MappingQ< dim, spacedim >::InternalData Class Reference

#include <deal.II/fe/mapping_q.h>

Inheritance diagram for MappingQ< dim, spacedim >::InternalData:

Public Types
using	VectorizedArrayType = VectorizedArray< double, std::min< std::size_t >(VectorizedArray< double >::size(),(dim<=2 ? 2 :4))>

Public Member Functions
	InternalData (const unsigned int polynomial_degree)
void	initialize (const UpdateFlags update_flags, const Quadrature< dim > &quadrature, const unsigned int n_original_q_points)
void	initialize_face (const UpdateFlags update_flags, const Quadrature< dim > &quadrature, const unsigned int n_original_q_points)
void	compute_shape_function_values (const std::vector< Point< dim > > &unit_points)
const double &	shape (const unsigned int qpoint, const unsigned int shape_nr) const
double &	shape (const unsigned int qpoint, const unsigned int shape_nr)
const Tensor< 1, dim > &	derivative (const unsigned int qpoint, const unsigned int shape_nr) const
Tensor< 1, dim > &	derivative (const unsigned int qpoint, const unsigned int shape_nr)
const Tensor< 2, dim > &	second_derivative (const unsigned int qpoint, const unsigned int shape_nr) const
Tensor< 2, dim > &	second_derivative (const unsigned int qpoint, const unsigned int shape_nr)
const Tensor< 3, dim > &	third_derivative (const unsigned int qpoint, const unsigned int shape_nr) const
Tensor< 3, dim > &	third_derivative (const unsigned int qpoint, const unsigned int shape_nr)
const Tensor< 4, dim > &	fourth_derivative (const unsigned int qpoint, const unsigned int shape_nr) const
Tensor< 4, dim > &	fourth_derivative (const unsigned int qpoint, const unsigned int shape_nr)
virtual std::size_t	memory_consumption () const override

Public Attributes
AlignedVector< double >	shape_values
AlignedVector< Tensor< 1, dim > >	shape_derivatives
AlignedVector< Tensor< 2, dim > >	shape_second_derivatives
AlignedVector< Tensor< 3, dim > >	shape_third_derivatives
AlignedVector< Tensor< 4, dim > >	shape_fourth_derivatives
std::array< std::vector< Tensor< 1, dim > >, GeometryInfo< dim >::faces_per_cell *(dim - 1)>	unit_tangentials
const unsigned int	polynomial_degree
const unsigned int	n_shape_functions
QGaussLobatto< 1 >	line_support_points
internal::MatrixFreeFunctions::ShapeInfo< VectorizedArrayType >	shape_info
AlignedVector< VectorizedArrayType >	scratch
bool	tensor_product_quadrature
AlignedVector< DerivativeForm< 1, dim, spacedim > >	covariant
AlignedVector< DerivativeForm< 1, dim, spacedim > >	contravariant
std::vector< AlignedVector< Tensor< 1, spacedim > > >	aux
std::vector< Point< spacedim > >	mapping_support_points
Triangulation< dim, spacedim >::cell_iterator	cell_of_current_support_points
AlignedVector< double >	volume_elements
UpdateFlags	update_each

Detailed Description

template<int dim, int spacedim = dim>
class MappingQ< dim, spacedim >::InternalData

Storage for internal data of polynomial mappings. See Mapping::InternalDataBase for an extensive description.

For the current class, the InternalData class stores data that is computed once when the object is created (in get_data()) as well as data the class wants to store from between the call to fill_fe_values(), fill_fe_face_values(), or fill_fe_subface_values() until possible later calls from the finite element to functions such as transform(). The latter class of member variables are marked as 'mutable'.

Definition at line 273 of file mapping_q.h.

Member Typedef Documentation

VectorizedArrayType

template<int dim, int spacedim = dim>

using MappingQ< dim, spacedim >::InternalData::VectorizedArrayType = VectorizedArray<double, std::min<std::size_t>(VectorizedArray<double>::size(), (dim <= 2 ? 2 : 4))>

For the fast tensor-product path of the MappingQ class, we choose SIMD vectors that are as wide as possible to minimize the number of arithmetic operations. However, we do not want to choose it wider than necessary, e.g., we avoid something like 8-wide AVX-512 when we only compute 3 components of a 3D computation. This is because the additional lanes would not do useful work, but a few operations on very wide vectors can already lead to a lower clock frequency of processors over long time spans (thousands of clock cycles). Hence, we choose 2-wide SIMD for 1D and 2D and 4-wide SIMD for 3D. Note that we do not immediately fall back to no SIMD for 1D because all architectures that support SIMD also support 128-bit vectors (and none is reported to reduce clock frequency for 128-bit SIMD).

