#include <deal.II/base/qprojector.h>

Classes
class	DataSetDescriptor

Public Types
using	SubQuadrature = Quadrature< dim - 1 >

Public Member Functions
void	project_to_face (const Quadrature< 0 > &, const unsigned int face_no, std::vector< Point< 1 >> &q_points)

void	project_to_face (const Quadrature< 1 > &quadrature, const unsigned int face_no, std::vector< Point< 2 >> &q_points)

void	project_to_face (const Quadrature< 2 > &quadrature, const unsigned int face_no, std::vector< Point< 3 >> &q_points)

void	project_to_subface (const Quadrature< 0 > &, const unsigned int face_no, const unsigned int, std::vector< Point< 1 >> &q_points, const RefinementCase< 0 > &)

void	project_to_subface (const Quadrature< 1 > &quadrature, const unsigned int face_no, const unsigned int subface_no, std::vector< Point< 2 >> &q_points, const RefinementCase< 1 > &)

void	project_to_subface (const Quadrature< 2 > &quadrature, const unsigned int face_no, const unsigned int subface_no, std::vector< Point< 3 >> &q_points, const RefinementCase< 2 > &ref_case)

Quadrature< 1 >	project_to_all_faces (const Quadrature< 0 > &quadrature)

Quadrature< 2 >	project_to_all_faces (const SubQuadrature &quadrature)

Quadrature< 3 >	project_to_all_faces (const SubQuadrature &quadrature)

Quadrature< 1 >	project_to_all_subfaces (const Quadrature< 0 > &quadrature)

Quadrature< 2 >	project_to_all_subfaces (const SubQuadrature &quadrature)

Quadrature< 3 >	project_to_all_subfaces (const SubQuadrature &quadrature)

Static Public Member Functions
static void	project_to_face (const SubQuadrature &quadrature, const unsigned int face_no, std::vector< Point< dim >> &q_points)

static Quadrature< dim >	project_to_face (const SubQuadrature &quadrature, const unsigned int face_no)

static void	project_to_subface (const SubQuadrature &quadrature, const unsigned int face_no, const unsigned int subface_no, std::vector< Point< dim >> &q_points, const RefinementCase< dim - 1 > &ref_case=RefinementCase< dim - 1 >::isotropic_refinement)

static Quadrature< dim >	project_to_subface (const SubQuadrature &quadrature, const unsigned int face_no, const unsigned int subface_no, const RefinementCase< dim - 1 > &ref_case=RefinementCase< dim - 1 >::isotropic_refinement)

static Quadrature< dim >	project_to_all_faces (const SubQuadrature &quadrature)

static Quadrature< dim >	project_to_all_subfaces (const SubQuadrature &quadrature)

static Quadrature< dim >	project_to_child (const Quadrature< dim > &quadrature, const unsigned int child_no)

static Quadrature< dim >	project_to_all_children (const Quadrature< dim > &quadrature)

static Quadrature< dim >	project_to_line (const Quadrature< 1 > &quadrature, const Point< dim > &p1, const Point< dim > &p2)

Static Private Member Functions
static Quadrature< 2 >	reflect (const Quadrature< 2 > &q)

static Quadrature< 2 >	rotate (const Quadrature< 2 > &q, const unsigned int n_times)

Detailed Description

template<int dim>
class QProjector< dim >

This class is a helper class to facilitate the usage of quadrature formulae on faces or subfaces of cells. It computes the locations of quadrature points on the unit cell from a quadrature object for a manifold of one dimension less than that of the cell and the number of the face. For example, giving the Simpson rule in one dimension and using the project_to_face() function with face number 1, the returned points will be (1,0), (1,0.5) and (1,1). Note that faces have an orientation, so when projecting to face 3, you will get (0,0), (0,0.5) and (0,1), which is in clockwise sense, while for face 1 the points were in counterclockwise sense.

