584 0 -0.15024142 -0.15024142 0.53519273 +DEAL::0.05352461 -0.29141850 -0.29141850 0 0.14170495 -0.11096004 -0.11096004 0 +DEAL::0.26791486 -0.23410942 -0.23410942 -0.20605054 0.54645813 0.31136944 0.31136944 -0.43821988 +DEAL::0 -0.21170570 -0.21170570 0.05286230 0 0.17060309 0.17060309 0.10129638 +DEAL::-0.05352461 -0.29141850 -0.29141850 0 0.14170495 0.11096004 0.11096004 0 +DEAL::-0.06235292 -0.08471018 -0.08471018 0 0.13804815 -0.38807799 -0.38807799 0 +DEAL::-1.20060584 -2.00320701 -2.00320701 0 0.53519273 -0.15024142 -0.15024142 0 +DEAL::-0.19695983 -0.34281858 -0.34281858 0.16416851 0.57584866 -0.04892231 -0.04892231 -0.45556798 +DEAL::0 -0.22743992 -0.22743992 -0.03424807 0 -0.13261732 -0.13261732 0.10900665 +DEAL::0 -0.20710678 -0.20710678 0 0 0.14644661 0.14644661 0 +DEAL::0 0.36695330 0.36695330 0.21058318 0 -0.90934959 -0.90934959 0.04775839 +DEAL::0 -0.20710678 -0.20710678 0 0 0.14644661 0.14644661 0 +DEAL::0 -0.20710678 -0.20710678 0 0 0.14644661 0.14644661 0 +DEAL::0 -0.20710678 -0.20710678 0 0 0.14644661 0.14644661 0 +DEAL::0 0 0 0 0 0 0 0 +DEAL::0 -0.20710678 -0.20710678 0 0 -0.14644661 -0.14644661 0 +DEAL::0 -0.20710678 -0.20710678 0 0 -0.14644661 -0.14644661 0 +DEAL::-0.21058318 -0.36695330 -0.36695330 0 0.04775839 -0.90934959 -0.90934959 0 +DEAL::0 -0.20710678 -0.20710678 0 0 -0.14644661 -0.14644661 0 +DEAL::0 -0.20710678 -0.20710678 0 0 -0.14644661 -0.14644661 0 +DEAL::0 0 0 0 0 0 0 0 +DEAL:: +DEAL::3d Jacobians: +DEAL::0.81350031 -0.01391837 0.44040642 -0.01226796 0.76623426 0.05864280 -0.12782348 -0.01391837 0.44040642 +DEAL::0.81350031 0.01391837 -0.44040642 0.01226796 0.76623426 0.05864280 0.12782348 -0.01391837 0.44040642 +DEAL::0.84873518 0.00765757 -0.02313163 0.00771271 0.91107165 0.48026545 0.00771271 -0.20424138 0.48026545 +DEAL::0.84873518 -0.00765757 -0.02313163 -0.00771271 0.91107165 -0.48026545 0.00771271 0.20424138 0.48026545 +DEAL::1.54975902 0.00633378 0.17578641 0.00928390 1.69941646 -0.08802805 -0.17567935 0.06510834 1.64714337 +DEAL::0.42264973 0 0.07640727 0 0.42264973 -0.03234765 0 0 0.53910786 +DEAL::0.20424138 -0.48026545 -0.00771271 0.91107165 0.48026545 0.00771271 0.00765757 -0.02313163 0.84873518 +DEAL::-0.20424138 -0.48026545 -0.00771271 0.91107165 -0.48026545 -0.00771271 -0.00765757 -0.02313163 0.84873518 +DEAL::-0.06510834 -1.64714337 0.17567935 1.69941646 -0.08802805 0.00928390 0.00633378 0.17578641 1.54975902 +DEAL::0 -0.53910786 0 0.42264973 0.08635470 0 0 -0.02861737 0.42264973 +DEAL::0.01391837 -0.44040642 0.12782348 0.76623426 0.05864280 -0.01226796 -0.01391837 0.44040642 0.81350031 +DEAL::0.01391837 -0.44040642 -0.12782348 0.76623426 0.05864280 0.01226796 0.01391837 -0.44040642 0.81350031 +DEAL::0.91107165 0.48026545 0.00771271 0.00765757 -0.02313163 0.84873518 0.20424138 -0.48026545 -0.00771271 +DEAL::0.82044863 -0.44040642 0.01391837 0.01337969 0.05864280 