Definition of the geometry of a single hyperedge. More...

Collaboration diagram for Geometry::UnitCube< hyEdge_dimT, space_dimT, pt_coord_t, ConstructorVecT, hyEdge_index_t >::hyEdge:

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Public Member Functions
	hyEdge (const hyEdge_index_t index, const UnitCube &geometry)
	Construct a orthotopic hyperedge from its index and the surrounding unit hypercube. More...

template<unsigned int n_vec>
SmallMat< space_dimT, n_vec, pt_coord_t >	map_ref_to_phys (const SmallMat< hyEdge_dimT, n_vec, pt_coord_t > &points) const
	Map n_vec points from reference to physical element. More...

template<unsigned int n_vec>
SmallMat< space_dimT, n_vec, pt_coord_t > &	map_ref_to_phys (SmallMat< space_dimT, n_vec, pt_coord_t > &points) const
	Map n_vec points from reference to physical element. More...

SmallVec< space_dimT, pt_coord_t >	span_vec (const unsigned int index) const
	Return matrix column of the affine-linear transformation. More...

const SmallSquareMat< hyEdge_dimT, pt_coord_t >	mat_r () const
	Return reduced matrix R of the QR decomposition of the linear transoformation. More...

const SmallSquareMat< space_dimT, pt_coord_t >	mat_q () const
	Return matrix Q of the QR decomposition of the linear transoformation. More...

pt_coord_t	area () const
	Return Haussdorff/Lebesque measure of the hyperedge. More...

pt_coord_t	face_area (const unsigned int index) const
	Return Haussdorff measure of the specified hypernode. More...

Point< hyEdge_dimT, pt_coord_t >	local_normal (const unsigned int index) const
	Return local normal of given index. More...

Point< space_dimT, pt_coord_t >	inner_normal (const unsigned int index) const
	Return inner normal of given index. More...

Point< space_dimT, pt_coord_t >	face_barycenter (const unsigned int index) const
	Return barycenter of face of given index. More...

Point< space_dimT, pt_coord_t >	outer_normal (const unsigned int index) const
	Return outer normal of given index. More...

template<unsigned int n_sub_points, typename one_dim_float_t >
Point< space_dimT, pt_coord_t >	lexicographic (unsigned int index, const SmallVec< n_sub_points, one_dim_float_t > &points_1d) const
	Return lexicographically ordered equidistant tensorial point of given index. More...

template<unsigned int n_sub_points, typename one_dim_float_t >
Point< space_dimT, pt_coord_t >	boundary_lexicographic (unsigned int index, unsigned int boundary_number, float boundary_scale, const SmallVec< n_sub_points, one_dim_float_t > &points_1d) const
	Return equidistant tensorial point of given index on a given boundary face (slightly moved away from the boundary using boundary_scale), ordered lexicographically. More...

Static Public Member Functions
static constexpr unsigned int	hyEdge_dim ()
	Return dimension of the hyperedge. More...

static constexpr unsigned int	space_dim ()
	Return dimension of the surrounding space. More...

Private Member Functions
template<unsigned int hyEdge_dimTT>
unsigned int	fill_data (unsigned int index, const Wrapper::tpcc_elem_t< hyEdge_dimTT, space_dimT > &elem, const UnitCube &geometry)
	Fill data of hyEdge. More...

void	adapt_data (const Wrapper::tpcc_elem_t< hyEdge_dimT, hyEdge_dimT > &elem, const UnitCube &geometry)
	Refine coarse elememnt. More...

Private Attributes
Point< space_dimT, pt_coord_t >	translation
	Translation vector of the origin. More...

SmallVec< hyEdge_dimT, unsigned int >	dim_indices
	The dimensions in wihch the orthotope evolves. More...

SmallVec< hyEdge_dimT, pt_coord_t >	char_length
	Lengths of the orthotope's lines which are parallel to the `dim_indices` axes. More...

Detailed Description

template<unsigned int hyEdge_dimT, unsigned int space_dimT, typename pt_coord_t = double, typename ConstructorVecT = SmallVec<space_dimT, unsigned int>, typename hyEdge_index_t = unsigned int>
class Geometry::UnitCube< hyEdge_dimT, space_dimT, pt_coord_t, ConstructorVecT, hyEdge_index_t >::hyEdge

Definition of the geometry of a single hyperedge.

A hyperege is uniquely defined by a translation, the spanning dimensions, and the lengths of the lines along the these spanning dimensions.

Authors: Guido Kanschat, Heidelberg University, 2019–2020.; Andreas Rupp, Heidelberg University, 2019–2020.

Constructor & Destructor Documentation

◆ hyEdge()

template<unsigned int hyEdge_dimT, unsigned int space_dimT, typename pt_coord_t = double, typename ConstructorVecT = SmallVec<space_dimT, unsigned int>, typename hyEdge_index_t = unsigned int>

Geometry::UnitCube< hyEdge_dimT, space_dimT, pt_coord_t, ConstructorVecT, hyEdge_index_t >::hyEdge::hyEdge	(	const hyEdge_index_t	index,
		const UnitCube &	geometry
	)

inline

Construct a orthotopic hyperedge from its index and the surrounding unit hypercube.

