From cf0180e14596088ba2e47b186560462c015fca2c Mon Sep 17 00:00:00 2001 From: Ivy Weber Date: Tue, 10 Jan 2023 15:04:03 +0100 Subject: [PATCH] Added files for the fe_hermite finite element object class, and test files Copied over changed for cut Hermite from experimental branch Rewrote interface for calling Hermite elements to use polynomial degree, rather than regularity. --- doc/news/changes/major/20230621IvyWeber | 3 + include/deal.II/fe/fe_hermite.h | 284 +++++ include/deal.II/fe/fe_update_flags.h | 8 +- .../numerics/matrix_creator.templates.h | 14 +- source/dofs/dof_tools_sparsity.cc | 13 +- source/fe/CMakeLists.txt | 2 + source/fe/fe_hermite.cc | 972 +++++++++++++++ source/fe/fe_hermite.inst.in | 51 + source/fe/fe_q.cc | 18 +- source/fe/fe_q_base.cc | 10 + tests/fe/2d_grid_projection_hermite.cc | 199 +++ tests/fe/2d_grid_projection_hermite.output | 25 + tests/fe/derivatives.h | 172 +++ tests/fe/derivatives_hermite.cc | 83 ++ tests/fe/derivatives_hermite.output | 206 +++ tests/fe/shapes.h | 6 +- tests/fe/shapes_hermite.cc | 91 ++ tests/fe/shapes_hermite.output | 1102 +++++++++++++++++ 18 files changed, 3252 insertions(+), 7 deletions(-) create mode 100644 doc/news/changes/major/20230621IvyWeber create mode 100644 include/deal.II/fe/fe_hermite.h create mode 100644 source/fe/fe_hermite.cc create mode 100644 source/fe/fe_hermite.inst.in create mode 100644 tests/fe/2d_grid_projection_hermite.cc create mode 100644 tests/fe/2d_grid_projection_hermite.output create mode 100644 tests/fe/derivatives.h create mode 100644 tests/fe/derivatives_hermite.cc create mode 100644 tests/fe/derivatives_hermite.output create mode 100644 tests/fe/shapes_hermite.cc create mode 100644 tests/fe/shapes_hermite.output diff --git a/doc/news/changes/major/20230621IvyWeber b/doc/news/changes/major/20230621IvyWeber new file mode 100644 index 0000000000..1960bd2e60 --- /dev/null +++ b/doc/news/changes/major/20230621IvyWeber @@ -0,0 +1,3 @@ +New: Added classes for conforming Hermite interpolation polynomials, allowing for higher levels of regularity between elements to be directly enforced. +
+(Ivy Weber, 2023/06/21) diff --git a/include/deal.II/fe/fe_hermite.h b/include/deal.II/fe/fe_hermite.h new file mode 100644 index 0000000000..ca66bdaa02 --- /dev/null +++ b/include/deal.II/fe/fe_hermite.h @@ -0,0 +1,284 @@ +// --------------------------------------------------------------------- +// +// Copyright (C) 2023 - 2023 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. +// +// --------------------------------------------------------------------- + +#ifndef dealii_fe_hermite_h +#define dealii_fe_hermite_h + +#include + +#include + +#include + +#include +#include + +DEAL_II_NAMESPACE_OPEN + +/** + * @addtogroup fe + * @{ + */ + + + +/** + * This class implements a Hermite interpolation basis of maximum regularity + * elements (see @cite CiarletRiavart1972interpolation). These bases are always + * of odd polynomial degree, have regularity $r=\frac{p-1}{2}$ and are defined + * up to polynomial degree $p=13$, with larger degrees currently being + * ill-conditioned. + * + * Each node has $(r+1)^{d}$ degrees of freedom (DoFs) assigned to it, + * corresponding to various derivatives up to order $r$ in each direction. + * DoFs at each node are not consecutive in lexicographic ordering for + * $d>1$ due to the tensor product construction of the basis. The + * ordering is determined by the direction of the derivative each function + * corresponds to; first by $x$-derivatives, then $y$, then $z$. Locally over + * each element the DoFs are ordered similarly. See below for the local ordering + * for $r=1$, where DoFs are ordered from 0 to $(2r+2)^{d}-1$: + * + * FE_Hermite<1>(3) + * + * @verbatim + * (0)________________(2) + * (1) (3) + * @endverbatim + * + * FE_Hermite<2>(3): + * + * @verbatim + * ( 8, 9)__________(10,11) + * (12,13) (14,15) + * | | + * | | + * | | + * | | + * | | + * | | + * ( 0, 1)__________( 2, 3) + * ( 4, 5) ( 6, 7) + * @endverbatim + * + * FE_Hermite<3>(3): + * + * @verbatim + * (40,41,44,45)__(42,43,46,47) (40,41,44,45)__(42,43,46,47) + * (56,57,60,61) (58,59,62,63) (56,57,60,61) (58,59,62,63) + * / | | / / | + * / | | / / | + * / | | / / | + *(32,33,36,37)| | (32,33,36,37)__(34,35,38,39) + *(48,49,52,53)| | (48,49,52,53) (50,51,54,55) + * | | | | | | + * |( 8,9,12,13 )__(10,11,14,15) | |(10,11,14,15) + * |(24,25,28,29) (26,27,30,31) | |(26,27,30,31) + * | / / | | / + * | / / | | / + * | / / | | / + * ( 0,1,4,5 )___( 2,3,6,7 ) ( 0,1,4,5 )___( 2,3,6,7 ) + * (16,17,20,21) (18,19,22,23) (16,17,20,21) (18,19,22,23) + * @endverbatim + * + * Due to the increased regularity constraints many of these functions are + * shared between elements, leading to fewer DoFs overall. + */ +template +class FE_Hermite : public FE_Poly +{ +public: + /** + * Constructor that creates an Hermite finite element object with + * continuity in derivatives up to and including order + * (fe_degree - 1)/2. + * Throws an exception if @p fe_degree is not an odd positive integer. + */ + FE_Hermite(const unsigned int fe_degree); + + // Other functions + /** + * Returns FE_Hermite(fe_degree) as a + * std::string with @p dim, @p spacedim and @p fe_degree + * replaced with the correct values. + */ + virtual std::string + get_name() const override; + + /** + * @copydoc dealii::FiniteElement::clone() + */ + virtual std::unique_ptr> + clone() const override; + + /** + * @copydoc dealii::FiniteElement::requires_update_flags() + */ + virtual UpdateFlags + requires_update_flags(const UpdateFlags update_flags) const override; + + /** + * @copydoc dealii::FiniteElement::hp_vertex_dof_identities() + */ + virtual std::vector> + hp_vertex_dof_identities( + const FiniteElement &fe_other) const override; + + /** + * @copydoc dealii::FiniteElement::hp_line_dof_identities() + */ + virtual std::vector> + hp_line_dof_identities( + const FiniteElement &fe_other) const override; + + /** + * @copydoc dealii::FiniteElement::hp_quad_dof_identities() + */ + virtual std::vector> + hp_quad_dof_identities(const FiniteElement &fe_other, + const unsigned int face_no = 0) const override; + + /** + * @copydoc FiniteElement::compare_for_domination() + */ + virtual FiniteElementDomination::Domination + compare_for_domination(const FiniteElement &other_fe, + const unsigned int codim) const override; + + /** + * Returns the mapping between lexicographic and hierarchic numbering + * schemes for Hermite. See the class documentation for diagrams of + * examples of lexicographic numbering for Hermite elements. + */ + std::vector + get_lexicographic_to_hierarchic_numbering() const; + + /** + * This re-implements FiniteElement::fill_fe_values() for a Hermite + * polynomial basis, to account for the more complicated shape function + * re-scaling that a Hermite basis requires. On a non-uniform grid, + * failing to rescale function values will lead to discontinuities across + * element boundaries in derivatives if elements have different sizes. + * + * At present this is done by only allowing certain cell mappings + * (currently only MappingCartesian) which guarantee + * rectangular cells, which ensures that the directions of derivatives + * does not change. The derivative continuity can then be enforced by + * re-scaling shape functions so that the magnitude of each derivative is + * equivalent to the derivative on the reference interval. + */ + virtual void + fill_fe_values( + const typename Triangulation::cell_iterator &cell, + const CellSimilarity::Similarity cell_similarity, + const Quadrature &quadrature, + const Mapping &mapping, + const typename