For the projection to subfaces (i.e. to the children of a face of the unit cell), the same applies as above. Note the order in which the children of a face are numbered, which in two dimensions coincides with the orientation of the face.

The second set of functions generates a quadrature formula by projecting a given quadrature rule on all faces and subfaces. This is used in the FEFaceValues and FESubfaceValues classes. Since we now have the quadrature points of all faces and subfaces in one array, we need to have a way to find the starting index of the points and weights corresponding to one face or subface within this array. This is done through the DataSetDescriptor member class.

The different functions are grouped into a common class to avoid putting them into global namespace. However, since they have no local data, all functions are declared static and can be called without creating an object of this class.

For the 3d case, you should note that the orientation of faces is even more intricate than for two dimensions. Quadrature formulae are projected upon the faces in their standard orientation, not to the inside or outside of the hexahedron. To make things more complicated, in 3d we allow faces in two orientations (which can be identified using cell->face_orientation(face)), so we have to project quadrature formula onto faces and subfaces in two orientations. (Refer to the documentation of the Triangulation class for a description of the orientation of the different faces, as well as to the glossary entry on face orientation for more information on this.) The DataSetDescriptor member class is used to identify where each dataset starts.

Author: Wolfgang Bangerth, Guido Kanschat, 1998, 1999, 2003, 2005

Definition at line 78 of file qprojector.h.

Member Typedef Documentation

◆ SubQuadrature

template<int dim>

using QProjector< dim >::SubQuadrature = Quadrature<dim - 1>

Define an alias for a quadrature that acts on an object of one dimension less. For cells, this would then be a face quadrature.

Definition at line 85 of file qprojector.h.

Member Function Documentation

◆ project_to_face() [1/5]

template<int dim>

static void QProjector< dim >::project_to_face	(	const SubQuadrature &	quadrature,
		const unsigned int	face_no,
		std::vector< Point< dim >> &	q_points
	)

static

Compute the quadrature points on the cell if the given quadrature formula is used on face face_no. For further details, see the general doc for this class.

◆ project_to_face() [2/5]

template<int dim>

Quadrature< dim > QProjector< dim >::project_to_face	(	const SubQuadrature &	quadrature,
		const unsigned int	face_no
	)

static

Compute the cell quadrature formula corresponding to using quadrature on face face_no. For further details, see the general doc for this class.

Definition at line 1506 of file quadrature.cc.

◆ project_to_subface() [1/5]

template<int dim>

static void QProjector< dim >::project_to_subface	(	const SubQuadrature &	quadrature,
		const unsigned int	face_no,
		const unsigned int	subface_no,
		std::vector< Point< dim >> &	q_points,
		const RefinementCase< dim - 1 > &	ref_case = `RefinementCase< dim - 1 >::isotropic_refinement`
	)

static

Compute the quadrature points on the cell if the given quadrature formula is used on face face_no, subface number subface_no corresponding to RefineCase::Type ref_case. The last argument is only used in 3D.

Note: Only the points are transformed. The quadrature weights are the same as those of the original rule.

◆ project_to_subface() [2/5]

template<int dim>

Quadrature< dim > QProjector< dim >::project_to_subface	(	const SubQuadrature &	quadrature,
		const unsigned int	face_no,
		const unsigned int	subface_no,
		const RefinementCase< dim - 1 > &	ref_case = `RefinementCase<dim - 1>::isotropic_refinement`
	)

static

Compute the cell quadrature formula corresponding to using quadrature on subface subface_no of face face_no with RefinementCase<dim-1> ref_case. The last argument is only used in 3D.

Note: Only the points are transformed. The quadrature weights are the same as those of the original rule.

Definition at line 1517 of file quadrature.cc.

◆ project_to_all_faces() [1/4]

template<int dim>

static Quadrature<dim> QProjector< dim >::project_to_all_faces ( const SubQuadrature & quadrature )

static

Take a face quadrature formula and generate a cell quadrature formula from it where the quadrature points of the given argument are projected on all faces.