Definition at line 489 of file mapping_q.h.

Constructor & Destructor Documentation

InternalData()

template<int dim, int spacedim>

MappingQ< dim, spacedim >::InternalData::InternalData

(

const unsigned int

polynomial_degree

)

Constructor. The argument denotes the polynomial degree of the mapping to which this object will correspond.

Definition at line 52 of file mapping_q.cc.

Member Function Documentation

initialize()

template<int dim, int spacedim>

void MappingQ< dim, spacedim >::InternalData::initialize	(	const UpdateFlags	update_flags,
		const Quadrature< dim > &	quadrature,
		const unsigned int	n_original_q_points
	)

Initialize the object's member variables related to cell data based on the given arguments.

The function also calls compute_shape_function_values() to actually set the member variables related to the values and derivatives of the mapping shape functions.

Definition at line 85 of file mapping_q.cc.

initialize_face()

template<int dim, int spacedim>

void MappingQ< dim, spacedim >::InternalData::initialize_face	(	const UpdateFlags	update_flags,
		const Quadrature< dim > &	quadrature,
		const unsigned int	n_original_q_points
	)

Initialize the object's member variables related to cell and face data based on the given arguments. In order to initialize cell data, this function calls initialize().

Definition at line 215 of file mapping_q.cc.

compute_shape_function_values()

template<int dim, int spacedim>

void MappingQ< dim, spacedim >::InternalData::compute_shape_function_values

(

const std::vector< Point< dim > > &

unit_points

)

Compute the values and/or derivatives of the shape functions used for the mapping.

Which values, derivatives, or higher order derivatives are computed is determined by which of the member arrays have nonzero sizes. They are typically set to their appropriate sizes by the initialize() and initialize_face() functions, which indeed call this function internally. However, it is possible (and at times useful) to do the resizing by hand and then call this function directly. An example is in a Newton iteration where we update the location of a quadrature point (e.g., in MappingQ::transform_real_to_uni_cell()) and need to re- compute the mapping and its derivatives at this location, but have already sized all internal arrays correctly.

Definition at line 271 of file mapping_q.cc.

shape() [1/2]

template<int dim, int spacedim = dim>

const double & MappingQ< dim, spacedim >::InternalData::shape	(	const unsigned int	qpoint,
		const unsigned int	shape_nr
	)		const

Shape function at quadrature point. Shape functions are in tensor product order, so vertices must be reordered to obtain transformation.

shape() [2/2]

template<int dim, int spacedim = dim>

double & MappingQ< dim, spacedim >::InternalData::shape	(	const unsigned int	qpoint,
		const unsigned int	shape_nr
	)

Shape function at quadrature point. See above.

derivative() [1/2]

template<int dim, int spacedim = dim>

const Tensor< 1, dim > & MappingQ< dim, spacedim >::InternalData::derivative	(	const unsigned int	qpoint,
		const unsigned int	shape_nr
	)		const

Gradient of shape function in quadrature point. See above.

derivative() [2/2]

template<int dim, int spacedim = dim>

Tensor< 1, dim > & MappingQ< dim, spacedim >::InternalData::derivative	(	const unsigned int	qpoint,
		const unsigned int	shape_nr
	)

Gradient of shape function in quadrature point. See above.

second_derivative() [1/2]

template<int dim, int spacedim = dim>

const Tensor< 2, dim > & MappingQ< dim, spacedim >::InternalData::second_derivative	(	const unsigned int	qpoint,
		const unsigned int	shape_nr
	)		const

Second derivative of shape function in quadrature point. See above.

second_derivative() [2/2]

template<int dim, int spacedim = dim>

Tensor< 2, dim > & MappingQ< dim, spacedim >::InternalData::second_derivative	(	const unsigned int	qpoint,
		const unsigned int	shape_nr
	)

Second derivative of shape function in quadrature point. See above.