Mapping::InternalDataBase &mapping_internal, + const dealii::internal::FEValuesImplementation::MappingRelatedData + &mapping_data, + const typename FiniteElement::InternalDataBase &fe_internal, + dealii::internal::FEValuesImplementation::FiniteElementRelatedData + &output_data) const override; + + using FiniteElement::fill_fe_face_values; + + /** + * This re-implements FiniteElement::fill_fe_face_values() for + * Hermite polynomial bases, for the same reasons as described for + * FEHermite::fill_fe_values(). + */ + virtual void + fill_fe_face_values( + const typename Triangulation::cell_iterator &cell, + const unsigned int face_no, + const hp::QCollection &quadrature, + const Mapping &mapping, + const typename Mapping::InternalDataBase &mapping_internal, + const dealii::internal::FEValuesImplementation::MappingRelatedData + &mapping_data, + const typename FiniteElement::InternalDataBase &fe_internal, + dealii::internal::FEValuesImplementation::FiniteElementRelatedData + &output_data) const override; + + + +protected: + /** + * Wrapper function for FE_Poly::get_data() that ensures relevant + * shape value data is copied to the new data object as well. + */ + virtual std::unique_ptr< + typename FiniteElement::InternalDataBase> + get_data( + const UpdateFlags update_flags, + const Mapping &mapping, + const Quadrature &quadrature, + dealii::internal::FEValuesImplementation::FiniteElementRelatedData + &output_data) const override + { + std::unique_ptr::InternalDataBase> + data_ptr = FE_Poly::get_data(update_flags, + mapping, + quadrature, + output_data); + auto &data = + dynamic_cast::InternalData &>(*data_ptr); + + const unsigned int n_q_points = quadrature.size(); + + if ((update_flags & update_values) && + ((output_data.shape_values.n_rows() > 0) && + (output_data.shape_values.n_cols() == n_q_points))) + data.shape_values = output_data.shape_values; + + return data_ptr; + } + + + +private: + /** + * Variable storing the order of the highest derivative that the current + * FE_Hermite object can enforce continuity for. Here the order + * of derivative only counts in one spatial direction, so the derivative + * $\frac{d^{2}f}{dx \; dy}$ would be counted as a first order derivative + * of $f$, as an example. + */ + unsigned int regularity; + + + +public: + /** + * Returns the regularity of the Hermite FE basis. + */ + inline unsigned int + get_regularity() const + { + return this->regularity; + }; +}; + +/** @} */ + + + +DEAL_II_NAMESPACE_CLOSE + +#endif diff --git a/include/deal.II/fe/fe_update_flags.h b/include/deal.II/fe/fe_update_flags.h index f8e1028884..d8225e631c 100644 --- a/include/deal.II/fe/fe_update_flags.h +++ b/include/deal.II/fe/fe_update_flags.h @@ -211,6 +211,10 @@ enum UpdateFlags * pushed forward to the real cell coordinates. */ update_jacobian_pushed_forward_3rd_derivatives = 0x1000000, + /** + * Update rescaling for Hermite elements. + */ + update_rescale = 0x2000000, //! Values needed for Piola transform /** * Combination of the flags needed for Piola transform of Hdiv elements. @@ -232,7 +236,9 @@ enum UpdateFlags update_covariant_transformation | update_contravariant_transformation | update_transformation_values | update_transformation_gradients | // Volume data - update_volume_elements + update_volume_elements | + // Hermite needs several DOFs to be rescaled each time + update_rescale }; diff --git a/include/deal.II/numerics/matrix_creator.templates.h b/include/deal.II/numerics/matrix_creator.templates.h index 7982242792..ab7e36e9aa 100644 --- a/include/deal.II/numerics/matrix_creator.templates.h +++ b/include/deal.II/numerics/matrix_creator.templates.h @@ -28,6 +28,7 @@ #include #include +#include #include #include @@ -999,7 +1000,9 @@ namespace MatrixCreator const unsigned int n_components = fe.n_components(); const unsigned int n_function_components = boundary_functions.begin()->second->n_components; - const bool fe_is_system = (n_components != 1); + const bool fe_is_system = (n_components != 1); + const bool fe_is_hermite = + (dynamic_cast *>(&fe) != nullptr); const bool fe_is_primitive = fe.is_primitive(); copy_data.cell = cell; @@ -1008,6 +1011,8 @@ namespace MatrixCreator UpdateFlags update_flags = UpdateFlags(update_values | update_JxW_values | update_normal_vectors | update_quadrature_points); + if (fe_is_hermite) + update_flags = update_flags | update_mapping; FEFaceValues fe_values(mapping, fe, q, update_flags); // two variables for the coefficient, one for the two cases @@ -1351,9 +1356,14 @@ namespace MatrixCreator const FiniteElement &fe = dof.get_fe(); const unsigned int n_components = fe.n_components(); + const bool fe_is_hermite = + (dynamic_cast *>(&fe) != nullptr); - Assert(matrix.n() == dof.n_boundary_dofs(boundary_functions), + Assert(fe_is_hermite || + matrix.n() == dof.n_boundary_dofs(boundary_functions), ExcInternalError()); + (void)fe_is_hermite; + Assert(matrix.n() == matrix.m(), ExcInternalError()); Assert(matrix.n() == rhs_vector.size(), ExcInternalError()); Assert(boundary_functions.size() != 0, ExcInternalError()); diff --git a/source/dofs/dof_tools_sparsity.cc b/source/dofs/dof_tools_sparsity.cc index cc1f656cfb..940d24a824 100644 --- a/source/dofs/dof_tools_sparsity.cc +++ b/source/dofs/dof_tools_sparsity.cc @@ -26,6 +26,7 @@ #include #include +#include #include #include @@ -467,12 +468,20 @@ namespace DoFTools Assert(boundary_ids.find(numbers::internal_face_boundary_id) == boundary_ids.end(), (typename DoFHandler::ExcInvalidBoundaryIndicator())); - Assert(sparsity.n_rows() == dof.n_boundary_dofs(boundary_ids), + + const bool fe_is_hermite = (dynamic_cast *>( + &(dof.get_fe())) != nullptr); + + Assert(fe_is_hermite || + sparsity.n_rows() == dof.n_boundary_dofs(boundary_ids), ExcDimensionMismatch(sparsity.n_rows(), dof.n_boundary_dofs(boundary_ids))); - Assert(sparsity.n_cols() == dof.n_boundary_dofs(boundary_ids), + Assert(fe_is_hermite || + sparsity.n_cols() == dof.n_boundary_dofs(boundary_ids), ExcDimensionMismatch(sparsity.n_cols(), dof.n_boundary_dofs(boundary_ids))); + (void)fe_is_hermite; + #ifdef DEBUG if (sparsity.n_rows() != 0) { diff --git a/source/fe/CMakeLists.txt b/source/fe/CMakeLists.txt index 361a293e35..29a20b28dd 100644 --- a/source/fe/CMakeLists.txt +++ b/source/fe/CMakeLists.txt @@ -29,6 +29,7 @@ set(_unity_include_src fe_dg_vector.cc fe_enriched.cc fe_face.cc + fe_hermite.cc fe_nedelec.cc fe_nedelec_sz.cc fe_nothing.cc @@ -100,6 +101,7 @@ set(_inst fe_dg_vector.inst.in fe_face.inst.in fe.inst.in + fe_hermite.inst.in fe_nedelec.inst.in fe_nedelec_sz.inst.in fe_nothing.inst.in diff --git a/source/fe/fe_hermite.cc b/source/fe/fe_hermite.cc new file mode 100644 index 0000000000..92be4a3c56 --- /dev/null +++ b/source/fe/fe_hermite.cc @@ -0,0 +1,972 @@ +// --------------------------------------------------------------------- +// +// Copyright (C) 2023 - 2023 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. +// +// --------------------------------------------------------------------- + +#include + +#include +#include +#include +#include + +#include + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include + +#include + +#include +#include +#include +#include +#include +#include +#include +#include +#include + +#include + +#include +#include +#include +#include +#include +#include + +DEAL_II_NAMESPACE_OPEN + + + +namespace internal +{ + inline unsigned int + get_regularity_from_degree(const unsigned int fe_degree) + { + return (fe_degree == 0) ? 