The weights of the new rule are replications of the original weights. Thus, the sum of the weights is not one, but the number of faces, which is the surface of the reference cell.

This in particular allows us to extract a subset of points corresponding to a single face and use it as a quadrature on this face, as is done in FEFaceValues.

Note: In 3D, this function produces eight sets of quadrature points for each face, in order to cope possibly different orientations of the mesh.

◆ project_to_all_subfaces() [1/4]

template<int dim>

static Quadrature<dim> QProjector< dim >::project_to_all_subfaces ( const SubQuadrature & quadrature )

static

Take a face quadrature formula and generate a cell quadrature formula from it where the quadrature points of the given argument are projected on all subfaces.

Like in project_to_all_faces(), the weights of the new rule sum up to the number of faces (not subfaces), which is the surface of the reference cell.

This in particular allows us to extract a subset of points corresponding to a single subface and use it as a quadrature on this face, as is done in FESubfaceValues.

◆ project_to_child()

template<int dim>

Quadrature< dim > QProjector< dim >::project_to_child	(	const Quadrature< dim > &	quadrature,
		const unsigned int	child_no
	)

static

Project a given quadrature formula to a child of a cell. You may want to use this function in case you want to extend an integral only over the area which a potential child would occupy. The child numbering is the same as the children would be numbered upon refinement of the cell.

As integration using this quadrature formula now only extends over a fraction of the cell, the weights of the resulting object are divided by GeometryInfo<dim>::children_per_cell.

Definition at line 1066 of file quadrature.cc.

◆ project_to_all_children()

template<int dim>

Quadrature< dim > QProjector< dim >::project_to_all_children ( const Quadrature< dim > & quadrature )

static

Project a quadrature rule to all children of a cell. Similarly to project_to_all_subfaces(), this function replicates the formula generated by project_to_child() for all children, such that the weights sum up to one, the volume of the total cell again.

The child numbering is the same as the children would be numbered upon refinement of the cell.

Definition at line 1092 of file quadrature.cc.

◆ project_to_line()

template<int dim>

Quadrature< dim > QProjector< dim >::project_to_line	(	const Quadrature< 1 > &	quadrature,
		const Point< dim > &	p1,
		const Point< dim > &	p2
	)

static

Project the one dimensional rule quadrature to the straight line connecting the points p1 and p2.

Definition at line 1118 of file quadrature.cc.

◆ reflect()

template<int dim>

Quadrature< 2 > QProjector< dim >::reflect ( const Quadrature< 2 > & q )

staticprivate

Given a quadrature object in 2d, reflect all quadrature points at the main diagonal and return them with their original weights.

This function is necessary for projecting a 2d quadrature rule onto the faces of a 3d cube, since there we need both orientations.

Definition at line 435 of file quadrature.cc.

◆ rotate()

template<int dim>

Quadrature< 2 > QProjector< dim >::rotate	(	const Quadrature< 2 > &	q,
		const unsigned int	n_times
	)

staticprivate

Given a quadrature object in 2d, rotate all quadrature points by n_times * 90 degrees counterclockwise and return them with their original weights.

This function is necessary for projecting a 2d quadrature rule onto the faces of a 3d cube, since there we need all rotations to account for face_flip and face_rotation of non-standard faces.

Definition at line 453 of file quadrature.cc.

◆ project_to_face() [3/5]

void QProjector< 1 >::project_to_face	(	const Quadrature< 0 > &	,
		const unsigned int	face_no,
		std::vector< Point< 1 >> &	q_points
	)

Definition at line 492 of file quadrature.cc.

◆ project_to_face() [4/5]

void QProjector< 2 >::project_to_face	(	const Quadrature< 1 > &	quadrature,
		const unsigned int	face_no,
		std::vector< Point< 2 >> &	q_points
	)

Definition at line 507 of file quadrature.cc.