third_derivative() [1/2]

template<int dim, int spacedim = dim>

const Tensor< 3, dim > & MappingQ< dim, spacedim >::InternalData::third_derivative	(	const unsigned int	qpoint,
		const unsigned int	shape_nr
	)		const

third derivative of shape function in quadrature point. See above.

third_derivative() [2/2]

template<int dim, int spacedim = dim>

Tensor< 3, dim > & MappingQ< dim, spacedim >::InternalData::third_derivative	(	const unsigned int	qpoint,
		const unsigned int	shape_nr
	)

third derivative of shape function in quadrature point. See above.

fourth_derivative() [1/2]

template<int dim, int spacedim = dim>

const Tensor< 4, dim > & MappingQ< dim, spacedim >::InternalData::fourth_derivative	(	const unsigned int	qpoint,
		const unsigned int	shape_nr
	)		const

fourth derivative of shape function in quadrature point. See above.

fourth_derivative() [2/2]

template<int dim, int spacedim = dim>

Tensor< 4, dim > & MappingQ< dim, spacedim >::InternalData::fourth_derivative	(	const unsigned int	qpoint,
		const unsigned int	shape_nr
	)

fourth derivative of shape function in quadrature point. See above.

memory_consumption()

template<int dim, int spacedim>

std::size_t MappingQ< dim, spacedim >::InternalData::memory_consumption

overridevirtual

Return an estimate (in bytes) for the memory consumption of this object.

Definition at line 64 of file mapping_q.cc.

Member Data Documentation

shape_values

template<int dim, int spacedim = dim>

AlignedVector<double> MappingQ< dim, spacedim >::InternalData::shape_values

Values of shape functions. Access by function shape.

Computed once.

Definition at line 398 of file mapping_q.h.

shape_derivatives

template<int dim, int spacedim = dim>

AlignedVector<Tensor<1, dim> > MappingQ< dim, spacedim >::InternalData::shape_derivatives

Values of shape function derivatives. Access by function derivative.

Computed once.

Definition at line 405 of file mapping_q.h.

shape_second_derivatives

template<int dim, int spacedim = dim>

AlignedVector<Tensor<2, dim> > MappingQ< dim, spacedim >::InternalData::shape_second_derivatives

Values of shape function second derivatives. Access by function second_derivative.

Computed once.

Definition at line 413 of file mapping_q.h.

shape_third_derivatives

template<int dim, int spacedim = dim>

AlignedVector<Tensor<3, dim> > MappingQ< dim, spacedim >::InternalData::shape_third_derivatives

Values of shape function third derivatives. Access by function second_derivative.

Computed once.

Definition at line 421 of file mapping_q.h.

shape_fourth_derivatives

template<int dim, int spacedim = dim>

AlignedVector<Tensor<4, dim> > MappingQ< dim, spacedim >::InternalData::shape_fourth_derivatives

Values of shape function fourth derivatives. Access by function second_derivative.

Computed once.

Definition at line 429 of file mapping_q.h.

unit_tangentials

template<int dim, int spacedim = dim>

std::array<std::vector<Tensor<1, dim> >, GeometryInfo<dim>::faces_per_cell *(dim - 1)> MappingQ< dim, spacedim >::InternalData::unit_tangentials

Unit tangential vectors. Used for the computation of boundary forms and normal vectors.

This array has (dim-1) * GeometryInfo::faces_per_cell entries. The first GeometryInfo::faces_per_cell contain the vectors in the first tangential direction for each face; the second set of GeometryInfo::faces_per_cell entries contain the vectors in the second tangential direction (only in 3d, since there we have 2 tangential directions per face), etc.

Filled once.

Definition at line 446 of file mapping_q.h.

polynomial_degree

template<int dim, int spacedim = dim>

const unsigned int MappingQ< dim, spacedim >::InternalData::polynomial_degree

The polynomial degree of the mapping. Since the objects here are also used (with minor adjustments) by MappingQ, we need to store this.

Definition at line 452 of file mapping_q.h.

n_shape_functions

template<int dim, int spacedim = dim>

const unsigned int MappingQ< dim, spacedim >::InternalData::n_shape_functions

Number of shape functions. If this is a Q1 mapping, then it is simply the number of vertices per cell. However, since also derived classes use this class (e.g. the Mapping_Q() class), the number of shape functions may also be different.