0 : (fe_degree - 1) / 2; + } + + + + inline std::vector + get_hermite_dpo_vector(const unsigned int dim, const unsigned int regularity) + { + std::vector result(dim + 1, 0); + result[0] = Utilities::pow(regularity + 1, dim); + + return result; + } + + + + /* + * Renumbering function. Function needs different levels of for loop nesting + * for different values of dim, so different definitions are used for + * simplicity. + */ + template + void + hermite_hierarchic_to_lexicographic_numbering(const unsigned int regularity, + std::vector &h2l); + + + + template <> + void + hermite_hierarchic_to_lexicographic_numbering<1>( + const unsigned int regularity, + std::vector &h2l) + { + const unsigned int node_dofs_1d = regularity + 1; + + AssertDimension(h2l.size(), 2 * node_dofs_1d); + + // Assign DOFs at vertices + for (unsigned int di = 0; di < 2; ++di) + for (unsigned int i = 0; i < node_dofs_1d; ++i) + h2l[i + di * node_dofs_1d] = i + di * node_dofs_1d; + } + + + + template <> + void + hermite_hierarchic_to_lexicographic_numbering<2>( + const unsigned int regularity, + std::vector &h2l) + { + const unsigned int node_dofs_1d = regularity + 1; + const unsigned int dim_dofs_1d = 2 * node_dofs_1d; + unsigned int offset = 0; + + AssertDimension(h2l.size(), dim_dofs_1d * dim_dofs_1d); + + // Assign DOFs at vertices + for (unsigned int di = 0; di < 2; ++di) + for (unsigned int dj = 0; dj < 2; ++dj) + { + for (unsigned int i = 0; i < node_dofs_1d; ++i) + for (unsigned int j = 0; j < node_dofs_1d; ++j) + h2l[j + i * node_dofs_1d + offset] = + j + i * dim_dofs_1d + (dj + di * dim_dofs_1d) * node_dofs_1d; + + offset += node_dofs_1d * node_dofs_1d; + } + } + + + + template <> + void + hermite_hierarchic_to_lexicographic_numbering<3>( + const unsigned int regularity, + std::vector &h2l) + { + const unsigned int node_dofs_1d = regularity + 1; + const unsigned int node_dofs_2d = node_dofs_1d * node_dofs_1d; + + const unsigned int dim_dofs_1d = 2 * node_dofs_1d; + const unsigned int dim_dofs_2d = dim_dofs_1d * dim_dofs_1d; + + unsigned int offset = 0; + + AssertDimension(h2l.size(), dim_dofs_2d * dim_dofs_1d); + + // Assign DOFs at nodes + for (unsigned int di = 0; di < 2; ++di) + for (unsigned int dj = 0; dj < 2; ++dj) + for (unsigned int dk = 0; dk < 2; ++dk) + { + for (unsigned int i = 0; i < node_dofs_1d; ++i) + for (unsigned int j = 0; j < node_dofs_1d; ++j) + for (unsigned int k = 0; k < node_dofs_1d; ++k) + h2l[k + j * node_dofs_1d + i * node_dofs_2d + offset] = + k + j * dim_dofs_1d + i * dim_dofs_2d + + node_dofs_1d * (dk + dj * dim_dofs_1d + di * dim_dofs_2d); + + offset += node_dofs_1d * node_dofs_2d; + } + } + + + + template + inline std::vector + hermite_hierarchic_to_lexicographic_numbering(const unsigned int regularity) + { + const std::vector dpo = + get_hermite_dpo_vector(dim, regularity); + const dealii::FiniteElementData face_data(dpo, 1, 2 * regularity + 1); + std::vector renumbering(face_data.dofs_per_cell); + + hermite_hierarchic_to_lexicographic_numbering(regularity, renumbering); + + return renumbering; + } + + + + template + std::vector + hermite_lexicographic_to_hierarchic_numbering(const unsigned int regularity) + { + return Utilities::invert_permutation( + hermite_hierarchic_to_lexicographic_numbering(regularity)); + } + + + + template + inline std::vector + hermite_face_lexicographic_to_hierarchic_numbering( + const unsigned int regularity) + { + return (dim > 1) ? hermite_lexicographic_to_hierarchic_numbering( + regularity) : + std::vector(); + } + + + + template + TensorProductPolynomials + get_hermite_polynomials(const unsigned int fe_degree) + { + const unsigned int regularity = get_regularity_from_degree(fe_degree); + + TensorProductPolynomials polynomial_basis( + Polynomials::PolynomialsHermite::generate_complete_basis(regularity)); + + std::vector renumber = + internal::hermite_hierarchic_to_lexicographic_numbering(regularity); + polynomial_basis.set_numbering(renumber); + + return polynomial_basis; + } + + + + /** + * The @p Rescaler class implements the re-scaling of individual shape + * functions required by Hermite bases on non-uniform meshes. The three + * cases for different element dimensions are all defined separately + * due to the requirement for different levels of nesting of for loops. + */ + template + class Rescaler + { + public: + template + void + rescale_fe_hermite_values( + Rescaler<1, spacedim, Number> & /*rescaler*/, + const FE_Hermite<1, spacedim> &fe_herm, + const typename Mapping<1, spacedim>::InternalDataBase &mapping_data, + Table<2, Number> &value_list) + { + unsigned int n_q_points; + double cell_extent = 1.0; + + // Check mapping_data is associated with a compatible mapping class + if (dynamic_cast::InternalData *>( + &mapping_data) != nullptr) + { + const typename MappingCartesian<1>::InternalData *data = + dynamic_cast::InternalData *>( + &mapping_data); + n_q_points = data->quadrature_points.size(); + cell_extent = data->cell_extents[0]; + } + else + Assert(false, ExcInternalError()); + + const unsigned int regularity = fe_herm.get_regularity(); + const unsigned int n_dofs_per_cell = fe_herm.n_dofs_per_cell(); + const unsigned int n_q_points_out = value_list.size(1); + (void)n_dofs_per_cell; + + AssertDimension(value_list.size(0), n_dofs_per_cell); + AssertDimension(n_dofs_per_cell, 2 * regularity + 2); + AssertIndexRange(n_q_points_out, n_q_points + 1); + (void)n_q_points; + + std::vector l2h = + hermite_lexicographic_to_hierarchic_numbering<1>(regularity); + + for (unsigned int q = 0; q < n_q_points_out; ++q) + { + double factor_1 = 1.0; + + for (unsigned int d1 = 0, d2 = regularity + 1; d2 < n_dofs_per_cell; + ++d1, ++d2) + { + /* + * d1 is used to count over indices on the left and d2 counts + * over indices on the right. These variables are used + * to avoid the need to loop over vertices. + */ + value_list(l2h[d1], q) *= factor_1; + value_list(l2h[d2], q) *= factor_1; + + factor_1 *= cell_extent; + } + } + } + + + + template + void + rescale_fe_hermite_values( + Rescaler<2, spacedim, Number> & /*rescaler*/, + const FE_Hermite<2, spacedim> &fe_herm, + const typename Mapping<2, spacedim>::InternalDataBase &mapping_data, + Table<2, Number> &value_list) + { + unsigned int n_q_points; + Tensor<1, 2> cell_extents; + + // Check mapping_data is associated with a compatible mapping class + if (dynamic_cast::InternalData *>( + &mapping_data) != nullptr) + { + const typename MappingCartesian<2>::InternalData *data = + dynamic_cast::InternalData *>( + &mapping_data); + n_q_points = data->quadrature_points.size(); + cell_extents = data->cell_extents; + } + else + Assert(false, ExcInternalError()); + + const unsigned int regularity = fe_herm.get_regularity(); + const unsigned int n_dofs_per_cell = fe_herm.n_dofs_per_cell(); + const unsigned int n_dofs_per_dim = 2 * regularity + 2; + const unsigned int n_q_points_out = value_list.size(1); + (void)n_dofs_per_cell; + + AssertDimension(value_list.size(0), n_dofs_per_cell); + AssertDimension(n_dofs_per_dim * n_dofs_per_dim, n_dofs_per_cell); + AssertIndexRange(n_q_points_out, n_q_points + 1); + (void)n_q_points; + + std::vector l2h = + hermite_lexicographic_to_hierarchic_numbering<2>(regularity); + + AssertDimension(l2h.size(), n_dofs_per_cell); + + for (unsigned int q = 0; q < n_q_points_out; ++q) + { + double factor_2 = 1.0; + + for (unsigned int d3 = 0, d4 = regularity + 1; d4 < n_dofs_per_dim; + ++d3, ++d4) + { + double factor_1 = factor_2; + + for (unsigned int d1 = 0, d2 = regularity + 1; + d2 < n_dofs_per_dim; + ++d1, ++d2) + { + /* + * d1 and d2 represent "left" and "right" in the + * x-direction, d3 and d4 represent "bottom" and "top" + * in the y-direction. As before, this is to avoid looping + * over vertices. + */ + value_list(l2h[d1 + d3 * n_dofs_per_dim], q) *= factor_1; + value_list(l2h[d2 + d3 * n_dofs_per_dim], q) *= factor_1; + value_list(l2h[d1 + d4 * n_dofs_per_dim], q) *= factor_1; + value_list(l2h[d2 + d4 * n_dofs_per_dim], q) *= factor_1; + + factor_1 *= cell_extents[0]; + } + + factor_2 *= cell_extents[1]; + } + } + } + + + + template + void + rescale_fe_hermite_values( + Rescaler<3, spacedim, Number> & /*rescaler*/, + const FE_Hermite<3, spacedim> &fe_herm, + const typename Mapping<3, spacedim>::InternalDataBase &mapping_data, + Table<2, Number> &value_list) + { + unsigned int n_q_points; + Tensor<1, 3> cell_extents; + + // Check mapping_data is associated with a compatible mapping class + if (dynamic_cast::InternalData *>( + &mapping_data) != nullptr) + { + const typename MappingCartesian<3>::InternalData *data = + dynamic_cast::InternalData *>( + &mapping_data); + n_q_points = data->quadrature_points.size(); + cell_extents = data->cell_extents; + } + else + Assert(false, ExcInternalError()); + + const unsigned int regularity = fe_herm.get_regularity(); + const unsigned int n_dofs_per_cell = fe_herm.n_dofs_per_cell(); + const unsigned int n_dofs_per_dim = 2 * regularity + 2; + const unsigned int n_dofs_per_quad = n_dofs_per_dim * n_dofs_per_dim; + const unsigned int n_q_points_out = value_list.size(1); + (void)n_dofs_per_cell; + + AssertDimension(value_list.size(0), n_dofs_per_cell); + AssertDimension(Utilities::pow(n_dofs_per_dim, 3), n_dofs_per_cell); + AssertIndexRange(n_q_points_out, n_q_points + 1); + (void)n_q_points; + + std::vector l2h = + hermite_lexicographic_to_hierarchic_numbering<3>(regularity); + + for (unsigned int q = 0; q < n_q_points_out; ++q) + { + double factor_3 = 1.0; + + for (unsigned int d5 = 0, d6 = regularity + 1; d6 < n_dofs_per_dim; + ++d5, ++d6) + { + double factor_2 = factor_3; + + for (unsigned int d3 = 0, d4 = regularity + 1; + d4 < n_dofs_per_dim; + ++d3, ++d4) + { + double factor_1 = factor_2; + + for (unsigned int d1 = 0, d2 = regularity + 1; + d2 < n_dofs_per_dim; + ++d1, ++d2) + { + /* + * d1, d2: "left" and "right" (x-direction) + * d3, d4: "bottom" and "top" (y-direction) + * d5, d6: "down" and "up" (z-direction) + * This avoids looping over vertices + */ + value_list( + l2h[d1 + d3 * n_dofs_per_dim + d5 * n_dofs_per_quad], + q) *= factor_1; + value_list( + l2h[d2 + d3 * n_dofs_per_dim + d5 * n_dofs_per_quad], + q) *= factor_1; + value_list( + l2h[d1 + d4 * n_dofs_per_dim + d5 * n_dofs_per_quad], + q) *= factor_1; + value_list( + l2h[d2 + d4 * n_dofs_per_dim + d5 * n_dofs_per_quad], + q) *= factor_1; + value_list( + l2h[d1 + d3 * n_dofs_per_dim + d6 * n_dofs_per_quad], + q) *= factor_1; + value_list( + l2h[d2 + d3 * n_dofs_per_dim + d6 * n_dofs_per_quad], + q) *= factor_1; + value_list( + l2h[d1 + d4 * n_dofs_per_dim + d6 * n_dofs_per_quad], + q) *= factor_1; + value_list( + l2h[d2 + d4 * n_dofs_per_dim + d6 * n_dofs_per_quad], + q) *= factor_1; + + factor_1 *= cell_extents[0]; + } + + factor_2 *= cell_extents[1]; + } + + factor_3 *= cell_extents[2]; + } + } + } + }; // class Rescaler +} // namespace internal + + + +// Constructors +template +FE_Hermite::FE_Hermite(const unsigned int fe_degree) + : FE_Poly( + internal::get_hermite_polynomials(fe_degree), + FiniteElementData(internal::get_hermite_dpo_vector( + dim, + internal::get_regularity_from_degree(fe_degree)), + 1, + std::max(1U, fe_degree), + ((fe_degree > 2) ? FiniteElementData::H2 : + FiniteElementData::H1)), + std::vector(Utilities::pow(std::max(2U, fe_degree + 1), dim), + false), + std::vector(Utilities::pow(std::max(2U, fe_degree + 1), + dim), + std::vector(1, true))) + , regularity(internal::get_regularity_from_degree(fe_degree)) +{ + Assert((fe_degree % 2 == 1), + ExcMessage( + "ERROR: The current implementation of Hermite interpolation " + "polynomials is only defined for odd polynomial degrees. Running " + "in release mode will use a polynomial degree of max(1,fe_degree-1) " + "to protect against unexpected internal bugs.")); +} + + + +template +std::string +FE_Hermite::get_name() const +{ + std::ostringstream name_buffer; + name_buffer << "FE_Hermite<" << dim << "," << spacedim << ">(" << this->degree + << ")"; + return name_buffer.str(); +} + + + +template +std::unique_ptr> +FE_Hermite::clone() const +{ + return std::make_unique>(*this); +} + + + +template +UpdateFlags +FE_Hermite::requires_update_flags(const UpdateFlags flags) const +{ + UpdateFlags out = FE_Poly::requires_update_flags(flags); + if (flags & (update_values | update_gradients | update_hessians | + update_3rd_derivatives)) + out |= update_rescale; // since we need to rescale values, gradients, ... + return out; +} + + + +/** + * A large part of the following function is copied from FE_Q_Base. At present + * the case of two Hermite bases meeting is not implemented as it is unlikely + * that two different Hermite bases would be used in an hp method. This may be + * implemented in a later update. + */ +template +std::vector> +FE_Hermite::hp_vertex_dof_identities( + const FiniteElement &fe_other) const +{ + if (dynamic_cast *>(&fe_other) != nullptr) + { + // there should be exactly one single DoF of FE_Q_Base at a vertex, and it + // should have an identical value to the first Hermite DoF + return {{0U, 0U}}; + } + else if (dynamic_cast *>(&fe_other) != + nullptr) + { + // there should be exactly one single DoF of FE_Q_Base at a vertex, and it + // should have an identical value to the first Hermite DoF + return {{0U, 0U}}; + } + else if (dynamic_cast *>(&fe_other) != nullptr) + { + // the FE_Nothing has no degrees of freedom, so there are no + // equivalencies to be recorded + return {}; + } + else if (fe_other.n_unique_faces() == 1 && fe_other.n_dofs_per_face(0) == 0) + { + // if the other element has no elements on faces at all, + // then it would be impossible to enforce any kind of + // continuity even if we knew exactly what kind of element + // we have -- simply because the other element declares + // that it is discontinuous because it has no DoFs on + // its faces. in that case, just state that we have no + // constraints to declare + return {}; + } + else if (const FE_Hermite *fe_herm_other = + dynamic_cast *>(&fe_other)) + { + Assert(false, ExcNotImplemented()); + return {}; + } + else + { + Assert(false, ExcNotImplemented()); + return {}; + } +} + + + +/** + * This function only supplies empty lists of pairs, since Hermite + * stores all DoFs on vertices meaning there is no continuity that + * could be enforced. + */ +template +std::vector> +FE_Hermite::hp_line_dof_identities( + const FiniteElement &fe_other) const +{ + (void)fe_other; + return {}; +} + + + +/** + * Similar to above, no continuity can be enforced on quads + * for Hermite. + */ +template +std::vector> +FE_Hermite::hp_quad_dof_identities( + const FiniteElement &fe_other, + const unsigned int face_no) const +{ + (void)fe_other; + (void)face_no; + return {}; +} + + + +/* + * The layout of this function is largely copied directly from FE_Q, + * however FE_Hermite can behave significantly differently in terms + * of domination due to how the function space is defined */ +template +FiniteElementDomination::Domination +FE_Hermite::compare_for_domination( + const FiniteElement &fe_other, + const unsigned int codim) const +{ + Assert(codim <= dim, ExcImpossibleInDim(dim)); + + if (codim > 0) + if (dynamic_cast *>(&fe_other) != nullptr) + // there are no requirements between continuous and discontinuous elements + return FiniteElementDomination::no_requirements; + + + // vertex/line/face domination + // (if fe_other is not derived from