0.76623426 -0.12782348 -0.44040642 0.01391837 +DEAL::1.69941646 -0.08802805 0.00928390 0.00633378 0.17578641 1.54975902 -0.06510834 -1.64714337 0.17567935 +DEAL::0.42264973 0.08635470 0 0 -0.02861737 0.42264973 0 -0.53910786 0 +DEAL::0.76623426 0.05864280 -0.01226796 -0.01391837 0.44040642 0.81350031 0.01391837 -0.44040642 0.12782348 +DEAL::0.76623426 0.05864280 0.01226796 0.01391837 -0.44040642 0.81350031 0.01391837 -0.44040642 -0.12782348 +DEAL::1.64714337 -0.17567935 0.06510834 0.17578641 1.54975902 0.00633378 -0.08802805 0.00928390 1.69941646 +DEAL::0.53910786 0 0 0.07640727 0.42264973 0 -0.03234765 0 0.42264973 +DEAL::0.44040642 -0.12782348 -0.01391837 0.44040642 0.81350031 -0.01391837 0.05864280 -0.01226796 0.76623426 +DEAL::0.44040642 0.12782348 -0.01391837 -0.44040642 0.81350031 0.01391837 0.05864280 0.01226796 0.76623426 +DEAL::0.44040642 -0.01391837 -0.12782348 0.05864280 0.76623426 -0.01337969 0.44040642 -0.01391837 0.82044863 +DEAL::0.48026545 0.00771271 0.20424138 -0.02313163 0.84873518 -0.00765757 -0.48026545 -0.00771271 0.91107165 +DEAL::0.82044863 0.44040642 -0.01391837 -0.12782348 0.44040642 -0.01391837 -0.01337969 0.05864280 0.76623426 +DEAL::0.91107165 -0.48026545 -0.00771271 0.20424138 0.48026545 0.00771271 -0.00765757 -0.02313163 0.84873518 +DEAL::1.69941646 -0.08802805 0.00928390 0.06510834 1.64714337 -0.17567935 0.00633378 0.17578641 1.54975902 +DEAL::0.42264973 -0.03234765 0 0 0.53910786 0 0 0.07640727 0.42264973 +DEAL::0.84873518 -0.02313163 0.00754376 0.00771271 0.48026545 -0.20424138 0.00771271 0.48026545 0.90917487 +DEAL::0.76623426 0.05864280 0.01226796 -0.01391837 0.44040642 0.12782348 0.01391837 -0.44040642 0.81350031 +DEAL::0.17578641 1.54975902 0.00633378 -1.64714337 0.17567935 -0.06510834 -0.08802805 0.00928390 1.69941646 +DEAL::-0.02861737 0.42264973 0 -0.53910786 0 0 0.08635470 0 0.42264973 +DEAL::0.44040642 0.81350031 -0.01391837 -0.44040642 0.12782348 0.01391837 0.05864280 -0.01226796 0.76623426 +DEAL::-0.48026545 0.90917487 -0.00771271 -0.48026545 -0.20424138 -0.00771271 -0.02313163 -0.00754376 0.84873518 +DEAL::-0.02313163 0.84873518 0.00765757 -0.48026545 -0.00771271 0.20424138 0.48026545 0.00771271 0.91107165 +DEAL::0.05864280 0.76623426 0.01337969 -0.44040642 0.01391837 -0.12782348 -0.44040642 0.01391837 0.82044863 +DEAL::0.21132487 0 0 0 0.21132487 0 0 0 0.21132487 +DEAL::0.47964215 0 0 0.25693002 0.42264973 0 0.22230805 0 0.42264973 +DEAL::0.21132487 0 0 0 0.21132487 0 0 0 0.21132487 +DEAL::0.21132487 0 0 0 0.21132487 0 0 0 0.21132487 +DEAL::0.42264973 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0 0.21132487 0 0 0 0.21132487 +DEAL::0.21132487 0 0 0 0.21132487 0 0 0 0.21132487 +DEAL::0.42264973 0.23197941 0 0 0.49679008 0 0 -0.18954257 0.42264973 +DEAL::0.21132487 0 0 0 0.21132487 0 0 0 0.21132487 +DEAL::0.21132487 0 0 0 0.21132487 0 0 0 0.21132487 +DEAL::0.21132487 