◆ project_to_face() [5/5]

void QProjector< 3 >::project_to_face	(	const Quadrature< 2 > &	quadrature,
		const unsigned int	face_no,
		std::vector< Point< 3 >> &	q_points
	)

Definition at line 540 of file quadrature.cc.

◆ project_to_subface() [3/5]

void QProjector< 1 >::project_to_subface	(	const Quadrature< 0 > &	,
		const unsigned int	face_no,
		const unsigned int	,
		std::vector< Point< 1 >> &	q_points,
		const RefinementCase< 0 > &
	)

Definition at line 586 of file quadrature.cc.

◆ project_to_subface() [4/5]

void QProjector< 2 >::project_to_subface	(	const Quadrature< 1 > &	quadrature,
		const unsigned int	face_no,
		const unsigned int	subface_no,
		std::vector< Point< 2 >> &	q_points,
		const RefinementCase< 1 > &
	)

Definition at line 603 of file quadrature.cc.

◆ project_to_subface() [5/5]

void QProjector< 3 >::project_to_subface	(	const Quadrature< 2 > &	quadrature,
		const unsigned int	face_no,
		const unsigned int	subface_no,
		std::vector< Point< 3 >> &	q_points,
		const RefinementCase< 2 > &	ref_case
	)

Definition at line 681 of file quadrature.cc.

◆ project_to_all_faces() [2/4]

Quadrature< 1 > QProjector< 1 >::project_to_all_faces ( const Quadrature< 0 > & quadrature )

Definition at line 767 of file quadrature.cc.

◆ project_to_all_faces() [3/4]

Quadrature< 2 > QProjector< 2 >::project_to_all_faces ( const SubQuadrature & quadrature )

Definition at line 805 of file quadrature.cc.

◆ project_to_all_faces() [4/4]

Quadrature< 3 > QProjector< 3 >::project_to_all_faces ( const SubQuadrature & quadrature )

Definition at line 843 of file quadrature.cc.

◆ project_to_all_subfaces() [2/4]

Quadrature< 1 > QProjector< 1 >::project_to_all_subfaces ( const Quadrature< 0 > & quadrature )

Definition at line 902 of file quadrature.cc.

◆ project_to_all_subfaces() [3/4]

Quadrature< 2 > QProjector< 2 >::project_to_all_subfaces ( const SubQuadrature & quadrature )

Definition at line 945 of file quadrature.cc.

◆ project_to_all_subfaces() [4/4]

Quadrature< 3 > QProjector< 3 >::project_to_all_subfaces ( const SubQuadrature & quadrature )

Definition at line 989 of file quadrature.cc.

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

include/deal.II/base/qprojector.h
source/base/quadrature.cc

Classes

Public Types

Public Member Functions

Static Public Member Functions

Static Private Member Functions

Detailed Description

template<int dim> class QProjector< dim >

Member Typedef Documentation

◆ SubQuadrature

Member Function Documentation

◆ project_to_face() [1/5]

◆ project_to_face() [2/5]

◆ project_to_subface() [1/5]

◆ project_to_subface() [2/5]

◆ project_to_all_faces() [1/4]

◆ project_to_all_subfaces() [1/4]

◆ project_to_child()

◆ project_to_all_children()

◆ project_to_line()

◆ reflect()

◆ rotate()

◆ project_to_face() [3/5]

◆ project_to_face() [4/5]

◆ project_to_face() [5/5]

◆ project_to_subface() [3/5]

◆ project_to_subface() [4/5]

◆ project_to_subface() [5/5]

◆ project_to_all_faces() [2/4]

◆ project_to_all_faces() [3/4]

◆ project_to_all_faces() [4/4]

◆ project_to_all_subfaces() [2/4]

◆ project_to_all_subfaces() [3/4]

◆ project_to_all_subfaces() [4/4]

template<int dim>
class QProjector< dim >