FE_DGQ) + // & cell domination + // ---------------------------------------- + if (const FE_Hermite *fe_hermite_other = + dynamic_cast *>(&fe_other)) + { + if (this->degree < fe_hermite_other->degree) + return FiniteElementDomination::this_element_dominates; + else if (this->degree == fe_hermite_other->degree) + return FiniteElementDomination::either_element_can_dominate; + else + return FiniteElementDomination::other_element_dominates; + } + if (const FE_Q *fe_q_other = + dynamic_cast *>(&fe_other)) + { + if (fe_q_other->degree == 1) + { + if (this->degree == 1) + return FiniteElementDomination::either_element_can_dominate; + else + return FiniteElementDomination::other_element_dominates; + } + else if (this->degree <= fe_q_other->degree) + return FiniteElementDomination::this_element_dominates; + else + return FiniteElementDomination::neither_element_dominates; + } + else if (const FE_SimplexP *fe_p_other = + dynamic_cast *>(&fe_other)) + { + if (fe_p_other->degree == 1) + { + if (this->degree == 1) + return FiniteElementDomination::either_element_can_dominate; + else + return FiniteElementDomination::other_element_dominates; + } + else if (this->degree <= fe_p_other->degree) + return FiniteElementDomination::this_element_dominates; + else + return FiniteElementDomination::neither_element_dominates; + } + else if (const FE_WedgeP *fe_wp_other = + dynamic_cast *>(&fe_other)) + { + if (fe_wp_other->degree == 1) + { + if (this->degree == 1) + return FiniteElementDomination::either_element_can_dominate; + else + return FiniteElementDomination::other_element_dominates; + } + else if (this->degree <= fe_wp_other->degree) + return FiniteElementDomination::this_element_dominates; + else + return FiniteElementDomination::neither_element_dominates; + } + else if (const FE_PyramidP *fe_pp_other = + dynamic_cast *>(&fe_other)) + { + if (fe_pp_other->degree == 1) + { + if (this->degree == 1) + return FiniteElementDomination::either_element_can_dominate; + else + return FiniteElementDomination::other_element_dominates; + } + else if (this->degree <= fe_pp_other->degree) + return FiniteElementDomination::this_element_dominates; + else + return FiniteElementDomination::neither_element_dominates; + } + else if (const FE_Nothing *fe_nothing = + dynamic_cast *>(&fe_other)) + { + if (fe_nothing->is_dominating()) + return FiniteElementDomination::other_element_dominates; + else + // the FE_Nothing has no degrees of freedom and it is typically used + // in a context where we don't require any continuity along the + // interface + return FiniteElementDomination::no_requirements; + } + + Assert(false, ExcNotImplemented()); + return FiniteElementDomination::neither_element_dominates; +} + + + +template +std::vector +FE_Hermite::get_lexicographic_to_hierarchic_numbering() const +{ + return internal::hermite_lexicographic_to_hierarchic_numbering( + this->regularity); +} + + + +template +void +FE_Hermite::fill_fe_values( + const typename Triangulation::cell_iterator &, + const CellSimilarity::Similarity cell_similarity, + const Quadrature & /*quadrature*/, + const Mapping &mapping, + const typename Mapping::InternalDataBase &mapping_internal, + const dealii::internal::FEValuesImplementation::MappingRelatedData + & /*mapping_data*/, + const typename FiniteElement::InternalDataBase &fe_internal, + dealii::internal::FEValuesImplementation::FiniteElementRelatedData + &output_data) const +{ + // Convert data object to internal data for this class. + // Fails with an exception if that is not possible. + Assert( + (dynamic_cast::InternalData *>( + &fe_internal) != nullptr), + ExcInternalError()); + const typename FE_Hermite::InternalData &fe_data = + static_cast::InternalData &>( + fe_internal); + + const UpdateFlags flags(fe_data.update_each); + + // Transform values, gradients and higher derivatives. Values also need to + // be rescaled according the the nodal derivative they correspond to. + if ((flags & update_values) && + (cell_similarity != CellSimilarity::translation)) + { + internal::Rescaler shape_fix; + for (unsigned int i = 0; i < output_data.shape_values.size(0); ++i) + for (unsigned int q = 0; q < output_data.shape_values.size(1); ++q) + output_data.shape_values(i, q) = fe_data.shape_values(i, q); + shape_fix.rescale_fe_hermite_values(shape_fix, + *this, + mapping_internal, + output_data.shape_values); + } + + if ((flags & update_gradients) && + (cell_similarity != CellSimilarity::translation)) + { + for (unsigned int k = 0; k < this->n_dofs_per_cell(); ++k) + mapping.transform(make_array_view(fe_data.shape_gradients, k), + mapping_covariant, + mapping_internal, + make_array_view(output_data.shape_gradients, k)); + + internal::Rescaler> grad_fix; + grad_fix.rescale_fe_hermite_values(grad_fix, + *this, + mapping_internal, + output_data.shape_gradients); + } + + if ((flags & update_hessians) && + (cell_similarity != CellSimilarity::translation)) + { + for (unsigned int k = 0; k < this->n_dofs_per_cell(); ++k) + mapping.transform(make_array_view(fe_data.shape_hessians, k), + mapping_covariant_gradient, + mapping_internal, + make_array_view(output_data.shape_hessians, k)); + + internal::Rescaler> hessian_fix; + hessian_fix.rescale_fe_hermite_values(hessian_fix, + *this, + mapping_internal, + output_data.shape_hessians); + } + + if ((flags & update_3rd_derivatives) && + (cell_similarity != CellSimilarity::translation)) + { + for (unsigned int k = 0; k < this->n_dofs_per_cell(); ++k) + mapping.transform(make_array_view(fe_data.shape_3rd_derivatives, k), + mapping_covariant_hessian, + mapping_internal, + make_array_view(output_data.shape_3rd_derivatives, + k)); + + internal::Rescaler> third_dev_fix; + third_dev_fix.rescale_fe_hermite_values( + third_dev_fix, + *this, + mapping_internal, + output_data.shape_3rd_derivatives); + } +} + + + +template +void +FE_Hermite::fill_fe_face_values( + const typename Triangulation::cell_iterator &cell, + const unsigned int face_no, + const hp::QCollection &quadrature, + const Mapping &mapping, + const typename Mapping::InternalDataBase &mapping_internal, + const dealii::internal::FEValuesImplementation::MappingRelatedData + &, + const typename FiniteElement::InternalDataBase &fe_internal, + dealii::internal::FEValuesImplementation::FiniteElementRelatedData + &output_data) const +{ + /* + * Convert data object to internal data for this class. Fails with + * an exception if that is not possible. + */ + Assert( + (dynamic_cast::InternalData *>( + &fe_internal) != nullptr), + ExcInternalError()); + const typename FE_Hermite::InternalData &fe_data = + static_cast::InternalData &>( + fe_internal); + + Assert((dynamic_cast< + const typename MappingCartesian::InternalData *>( + &mapping_internal) != nullptr), + ExcInternalError()); + + AssertDimension(quadrature.size(), 1U); + + /* + * offset determines which data set to take (all data sets for all + * faces are stored contiguously) + */ + const typename QProjector::DataSetDescriptor offset = + QProjector::DataSetDescriptor::face( + ReferenceCells::get_hypercube(), + face_no, + cell->face_orientation(face_no), + cell->face_flip(face_no), + cell->face_rotation(face_no), + quadrature[0].size()); + + const UpdateFlags flags(fe_data.update_each); + + // Transform values, gradients and higher derivatives. + if (flags & update_values) + { + for (unsigned int k = 0; k < this->dofs_per_cell; ++k) + for (unsigned int i = 0; i < quadrature[0].size(); ++i) + output_data.shape_values(k, i) = fe_data.shape_values[k][i + offset]; + + internal::Rescaler shape_face_fix; + shape_face_fix.rescale_fe_hermite_values(shape_face_fix, + *this, + mapping_internal, + output_data.shape_values); + } + + if (flags & update_gradients) + { + for (unsigned int k = 0; k < this->dofs_per_cell; ++k) + mapping.transform(make_array_view(fe_data.shape_gradients, + k, + offset, + quadrature[0].size()), + mapping_covariant, + mapping_internal, + make_array_view(output_data.shape_gradients, k)); + + internal::Rescaler> grad_face_fix; + grad_face_fix.rescale_fe_hermite_values(grad_face_fix, + *this, + mapping_internal, + output_data.shape_gradients); + } + + if (flags & update_hessians) + { + for (unsigned int k = 0; k < this->dofs_per_cell; ++k) + mapping.transform(make_array_view(fe_data.shape_hessians, + k, + offset, + quadrature[0].size()), + mapping_covariant_gradient, + mapping_internal, + make_array_view(output_data.shape_hessians, k)); + + internal::Rescaler> hessian_face_fix; + hessian_face_fix.rescale_fe_hermite_values(hessian_face_fix, + *this, + mapping_internal, + output_data.shape_hessians); + } + + if (flags & update_3rd_derivatives) + { + for (unsigned int k = 0; k < this->dofs_per_cell; ++k) + mapping.transform(make_array_view(fe_data.shape_3rd_derivatives, + k, + offset, + quadrature[0].size()), + mapping_covariant_hessian, + mapping_internal, + make_array_view(output_data.shape_3rd_derivatives, + k)); + + internal::Rescaler> shape_3rd_face_fix; + shape_3rd_face_fix.rescale_fe_hermite_values( + shape_3rd_face_fix, + *this, + mapping_internal, + output_data.shape_3rd_derivatives); + } +} + + + +// Explicit instantiations +#include "fe_hermite.inst" + +DEAL_II_NAMESPACE_CLOSE diff --git a/source/fe/fe_hermite.inst.in b/source/fe/fe_hermite.inst.in new file mode 100644 index 0000000000..be459e6eec --- /dev/null +++ b/source/fe/fe_hermite.inst.in @@ -0,0 +1,51 @@ +// --------------------------------------------------------------------- +// +// Copyright (C) 2023 - 2023 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. +// +// --------------------------------------------------------------------- + + + +for (deal_II_dimension : DIMENSIONS) + { + template std::vector + internal::hermite_lexicographic_to_hierarchic_numbering( + const unsigned int regularity); + + template std::vector internal:: + hermite_face_lexicographic_to_hierarchic_numbering( + const unsigned int regularity); + } + + + +for (deal_II_dimension : DIMENSIONS; deal_II_space_dimension : SPACE_DIMENSIONS; + tensor_rank : RANKS) + { +#if deal_II_dimension <= deal_II_space_dimension + template class internal::Rescaler< + deal_II_dimension, + deal_II_space_dimension, + Tensor>; +#endif + } + + + +for (deal_II_dimension : DIMENSIONS; deal_II_space_dimension : SPACE_DIMENSIONS) + { +#if deal_II_dimension <= deal_II_space_dimension + template class internal::Rescaler; + template class FE_Hermite; +#endif + } diff --git a/source/fe/fe_q.cc b/source/fe/fe_q.cc index 356da8045e..198e85c6d1 100644 --- a/source/fe/fe_q.cc +++ b/source/fe/fe_q.cc @@ -1,6 +1,6 @@ // --------------------------------------------------------------------- // -// Copyright (C) 2000 - 2021 by the deal.II authors +// Copyright (C) 2000 - 2023 by the deal.II authors // // This file is part of the deal.II library. // @@ -17,6 +17,7 @@ #include #include +#include #include #include #include @@ -251,6 +252,21 @@ FE_Q::compare_for_domination( // interface return FiniteElementDomination::no_requirements; } + else if (const FE_Hermite *fe_hermite_other = + dynamic_cast *>(&fe_other)) + { + if (this->degree == 1) + { + if (fe_hermite_other->degree > 1) + return FiniteElementDomination::this_element_dominates; + else + return FiniteElementDomination::either_element_can_dominate; + } + else if (this->degree >= fe_hermite_other->degree) + return FiniteElementDomination::other_element_dominates; + else + return FiniteElementDomination::neither_element_dominates; + } Assert(false, ExcNotImplemented()); return FiniteElementDomination::neither_element_dominates; diff --git a/source/fe/fe_q_base.cc b/source/fe/fe_q_base.cc index d7ac577997..5c84fc00af 100644 --- a/source/fe/fe_q_base.cc +++ b/source/fe/fe_q_base.cc @@ -26,6 +26,7 @@ #include #include +#include #include #include #include @@ -753,6 +754,15 @@ FE_Q_Base::hp_vertex_dof_identities( // should have identical value return {{0U, 0U}}; } + else if (dynamic_cast *>(&fe_other) != + nullptr) + { + // FE_Hermite will usually have several degrees of freedom on + // each vertex, however only the first one will actually + // correspond to the shape value at the vertex, meaning it's + // the only one of interest for FE_Q_Base + return {{0U, 0U}}; + } else if (dynamic_cast *>(&fe_other) != nullptr) { // the FE_Nothing has no degrees of freedom, so there are no diff --git a/tests/fe/2d_grid_projection_hermite.cc b/tests/fe/2d_grid_projection_hermite.cc new file mode 100644 index 0000000000..e7efc4b125 --- /dev/null +++ b/tests/fe/2d_grid_projection_hermite.cc @@ -0,0 +1,199 @@ +// --------------------------------------------------------------------- +// +// Copyright (C) 2023 - 2023 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. +// +// --------------------------------------------------------------------- + +#include + +#include +#include +#include +#include + +#include +#include +#include + +#include +#include +#include + +#include +#include +#include +#include + +#include +#include +#include +#include +#include +#include +#include + +#include +#include +#include + +#include +#include +#include +#include +#include +#include + +#define PRECISION 8 + +/** + * Test case for Hermite interpolation elements on an regular square grid, + * to check the assembly of the mass matrix works as intended and + * representation of polynomials up to $1D$ degree @p poly_degree by + * FE_Hermite(poly_degree)<\code> is exact. + */ + +using namespace dealii; + +// Define a function to project onto the domain [-1,1]^2 +class Solution : public Function<2> +{ +public: + virtual double + value(const Point<2> &p, unsigned int c = 0) const override + { + (void)c; + return p(0) * p(1); + } + + + std::string + get_function_string() + { + return "XY"; + } +}; + + +void +test_fe_on_domain(const unsigned int regularity) +{ + deallog << std::endl; + char fname[50]; + sprintf(fname, "Cell-%dd-Hermite-%d", 2, 2 * regularity + 1); + deallog.push(fname); + deallog.depth_file(2); + + Triangulation<2> tr; + DoFHandler<2> dof(tr); + + double left = -1.0, right = 1.0; + Point<2> left_point, right_point; + for (unsigned int i = 0; i < 2; ++i) + left_point(i) = left, right_point(i) = right; + GridGenerator::subdivided_hyper_cube(tr, 4, left, right); + + FE_Hermite<2> herm(2 * regularity + 1); + dof.distribute_dofs(herm); + + MappingCartesian<2> mapping; + + QGauss<2> quadr(2 * regularity + 2); + + Vector sol(dof.n_dofs()); + Vector rhs(dof.n_dofs()); + + Solution sol_object; + + AffineConstraints constraints; + constraints.close(); + + DynamicSparsityPattern dsp(dof.n_dofs()); + DoFTools::make_sparsity_pattern(dof, dsp); + SparsityPattern sp; + sp.copy_from(dsp); + + SparseMatrix mass_matrix; + mass_matrix.reinit(sp); + MatrixCreator::create_mass_matrix(mapping, dof, quadr, mass_matrix); + + FEValues<2> fe_herm(mapping, + herm, + quadr, + update_values | update_quadrature_points | + update_JxW_values); + + std::vector local_to_global(herm.n_dofs_per_cell()); + + for (const auto &cell : dof.active_cell_iterators()) + { + fe_herm.reinit(cell); + cell->get_dof_indices(local_to_global); + for (const unsigned int i : fe_herm.dof_indices()) + { + double rhs_temp = 0; + for (const unsigned int q : fe_herm.quadrature_point_indices()) + rhs_temp += fe_herm.shape_value(i, q) * + sol_object.value(fe_herm.quadrature_point(q)) * + fe_herm.JxW(q); + rhs(local_to_global[i]) += rhs_temp; + } + } + + IterationNumberControl solver_control_values(8000, 1e-11); + SolverCG<> solver(solver_control_values); + + solver.solve(mass_matrix, sol, rhs, PreconditionIdentity()); + + double err_sq = 0; + + for (auto &cell : dof.active_cell_iterators()) + { + fe_herm.reinit(cell); + cell->get_dof_indices(local_to_global); + for (const unsigned int q : fe_herm.quadrature_point_indices()) + { + double sol_at_point = 0; + for (const unsigned int i : fe_herm.dof_indices()) + sol_at_point += fe_herm.shape_value(i, q) * sol(local_to_global[i]); + + sol_at_point -= sol_object.value(fe_herm.quadrature_point(q)); + err_sq += sol_at_point * sol_at_point * fe_herm.JxW(q); + } + } + + err_sq = std::sqrt(err_sq); + + deallog << "Test polynomial:" << std::endl; + deallog << sol_object.get_function_string() << std::endl; + deallog << std::endl; + + deallog << "Interpolation error:" << std::endl; + deallog << err_sq << "\n\n" << std::endl; + deallog.pop(); +} + + + +int +main() +{ + std::ofstream logfile("output"); + deallog << std::setprecision(PRECISION) << std::fixed; + deallog.attach(logfile); + MultithreadInfo::set_thread_limit(1); + + test_fe_on_domain(0); + test_fe_on_domain(1); + test_fe_on_domain(2); + + return 0; +} diff --git a/tests/fe/2d_grid_projection_hermite.output b/tests/fe/2d_grid_projection_hermite.output new file mode 100644 index 0000000000..3d90619bda --- /dev/null +++ b/tests/fe/2d_grid_projection_hermite.output @@ -0,0 +1,25 @@ + +DEAL:: +DEAL:Cell-2d-Hermite-1::Test polynomial: +DEAL:Cell-2d-Hermite-1::XY +DEAL:Cell-2d-Hermite-1:: +DEAL:Cell-2d-Hermite-1::Interpolation error: +DEAL:Cell-2d-Hermite-1::0.00000000 + + +DEAL:: +DEAL:Cell-2d-Hermite-3::Test polynomial: +DEAL:Cell-2d-Hermite-3::XY +DEAL:Cell-2d-Hermite-3:: +DEAL:Cell-2d-Hermite-3::Interpolation error: +DEAL:Cell-2d-Hermite-3::0.00000000 + + +DEAL:: +DEAL:Cell-2d-Hermite-5::Test polynomial: +DEAL:Cell-2d-Hermite-5::XY +DEAL:Cell-2d-Hermite-5:: +DEAL:Cell-2d-Hermite-5::Interpolation error: +DEAL:Cell-2d-Hermite-5::0.00000000 + + diff --git a/tests/fe/derivatives.h b/tests/fe/derivatives.h new file mode 100644 index 0000000000..47a7b4165a --- /dev/null +++ b/tests/fe/derivatives.h @@ -0,0 +1,172 @@ +// --------------------------------------------------------------------- +// +// Copyright (C) 2023 - 2023 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. +// +// --------------------------------------------------------------------- + +#ifndef dealii_tests_derivatives_h +#define dealii_tests_derivatives_h + +#include + +#include + +#include +#include + +#include +#include +#include + +#include + +#include +#include +#include +#include + +#include "../tests.h" + +char fname[50]; + + + +////////////////////////////////////////////////////////////////////////////////////////////////////// +// Plot derivatives of the shape functions at the corner nodes of [0,1]^d +// +// Output values on each line take the form +// +// x (y) (z) xderiv_index (yderiv_index) (zderiv_index) value[0]+1. +// value[1]+1. ... +////////////////////////////////////////////////////////////////////////////////////////////////////// + +template +inline void +plot_function_derivatives(Mapping &mapping, + FiniteElement &finel, + const char *name) +{ + Triangulation tr; + DoFHandler dof(tr); + GridGenerator::hyper_cube(tr, 0., 1.); + dof.distribute_dofs(finel); + + typename DoFHandler::cell_iterator c = dof.begin(); + + const unsigned int sz = finel.n_dofs_per_cell(); + const unsigned int degree = finel.tensor_degree(); + const unsigned int max_test_deriv = + std::min(((dim == 1) ? 3 : 1), static_cast(degree - 1) / 2); + const unsigned int div = 1; + + QTrapezoid q; + FEValues fe(mapping, + finel, + q, + UpdateFlags(update_values | update_gradients | + update_hessians | update_3rd_derivatives)); + + sprintf(fname, "Cell-%dd-%s", dim, name); + deallog.push(fname); + + fe.reinit(c); + + unsigned int k = 0; + + // iterate over vertices + for (unsigned int mz = 0; mz <= ((dim > 2) ? div : 0); ++mz) + { + for (unsigned int my = 0; my <= ((dim > 1) ? div : 0); ++my) + { + for (unsigned int mx = 0; mx <= div; ++mx) + { + // iterate over derivatives + for (unsigned int dz = 0; dz <= ((dim > 2) ? max_test_deriv : 0); + ++dz) + { + for (unsigned int dy = 0; + dy <= ((dim > 1) ? max_test_deriv : 0); + ++dy) + { + for (unsigned int dx = 0; dx <= max_test_deriv; ++dx) + { + deallog << q.point(k) << " " << dx; + if (dim > 1) + deallog << " " << dy; + if (dim > 2) + deallog << " " << dz; + + for (unsigned int i = 0; i < sz; ++i) + { + unsigned int deriv_level = dx + dy + dz; + unsigned int entry_1, entry_2, entry_3; + + switch (deriv_level) + { + case 0: + deallog << " " << fe.shape_value(i, k) + 1.; + break; + + case 1: + entry_1 = dy + 2 * dz; + deallog + << " " + << fe.shape_grad(i, k)[entry_1] + 1.; + break; + + case 2: + entry_1 = (dx == 0) ? 1 : 0; + entry_2 = 2 * dz - dy * dz + dy; + deallog + << " " + << fe.shape_hessian(i, + k)[entry_1][entry_2] + + 1.; + break; + + case 3: + if (dz == 1) + entry_1 = 0, entry_2 = 1, + entry_3 = 2; // only occurs for dx=dy=dz=1 + else if (dx * dy == 0) + entry_1 = entry_2 = entry_3 = dy / 3; + else + entry_1 = 0, entry_2 = dy - 1, + entry_3 = 1; + deallog + << " " + << fe.shape_3rd_derivative( + i, k)[entry_1][entry_2][entry_3] + + 1.; + break; + + default: + ExcMessage( + "Requested order of derivative is too high for current implementation."); + break; + } + } + deallog << std::endl; + } + } + } + deallog << std::endl; + ++k; + } + deallog << std::endl; + } + deallog << std::endl; + } + deallog.pop(); +} + +#endif diff --git a/tests/fe/derivatives_hermite.cc b/tests/fe/derivatives_hermite.cc new file mode 100644 index 0000000000..0f3324e9ab --- /dev/null +++ b/tests/fe/derivatives_hermite.cc @@ -0,0 +1,83 @@ +// --------------------------------------------------------------------- +// +// Copyright (C) 2023 - 2023 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. +// +// --------------------------------------------------------------------- + +#include "../tests.h" + +#define PRECISION 8 + + +#include +#include + +#include + +#include "derivatives.h" + + + +/** + * Test case to check the derivative values up to @p regularity + * of FE_Hermite(2 \times regularity + 1)<\code> at the vertices + * of a hypercube reference element are calculated correctly. + * This checks that the basis is assembled correctly and will not + * accidentally enforce discontinuities rather than continuity + * in derivatives across element boundaries. + */ + + +template +void +print_hermite_endpoint_derivatives() +{ + MappingCartesian m; + + FE_Hermite herm_1(1); + plot_function_derivatives(m, herm_1, "Hermite-1"); + + FE_Hermite herm_3(3); + plot_function_derivatives(m, herm_3, "Hermite-3"); + + // Skip the following for dim 3 or greater + if (dim < 3) + { + FE_Hermite herm_5(5); + plot_function_derivatives(m, herm_5, "Hermite-5"); + } + if (dim == 1) + { + FE_Hermite herm_7(7); + plot_function_derivatives(m, herm_7, "Hermite-7"); + + FE_Hermite herm_9(9); + plot_function_derivatives(m, herm_9, "Hermite-9"); + } +} + + + +int +main() +{ + std::ofstream logfile("output"); + + deallog << std::setprecision(PRECISION) << std::fixed; + deallog.attach(logfile); + + print_hermite_endpoint_derivatives<1>(); + print_hermite_endpoint_derivatives<2>(); + print_hermite_endpoint_derivatives<3>(); + + return 0; +} diff --git a/tests/fe/derivatives_hermite.output b/tests/fe/derivatives_hermite.output new file mode 100644 index 0000000000..614e1324f1 --- /dev/null +++ b/tests/fe/derivatives_hermite.output @@ -0,0 +1,206 @@ + +DEAL:Cell-1d-Hermite-1::0.00000000 0 2.00000000 1.00000000 +DEAL:Cell-1d-Hermite-1:: +DEAL:Cell-1d-Hermite-1::1.00000000 0 1.00000000 2.00000000 +DEAL:Cell-1d-Hermite-1:: +DEAL:Cell-1d-Hermite-1:: +DEAL:Cell-1d-Hermite-1:: +DEAL:Cell-1d-Hermite-3::0.00000000 0 2.00000000 1.00000000 1.00000000 1.00000000 +DEAL:Cell-1d-Hermite-3::0.00000000 1 1.00000000 5.00000000 1.00000000 1.00000000 +DEAL:Cell-1d-Hermite-3:: +DEAL:Cell-1d-Hermite-3::1.00000000 0 1.00000000 1.00000000 2.00000000 1.00000000 +DEAL:Cell-1d-Hermite-3::1.00000000 1 1.00000000 1.00000000 1.00000000 5.00000000 +DEAL:Cell-1d-Hermite-3:: +DEAL:Cell-1d-Hermite-3:: +DEAL:Cell-1d-Hermite-3:: +DEAL:Cell-1d-Hermite-5::0.00000000 0 2.