0 0 0 0.21132487 0 0 0 0.21132487 +DEAL::0.42264973 0.27613207 0 0 0.20674777 0.42264973 0 -0.47964215 0 +DEAL::0.21132487 0 0 0 0.21132487 0 0 0 0.21132487 +DEAL::0.21132487 0 0 0 0.21132487 0 0 0 0.21132487 +DEAL::0 -0.47367981 0 0.42264973 0.27203859 0 0 -0.23160365 0.42264973 +DEAL::0.21132487 0 0 0 0.21132487 0 0 0 0.21132487 +DEAL::0.42264973 -0.25822136 0 0 0.49017924 0 0 -0.18752406 0.42264973 +DEAL::0.21132487 0 0 0 0.21132487 0 0 0 0.21132487 +DEAL::0.21132487 0 0 0 0.21132487 0 0 0 0.21132487 +DEAL::0.21132487 0 0 0 0.21132487 0 0 0 0.21132487 +DEAL::0.42264973 -0.20680010 0 0 0.21266741 0.42264973 0 -0.49679008 0 +DEAL::0.21132487 0 0 0 0.21132487 0 0 0 0.21132487 +DEAL::0.49017924 0 0 -0.18752406 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Jacobians: +DEAL::1.06233372 0 -1.06233372 -0.00657316 1.30193488 -0.16678741 0.30812381 0.04114567 1.95702733 +DEAL::1.06233372 0 1.06233372 0.00657316 1.30193488 -0.16678741 -0.30812381 0.04114567 1.95702733 +DEAL::1.17770835 0.00230150 0.05442195 0 0.89660927 -0.89660927 -0.01891314 0.38126200 1.70000893 +DEAL::1.17770835 -0.00230150 0.05442195 0 0.89660927 0.89660927 -0.01891314 -0.38126200 1.70000893 +DEAL::0.63754862 0.00023014 -0.06802816 0.00003928 0.58723492 0.03137932 0.06799746 -0.02318770 0.59861565 +DEAL::2.36602540 0 -0.33533464 0 2.36602540 0.14196671 0 0 1.85491639 +DEAL::0.89660927 0.89660927 0 -1.70000893 0.38126200 -0.01891314 -0.05442195 0.00230150 1.17770835 +DEAL::-0.89660927 0.89660927 0 -1.70000893 -0.38126200 -0.01891314 -0.05442195 -0.00230150 1.17770835 +DEAL::-0.03137932 0.58723492 0.00003928 -0.59861565 -0.02318770 0.06799746 0.06802816 0.00023014 0.63754862 +DEAL::0.37899171 2.36602540 0 -1.85491639 0 0 -0.12559531 0 2.36602540 +DEAL::0.16678741 1.30193488 -0.00657316 -1.95702733 0.04114567 0.30812381 1.06233372 0 1.06233372 +DEAL::0.16678741 1.30193488 0.00657316 -1.95702733 0.04114567 -0.30812381 -1.06233372 0 1.06233372 +DEAL::0.89660927 0 0.89660927 0.38126200 -0.01891314 -1.70000893 0.00230150 1.17770835 -0.05442195 +DEAL::1.05454962 0 -1.05454962 -0.30591432 0.04114567 -1.95923683 0.00499864 1.30193488 0.16836194 +DEAL::0.58723492 0.00003928 -0.03137932 -0.02318770 0.06799746 -0.59861565 0.00023014 0.63754862 0.06802816 +DEAL::2.36602540 0 0.37899171 0 0 -1.85491639 0 2.36602540 -0.12559531 +DEAL::1.30193488 -0.00657316 0.16678741 0.04114567 0.30812381 -1.95702733 0 1.06233372 1.06233372 +DEAL::1.30193488 0.00657316 0.16678741 0.04114567 -0.30812381 -1.95702733 0 1.06233372 -1.06233372 +DEAL::0.59861565 0.06799746 -0.02318770 -0.06802816 0.63754862 0.00023014 0.03137932 0.00003928 0.58723492 +DEAL::1.85491639 0 0 -0.33533464 2.36602540 0 0.14196671 0 2.36602540 +DEAL::1.95702733 0.30812381 0.04114567 -1.06233372 1.06233372 0 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4.73205081 0 0 0 4.73205081 