In general, it is \((p+1)^\text{dim}\), where \(p\) is the polynomial degree of the mapping.

Definition at line 463 of file mapping_q.h.

line_support_points

template<int dim, int spacedim = dim>

QGaussLobatto<1> MappingQ< dim, spacedim >::InternalData::line_support_points

Definition at line 473 of file mapping_q.h.

shape_info

template<int dim, int spacedim = dim>

internal::MatrixFreeFunctions::ShapeInfo<VectorizedArrayType> MappingQ< dim, spacedim >::InternalData::shape_info

In case the quadrature rule given represents a tensor product we need to store the evaluations of the 1d polynomials at the 1d quadrature points. That is what this variable is for.

Definition at line 499 of file mapping_q.h.

scratch

template<int dim, int spacedim = dim>

AlignedVector<VectorizedArrayType> MappingQ< dim, spacedim >::InternalData::scratch

mutable

In case the quadrature rule given represents a tensor product we need to store temporary data in this object.

Definition at line 505 of file mapping_q.h.

tensor_product_quadrature

template<int dim, int spacedim = dim>

bool MappingQ< dim, spacedim >::InternalData::tensor_product_quadrature

Indicates whether the given Quadrature object is a tensor product.

Definition at line 510 of file mapping_q.h.

covariant

template<int dim, int spacedim = dim>

AlignedVector<DerivativeForm<1, dim, spacedim> > MappingQ< dim, spacedim >::InternalData::covariant

mutable

Tensors of covariant transformation at each of the quadrature points. The matrix stored is the Jacobian * G^{-1}, where G = Jacobian^{t} * Jacobian, is the first fundamental form of the map; if dim=spacedim then it reduces to the transpose of the inverse of the Jacobian matrix, which itself is stored in the contravariant field of this structure.

Computed on each cell.

Definition at line 521 of file mapping_q.h.

contravariant

template<int dim, int spacedim = dim>

AlignedVector<DerivativeForm<1, dim, spacedim> > MappingQ< dim, spacedim >::InternalData::contravariant

mutable

Tensors of contravariant transformation at each of the quadrature points. The contravariant matrix is the Jacobian of the transformation, i.e. \(J_{ij}=dx_i/d\hat x_j\).

Computed on each cell.

Definition at line 530 of file mapping_q.h.

aux

template<int dim, int spacedim = dim>

std::vector<AlignedVector<Tensor<1, spacedim> > > MappingQ< dim, spacedim >::InternalData::aux

mutable

Auxiliary vectors for internal use.

Definition at line 535 of file mapping_q.h.

mapping_support_points

template<int dim, int spacedim = dim>

std::vector<Point<spacedim> > MappingQ< dim, spacedim >::InternalData::mapping_support_points

mutable

Stores the support points of the mapping shape functions on the cell_of_current_support_points.

Definition at line 541 of file mapping_q.h.

cell_of_current_support_points

template<int dim, int spacedim = dim>

Triangulation<dim,spacedim>::cell_iterator MappingQ< dim, spacedim >::InternalData::cell_of_current_support_points

mutable

Stores the cell of which the mapping_support_points are stored.

Definition at line 547 of file mapping_q.h.

volume_elements

template<int dim, int spacedim = dim>

AlignedVector<double> MappingQ< dim, spacedim >::InternalData::volume_elements

mutable

The determinant of the Jacobian in each quadrature point. Filled if update_volume_elements.

Definition at line 553 of file mapping_q.h.

update_each

UpdateFlags Mapping< dim, spacedim >::InternalDataBase::update_each

inherited

A set of update flags specifying the kind of information that an implementation of the Mapping interface needs to compute on each cell or face, i.e., in Mapping::fill_fe_values() and friends.

This set of flags is stored here by implementations of Mapping::get_data(), Mapping::get_face_data(), or Mapping::get_subface_data(), and is that subset of the update flags passed to those functions that require re-computation on every cell. (The subset of the flags corresponding to information that can be computed once and for all already at the time of the call to Mapping::get_data() – or an implementation of that interface – need not be stored here because it has already been taken care of.)

Definition at line 659 of file mapping.h.

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The documentation for this class was generated from the following files:

• include/deal.II/fe/mapping_q.h
• source/fe/mapping_q.cc