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deal.II version GIT relicensing-2167-g9622207b8f 2024-11-21 12:40:00+00:00
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deal.II version GIT relicensing-2167-g9622207b8f 2024-11-21 12:40:00+00:00
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#include <deal.II/matrix_free/shape_info.h>
Public Member Functions | |
| UnivariateShapeData () | |
| std::size_t | memory_consumption () const |
| template<int dim, int spacedim> | |
| void | evaluate_shape_functions (const FiniteElement< dim, spacedim > &fe, const Quadrature< 1 > &quad, const std::vector< unsigned int > &lexicographic, const unsigned int direction) |
| template<int dim, int spacedim> | |
| void | evaluate_collocation_space (const FiniteElement< dim, spacedim > &fe, const Quadrature< 1 > &quad, const std::vector< unsigned int > &lexicographic, const unsigned int direction) |
| bool | check_and_set_shapes_symmetric () |
| bool | check_shapes_collocation () const |
This struct stores the shape functions, their gradients and Hessians evaluated for a one-dimensional section of a tensor product finite element and tensor product quadrature formula in reference coordinates. This data structure also includes the evaluation of quantities at the cell boundary and on the sub-interval \((0, 0.5)\) and \((0.5, 1)\) for face integrals.
Definition at line 133 of file shape_info.h.
| internal::MatrixFreeFunctions::UnivariateShapeData< Number >::UnivariateShapeData | ( | ) |
Empty constructor. Sets default configuration.
| std::size_t internal::MatrixFreeFunctions::UnivariateShapeData< Number >::memory_consumption | ( | ) | const |
Return the memory consumption of this class in bytes.
| void internal::MatrixFreeFunctions::UnivariateShapeData< Number >::evaluate_shape_functions | ( | const FiniteElement< dim, spacedim > & | fe, |
| const Quadrature< 1 > & | quad, | ||
| const std::vector< unsigned int > & | lexicographic, | ||
| const unsigned int | direction | ||
| ) |
Evaluate the finite element shape functions at the points of the given quadrature formula, filling the fields shape_[values,gradients,hessians] and related information.
The two last arguments 'lexicographic' and 'direction' are used to describe the unknowns along a single dimension, and the respective direction of derivatives.
| void internal::MatrixFreeFunctions::UnivariateShapeData< Number >::evaluate_collocation_space | ( | const FiniteElement< dim, spacedim > & | fe, |
| const Quadrature< 1 > & | quad, | ||
| const std::vector< unsigned int > & | lexicographic, | ||
| const unsigned int | direction | ||
| ) |
Evaluate the auxiliary polynomial space associated with the Lagrange polynomials in points of the given quadrature formula, filling the fields shape_[gradients,hessians]_collocation and related information.
| bool internal::MatrixFreeFunctions::UnivariateShapeData< Number >::check_and_set_shapes_symmetric | ( | ) |
Check whether we have symmetries in the shape values. In that case, also fill the shape_???_eo fields.
| bool internal::MatrixFreeFunctions::UnivariateShapeData< Number >::check_shapes_collocation | ( | ) | const |
Check whether symmetric 1d basis functions are such that the shape values form a diagonal matrix, i.e., the nodal points are collocated with the quadrature points. This allows for specialized algorithms that save some operations in the evaluation.
| ElementType internal::MatrixFreeFunctions::UnivariateShapeData< Number >::element_type |
Encodes the type of element detected at construction. FEEvaluation will select the most efficient algorithm based on the given element type.
Definition at line 196 of file shape_info.h.
| AlignedVector<Number> internal::MatrixFreeFunctions::UnivariateShapeData< Number >::shape_values |
Stores the shape values of the 1d finite element evaluated at all 1d quadrature points. The length of this array is n_dofs_1d * n_q_points_1d and quadrature points are the index running fastest.
Definition at line 204 of file shape_info.h.
| AlignedVector<Number> internal::MatrixFreeFunctions::UnivariateShapeData< Number >::shape_gradients |
Stores the shape gradients of the 1d finite element evaluated at all 1d quadrature points. The length of this array is n_dofs_1d * n_q_points_1d and quadrature points are the index running fastest.
Definition at line 212 of file shape_info.h.
| AlignedVector<Number> internal::MatrixFreeFunctions::UnivariateShapeData< Number >::shape_hessians |
Stores the shape Hessians of the 1d finite element evaluated at all 1d quadrature points. The length of this array is n_dofs_1d * n_q_points_1d and quadrature points are the index running fastest.
Definition at line 220 of file shape_info.h.
| AlignedVector<Number> internal::MatrixFreeFunctions::UnivariateShapeData< Number >::shape_gradients_collocation |
Stores the shape gradients of the shape function space associated to the quadrature (collocation), given by FE_DGQ<1>(Quadrature<1>).
Definition at line 226 of file shape_info.h.
| AlignedVector<Number> internal::MatrixFreeFunctions::UnivariateShapeData< Number >::shape_hessians_collocation |
Stores the shape hessians of the shape function space associated to the quadrature (collocation), given by FE_DGQ<1>(Quadrature<1>).
Definition at line 232 of file shape_info.h.
| AlignedVector<Number> internal::MatrixFreeFunctions::UnivariateShapeData< Number >::shape_values_eo |
Stores the shape values in a different format, namely the so-called even-odd scheme where the symmetries in shape_values are used for faster evaluation.
Definition at line 239 of file shape_info.h.
| AlignedVector<Number> internal::MatrixFreeFunctions::UnivariateShapeData< Number >::shape_gradients_eo |
Stores the shape gradients in a different format, namely the so-called even-odd scheme where the symmetries in shape_gradients are used for faster evaluation.