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::1.36213110 2.36602540 0 -2.08488766 0 0 1.01986550 0 2.36602540 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::2.36602540 1.23775345 0 0 2.11113071 0 0 -1.27030225 2.36602540 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::2.36602540 0 0.90272038 0 2.36602540 -1.10483122 0 0 2.01292265 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::2.01292265 0 0 0.90272038 2.36602540 0 -1.10483122 0 2.36602540 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::0 -2.08488766 0 2.36602540 1.01986550 0 0 1.36213110 2.36602540 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::2.36602540 0 -1.27030225 0 2.36602540 1.23775345 0 0 2.11113071 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::-0.98491156 2.36602540 0 -2.01292265 0 0 1.01285538 0 2.36602540 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::0 -2.11113071 0 2.36602540 -1.15685766 0 0 1.35882972 2.36602540 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::2.36602540 0 0.90515195 0 2.36602540 1.24639776 0 0 2.04007008 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::2.11113071 0 0 -1.27030225 2.36602540 0 1.23775345 0 2.36602540 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::2.36602540 -1.10483122 0 0 2.01292265 0 0 0.90272038 2.36602540 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::2.36602540 0 1.36213110 0 0 -2.08488766 0 2.36602540 1.01986550 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::1.35882972 2.36602540 0 -2.11113071 0 0 -1.15685766 0 2.36602540 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::2.36602540 1.24639776 0 0 2.04007008 0 0 0.90515195 2.36602540 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::2.36602540 0 -0.98491156 0 0 -2.01292265 0 2.36602540 1.01285538 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::2.04007008 0 0 0.90515195 2.36602540 0 1.24639776 0 2.36602540 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::0 -2.01292265 0 2.36602540 1.01285538 0 0 -0.98491156 2.36602540 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::2.36602540 0 1.35882972 0 0 -2.11113071 0 2.36602540 -1.15685766 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::-0.98203654 2.36602540 0 -2.04007008 0 0 -1.14937673 0 2.36602540 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::0 -2.04007008 0 2.36602540 -1.14937673 0 0 -0.98203654 2.36602540 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::4.73205081 0 0 0 4.73205081 0 0 0 4.73205081 +DEAL::2.36602540 0 -0.98203654 0 0 -2.04007008 0 2.36602540 -1.14937673 +DEAL:: +DEAL::3d Jacobian gradients: +DEAL::-0.02643148 0.03004810 -0.89081368 0.03004810 0.17397969 0.04885453 -0.89081368 0.04885453 -0.28361854 0.02453591 0.15443348 0.04296177 0.15443348 -0.00099692 -0.73298331 0.04296177 -0.73298331 -0.02018433 0.25564696 -0.02682012 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