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 +DEAL:Cell-1d-Hermite-5::0.00000000 1 1.00000000 5.00000000 1.00000000 1.00000000 1.00000000 1.00000000 +DEAL:Cell-1d-Hermite-5::0.00000000 2 1.00000000 1.00000000 33.00000000 1.00000000 1.00000000 1.00000000 +DEAL:Cell-1d-Hermite-5:: +DEAL:Cell-1d-Hermite-5::1.00000000 0 1.00000000 1.00000000 1.00000000 2.00000000 1.00000000 1.00000000 +DEAL:Cell-1d-Hermite-5::1.00000000 1 1.00000000 1.00000000 1.00000000 1.00000000 5.00000000 1.00000000 +DEAL:Cell-1d-Hermite-5::1.00000000 2 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 33.00000000 +DEAL:Cell-1d-Hermite-5:: +DEAL:Cell-1d-Hermite-5:: +DEAL:Cell-1d-Hermite-5:: +DEAL:Cell-1d-Hermite-7::0.00000000 0 2.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 +DEAL:Cell-1d-Hermite-7::0.00000000 1 1.00000000 5.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 +DEAL:Cell-1d-Hermite-7::0.00000000 2 1.00000000 1.00000000 33.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 +DEAL:Cell-1d-Hermite-7::0.00000000 3 1.00000000 1.00000000 1.00000000 385.00000000 1.00000000 1.00000000 1.00000000 1.00000000 +DEAL:Cell-1d-Hermite-7:: +DEAL:Cell-1d-Hermite-7::1.00000000 0 1.00000000 1.00000000 1.00000000 1.00000000 2.00000000 1.00000000 1.00000000 1.00000000 +DEAL:Cell-1d-Hermite-7::1.00000000 1 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 5.00000000 1.00000000 1.00000000 +DEAL:Cell-1d-Hermite-7::1.00000000 2 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 33.00000000 1.00000000 +DEAL:Cell-1d-Hermite-7::1.00000000 3 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 385.00000000 +DEAL:Cell-1d-Hermite-7:: +DEAL:Cell-1d-Hermite-7:: +DEAL:Cell-1d-Hermite-7:: +DEAL:Cell-1d-Hermite-9::0.00000000 0 2.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 +DEAL:Cell-1d-Hermite-9::0.00000000 1 1.00000000 5.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 +DEAL:Cell-1d-Hermite-9::0.00000000 2 1.00000000 1.00000000 33.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 +DEAL:Cell-1d-Hermite-9::0.00000000 3 1.00000000 1.00000000 1.00000000 385.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 +DEAL:Cell-1d-Hermite-9:: +DEAL:Cell-1d-Hermite-9::1.00000000 0 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 2.00000000 1.00000000 1.00000000 1.00000000 1.00000000 +DEAL:Cell-1d-Hermite-9::1.00000000 1 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 5.00000000 1.00000000 1.00000000 1.00000000 +DEAL:Cell-1d-Hermite-9::1.00000000 2 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 33.00000000 1.00000000 1.00000000 +DEAL:Cell-1d-Hermite-9::1.00000000 3 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 385.00000000 1.00000000 +DEAL:Cell-1d-Hermite-9:: +DEAL:Cell-1d-Hermite-9:: +DEAL:Cell-1d-Hermite-9:: +DEAL:Cell-2d-Hermite-1::0.00000000 0.00000000 0 0 2.00000000 1.00000000 1.00000000 1.00000000 +DEAL:Cell-2d-Hermite-1:: +DEAL:Cell-2d-Hermite-1::1.00000000 0.00000000 0 0 1.00000000 2.00000000 1.00000000 1.00000000 +DEAL:Cell-2d-Hermite-1:: +DEAL:Cell-2d-Hermite-1:: +DEAL:Cell-2d-Hermite-1::0.00000000 1.00000000 0 0 1.00000000 1.00000000 2.00000000 1.00000000 +DEAL:Cell-2d-Hermite-1:: +DEAL:Cell-2d-Hermite-1::1.00000000 1.00000000 0 0 1.00000000 1.00000000 1.00000000 2.00000000 +DEAL:Cell-2d-Hermite-1:: +DEAL:Cell-2d-Hermite-1:: +DEAL:Cell-2d-Hermite-1:: +DEAL:Cell-2d-Hermite-3::0.00000000 0.00000000 0 0 2.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 +DEAL:Cell-2d-Hermite-3::0.00000000 0.00000000 1 0 1.00000000 5.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 +DEAL:Cell-2d-Hermite-3::0.00000000 0.00000000 0 1 1.00000000 1.00000000 5.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 +DEAL:Cell-2d-Hermite-3::0.00000000 0.00000000 1 1 1.00000000 1.00000000 1.00000000 17.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 +DEAL:Cell-2d-Hermite-3:: +DEAL:Cell-2d-Hermite-3::1.00000000 0.00000000 0 0 1.00000000 1.00000000 1.00000000 1.00000000 2.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 +DEAL:Cell-2d-Hermite-3::1.00000000 0.00000000 1 0 1.00000000 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diff --git a/tests/fe/shapes_hermite.cc b/tests/fe/shapes_hermite.cc new file mode 100644 index 0000000000..79adcf11f2 --- /dev/null +++ b/tests/fe/shapes_hermite.cc @@ -0,0 +1,91 @@ +// --------------------------------------------------------------------- +// +// Copyright (C) 2023 - 2023 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. +// +// --------------------------------------------------------------------- + +#include "../tests.h" + +#define PRECISION 8 + + +#include +#include + +#include + +#include "shapes.h" + + + +/* + * Test case on various hypercube reference cells to check that the shape + * values of FE_Hermite(reg)<\code> are correct. Values of + * derivatives at the vertices are checked in the test case + * derivatives_hermite.cc. + */ + +template +void +plot_FE_Hermite_shape_functions() +{ + MappingCartesian m; + + FE_Hermite herm_1(1); + plot_shape_functions(m, herm_1, "Hermite-1"); + plot_face_shape_functions(m, herm_1, "Hermite-1"); + test_compute_functions(m, herm_1, "Hermite-1"); + + FE_Hermite herm_3(3); + plot_shape_functions(m, herm_3, "Hermite-3"); + plot_face_shape_functions(m, herm_3, "Hermite-3"); + test_compute_functions(m, herm_3, "Hermite-3"); + + // skip the following tests to + // reduce run-time + if (dim < 3) + { + FE_Hermite herm_5(5); + plot_shape_functions(m, herm_5, "Hermite-5"); + plot_face_shape_functions(m, herm_5, "Hermite-5"); + test_compute_functions(m, herm_5, "Hermite-5"); + } + + if (dim == 1) + { + FE_Hermite herm_7(7); + plot_shape_functions(m, herm_7, "Hermite-7"); + plot_face_shape_functions(m, herm_7, "Hermite-7"); + test_compute_functions(m, herm_7, "Hermite-7"); + + FE_Hermite herm_9(9); + plot_shape_functions(m, herm_9, "Hermite-9"); + plot_face_shape_functions(m, herm_9, "Hermite-9"); + test_compute_functions(m, herm_9, "Hermite-9"); + }; +} + + + +int +main() +{ + std::ofstream logfile("output"); + deallog << std::setprecision(PRECISION) << std::fixed; + deallog.attach(logfile); + + plot_FE_Hermite_shape_functions<1>(); + plot_FE_Hermite_shape_functions<2>(); + plot_FE_Hermite_shape_functions<3>(); + + return 0; +} diff --git a/tests/fe/shapes_hermite.output b/tests/fe/shapes_hermite.output new file mode 100644 index 0000000000..8fa58e373b --- /dev/null +++ b/tests/fe/shapes_hermite.output @@ -0,0 +1,1102 @@ + +DEAL:Cell1d-Hermite-1::0.00000000 2.00000000 1.00000000 +DEAL:Cell1d-Hermite-1::0.25000000 1.75000000 1.25000000 +DEAL:Cell1d-Hermite-1::0.50000000 1.50000000 1.50000000 +DEAL:Cell1d-Hermite-1::0.75000000 1.25000000 1.75000000 +DEAL:Cell1d-Hermite-1::1.00000000 1.00000000 2.00000000 +DEAL:Cell1d-Hermite-1:: +DEAL:Cell1d-Hermite-1:: 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