Definition at line 246 of file shape_info.h.
| AlignedVector<Number> internal::MatrixFreeFunctions::UnivariateShapeData< Number >::shape_hessians_eo |
Stores the shape second derivatives in a different format, namely the so-called even-odd scheme where the symmetries in shape_hessians are used for faster evaluation.
Definition at line 253 of file shape_info.h.
| AlignedVector<Number> internal::MatrixFreeFunctions::UnivariateShapeData< Number >::shape_gradients_collocation_eo |
Stores the shape gradients of the shape function space associated to the quadrature (collocation), given by FE_DGQ<1>(Quadrature<1>). This array provides an alternative representation of the shape_gradients_collocation field in the even-odd format.
Definition at line 261 of file shape_info.h.
| AlignedVector<Number> internal::MatrixFreeFunctions::UnivariateShapeData< Number >::shape_hessians_collocation_eo |
Stores the shape hessians of the shape function space associated to the quadrature (collocation), given by FE_DGQ<1>(Quadrature<1>). This array provides an alternative representation of the shape_hessians_collocation field in the even-odd format.
Definition at line 269 of file shape_info.h.
| AlignedVector<Number> internal::MatrixFreeFunctions::UnivariateShapeData< Number >::inverse_shape_values |
Stores the inverse transformation from the data at quadrature points to the basis defined by the shape_values fields. The data at quadrature points is interpreted either implicitly by its polynomial interpolation, or explicitly in terms of separate polynomials such as with the _collocation fields. The size of the array equals the layout of the shape_values array, and it is combined with the shape values array such that this matrix is the pseudo inverse of shape_values. In case the number of 1d quadrature points equals the size of the basis, this array is exactly the inverse of the shape_values array. The length of this array is n_dofs_1d * n_q_points_1d and quadrature points are the index running fastest.
Definition at line 285 of file shape_info.h.
| AlignedVector<Number> internal::MatrixFreeFunctions::UnivariateShapeData< Number >::inverse_shape_values_eo |
Stores the even-odd variant of the inverse_shape_values field.
Definition at line 290 of file shape_info.h.
| std::array<AlignedVector<Number>, 2> internal::MatrixFreeFunctions::UnivariateShapeData< Number >::shape_data_on_face |
Collects all data of 1d shape values evaluated at the point 0 and 1 (the vertices) in one data structure. The sorting of data is to start with the values, then gradients, then second derivatives.
Definition at line 297 of file shape_info.h.
| std::array<AlignedVector<Number>, 2> internal::MatrixFreeFunctions::UnivariateShapeData< Number >::quadrature_data_on_face |
Collects all data of 1d nodal shape values (defined by the Lagrange polynomials in the points of the quadrature rule) evaluated at the point 0 and 1 (the vertices) in one data structure.
This data structure can be used to interpolate from the cell to the face quadrature points. The sorting of data is to start with the values, then gradients, then second derivatives.
Definition at line 308 of file shape_info.h.
| std::array<AlignedVector<Number>, 2> internal::MatrixFreeFunctions::UnivariateShapeData< Number >::values_within_subface |
Stores one-dimensional values of shape functions on subface. Since there are two subfaces, store two variants.
Definition at line 314 of file shape_info.h.
| std::array<AlignedVector<Number>, 2> internal::MatrixFreeFunctions::UnivariateShapeData< Number >::gradients_within_subface |
Stores one-dimensional gradients of shape functions on subface. Since there are two subfaces, store two variants.
Definition at line 320 of file shape_info.h.
| std::array<AlignedVector<Number>, 2> internal::MatrixFreeFunctions::UnivariateShapeData< Number >::hessians_within_subface |
Stores one-dimensional gradients of shape functions on subface. Since there are two subfaces, store two variants.
Definition at line 326 of file shape_info.h.
| std::array<AlignedVector<Number>, 2> internal::MatrixFreeFunctions::UnivariateShapeData< Number >::subface_interpolation_matrices |
A 1d subface interpolation matrices to the first and second quadrant. This data structure is only set up for FE_Q for dim > 1.
Definition at line 332 of file shape_info.h.
| std::array<AlignedVector<typename ::internal::VectorizedArrayTrait< Number>::value_type>, 2> internal::MatrixFreeFunctions::UnivariateShapeData< Number >::subface_interpolation_matrices_scalar |
Same as above but stored in a scalar format independent of the type of Number
Definition at line 341 of file shape_info.h.
| Quadrature<1> internal::MatrixFreeFunctions::UnivariateShapeData< Number >::quadrature |
We store a copy of the one-dimensional quadrature formula used for initialization.
Definition at line 347 of file shape_info.h.
| unsigned int internal::MatrixFreeFunctions::UnivariateShapeData< Number >::fe_degree |
Stores the degree of the element.
Definition at line 352 of file shape_info.h.
| unsigned int internal::MatrixFreeFunctions::UnivariateShapeData< Number >::n_q_points_1d |
Stores the number of quadrature points per dimension.
Definition at line 357 of file shape_info.h.
| bool internal::MatrixFreeFunctions::UnivariateShapeData< Number >::nodal_at_cell_boundaries |
Indicates whether the basis functions are nodal in 0 and 1, i.e., the end points of the unit cell.
Definition at line 363 of file shape_info.h.
| Table<3, Number> internal::MatrixFreeFunctions::UnivariateShapeData< Number >::shape_values_face |
Stores the shape values of the finite element evaluated at all quadrature points for all faces and orientations (no tensor-product structure exploited).
Definition at line 370 of file shape_info.h.
| Table<3, Number> internal::MatrixFreeFunctions::UnivariateShapeData< Number >::shape_gradients_face |
Stores the shape gradients of the finite element evaluated at all quadrature points for all faces, orientations, and directions (no tensor-product structure exploited).
Definition at line 377 of file shape_info.h.
1.9.8