Reference documentation for deal.II version 9.3.3
internal::MatrixFreeFunctions::UnivariateShapeData< Number > Struct Template Reference

#include <deal.II/matrix_free/shape_info.h>

Inheritance diagram for internal::MatrixFreeFunctions::UnivariateShapeData< Number >:
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## Public Member Functions

UnivariateShapeData ()

std::size_t memory_consumption () const

## Public Attributes

ElementType element_type

AlignedVector< Number > shape_values

AlignedVector< Number > shape_hessians

AlignedVector< Number > shape_hessians_collocation

AlignedVector< Number > shape_values_eo

AlignedVector< Number > shape_hessians_eo

AlignedVector< Number > shape_hessians_collocation_eo

AlignedVector< Number > inverse_shape_values

AlignedVector< Number > inverse_shape_values_eo

std::array< AlignedVector< Number >, 2 > shape_data_on_face

std::array< AlignedVector< Number >, 2 > quadrature_data_on_face

std::array< AlignedVector< Number >, 2 > values_within_subface

std::array< AlignedVector< Number >, 2 > gradients_within_subface

std::array< AlignedVector< Number >, 2 > hessians_within_subface

unsigned int fe_degree

unsigned int n_q_points_1d

bool nodal_at_cell_boundaries

Table< 3, Number > shape_values_face

## Detailed Description

template<typename Number>
struct internal::MatrixFreeFunctions::UnivariateShapeData< Number >

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 113 of file shape_info.h.

## ◆ UnivariateShapeData()

template<typename Number >
 internal::MatrixFreeFunctions::UnivariateShapeData< Number >::UnivariateShapeData ( )

Empty constructor. Sets default configuration.

## ◆ memory_consumption()

template<typename Number >
 std::size_t internal::MatrixFreeFunctions::UnivariateShapeData< Number >::memory_consumption ( ) const

Return the memory consumption of this class in bytes.

## ◆ element_type

template<typename Number >
 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 131 of file shape_info.h.

## ◆ shape_values

template<typename Number >
 AlignedVector internal::MatrixFreeFunctions::UnivariateShapeData< Number >::shape_values

Stores the shape values of the 1D finite element evaluated on 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 139 of file shape_info.h.

template<typename Number >

Stores the shape gradients of the 1D finite element evaluated on 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 147 of file shape_info.h.

## ◆ shape_hessians

template<typename Number >
 AlignedVector internal::MatrixFreeFunctions::UnivariateShapeData< Number >::shape_hessians

Stores the shape Hessians of the 1D finite element evaluated on 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 155 of file shape_info.h.

template<typename Number >

Stores the shape gradients of the shape function space associated to the quadrature (collocation), given by FE_DGQ<1>(Quadrature<1>).

Definition at line 161 of file shape_info.h.

## ◆ shape_hessians_collocation

template<typename Number >
 AlignedVector 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 167 of file shape_info.h.

## ◆ shape_values_eo

template<typename Number >
 AlignedVector 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 174 of file shape_info.h.

template<typename Number >

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 181 of file shape_info.h.

## ◆ shape_hessians_eo

template<typename Number >
 AlignedVector 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 188 of file shape_info.h.

template<typename Number >

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 196 of file shape_info.h.

## ◆ shape_hessians_collocation_eo

template<typename Number >
 AlignedVector 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 204 of file shape_info.h.

## ◆ inverse_shape_values

template<typename Number >
 AlignedVector 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 220 of file shape_info.h.

## ◆ inverse_shape_values_eo

template<typename Number >
 AlignedVector internal::MatrixFreeFunctions::UnivariateShapeData< Number >::inverse_shape_values_eo

Stores the even-odd variant of the inverse_shape_values field.

Definition at line 225 of file shape_info.h.

## ◆ shape_data_on_face

template<typename Number >
 std::array, 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. Sorting is first the values, then gradients, then second derivatives.

Definition at line 232 of file shape_info.h.

template<typename Number >

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.

Note
In contrast to shape_data_on_face, only the vales are evaluated.

Definition at line 244 of file shape_info.h.

## ◆ values_within_subface

template<typename Number >
 std::array, 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 250 of file shape_info.h.

template<typename Number >

Stores one-dimensional gradients of shape functions on subface. Since there are two subfaces, store two variants.

Definition at line 256 of file shape_info.h.

## ◆ hessians_within_subface

template<typename Number >
 std::array, 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 262 of file shape_info.h.

template<typename Number >

We store a copy of the one-dimensional quadrature formula used for initialization.

Definition at line 268 of file shape_info.h.

## ◆ fe_degree

template<typename Number >
 unsigned int internal::MatrixFreeFunctions::UnivariateShapeData< Number >::fe_degree

Stores the degree of the element.

Definition at line 273 of file shape_info.h.

## ◆ n_q_points_1d

template<typename Number >
 unsigned int internal::MatrixFreeFunctions::UnivariateShapeData< Number >::n_q_points_1d

Stores the number of quadrature points per dimension.

Definition at line 278 of file shape_info.h.

## ◆ nodal_at_cell_boundaries

template<typename Number >
 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 284 of file shape_info.h.

## ◆ shape_values_face

template<typename Number >
 Table<3, Number> internal::MatrixFreeFunctions::UnivariateShapeData< Number >::shape_values_face

Stores the shape values of the finite element evaluated on all quadrature points for all faces and orientations (no tensor-product structure exploited).

Definition at line 291 of file shape_info.h.