Parameters

index	The index of the hyperedge to be created.
geometry	The surrounding unit hypercube.

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Member Function Documentation

◆ adapt_data()

template<unsigned int hyEdge_dimT, unsigned int space_dimT, typename pt_coord_t = double, typename ConstructorVecT = SmallVec<space_dimT, unsigned int>, typename hyEdge_index_t = unsigned int>

void Geometry::UnitCube< hyEdge_dimT, space_dimT, pt_coord_t, ConstructorVecT, hyEdge_index_t >::hyEdge::adapt_data	(	const Wrapper::tpcc_elem_t< hyEdge_dimT, hyEdge_dimT > &	elem,
		const UnitCube &	geometry
	)

inlineprivate

Refine coarse elememnt.

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◆ area()

template<unsigned int hyEdge_dimT, unsigned int space_dimT, typename pt_coord_t = double, typename ConstructorVecT = SmallVec<space_dimT, unsigned int>, typename hyEdge_index_t = unsigned int>

pt_coord_t Geometry::UnitCube< hyEdge_dimT, space_dimT, pt_coord_t, ConstructorVecT, hyEdge_index_t >::hyEdge::area ( ) const

inline

Return Haussdorff/Lebesque measure of the hyperedge.

◆ boundary_lexicographic()

template<unsigned int hyEdge_dimT, unsigned int space_dimT, typename pt_coord_t = double, typename ConstructorVecT = SmallVec<space_dimT, unsigned int>, typename hyEdge_index_t = unsigned int>

template<unsigned int n_sub_points, typename one_dim_float_t >

Point<space_dimT, pt_coord_t> Geometry::UnitCube< hyEdge_dimT, space_dimT, pt_coord_t, ConstructorVecT, hyEdge_index_t >::hyEdge::boundary_lexicographic	(	unsigned int	index,
		unsigned int	boundary_number,
		float	boundary_scale,
		const SmallVec< n_sub_points, one_dim_float_t > &	points_1d
	)		const

inline

Return equidistant tensorial point of given index on a given boundary face (slightly moved away from the boundary using boundary_scale), ordered lexicographically.

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◆ face_area()

template<unsigned int hyEdge_dimT, unsigned int space_dimT, typename pt_coord_t = double, typename ConstructorVecT = SmallVec<space_dimT, unsigned int>, typename hyEdge_index_t = unsigned int>

pt_coord_t Geometry::UnitCube< hyEdge_dimT, space_dimT, pt_coord_t, ConstructorVecT, hyEdge_index_t >::hyEdge::face_area ( const unsigned int index ) const

inline

Return Haussdorff measure of the specified hypernode.

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◆ face_barycenter()

template<unsigned int hyEdge_dimT, unsigned int space_dimT, typename pt_coord_t = double, typename ConstructorVecT = SmallVec<space_dimT, unsigned int>, typename hyEdge_index_t = unsigned int>

Point<space_dimT, pt_coord_t> Geometry::UnitCube< hyEdge_dimT, space_dimT, pt_coord_t, ConstructorVecT, hyEdge_index_t >::hyEdge::face_barycenter ( const unsigned int index ) const

inline

Return barycenter of face of given index.

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◆ fill_data()

template<unsigned int hyEdge_dimT, unsigned int space_dimT, typename pt_coord_t = double, typename ConstructorVecT = SmallVec<space_dimT, unsigned int>, typename hyEdge_index_t = unsigned int>

template<unsigned int hyEdge_dimTT>

unsigned int Geometry::UnitCube< hyEdge_dimT, space_dimT, pt_coord_t, ConstructorVecT, hyEdge_index_t >::hyEdge::fill_data	(	unsigned int	index,
		const Wrapper::tpcc_elem_t< hyEdge_dimTT, space_dimT > &	elem,
		const UnitCube &	geometry
	)

inlineprivate

Fill data of hyEdge.

Recursive function that fills translation, dim_indices, and \¢ char_length. To do so, it considers a single hyperedge and takes its zeroth and first faces, and the zeroth and first faces of these faces, and so on to determine the positions of the translation and the other spanning points of the interface.

Template Parameters

hyEdge_dimTT Dimension of the hyperedge or face that is considered.

Parameters

index	Variable that indicates which point is investigated. Supposed to be 0, initially.
elem	Hyperedge or face which is considered.
geometry	The overall unit cube of which the initial elem is a hyperedge of.

Return values

index Index that is used for further (recursive) executions of the function.

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◆ hyEdge_dim()

template<unsigned int hyEdge_dimT, unsigned int space_dimT, typename pt_coord_t = double, typename ConstructorVecT = SmallVec<space_dimT, unsigned int>, typename hyEdge_index_t = unsigned int>

static constexpr unsigned int Geometry::UnitCube< hyEdge_dimT, space_dimT, pt_coord_t, ConstructorVecT, hyEdge_index_t >::hyEdge::hyEdge_dim ( )

inlinestaticconstexpr

Return dimension of the hyperedge.

◆ inner_normal()

template<unsigned int hyEdge_dimT, unsigned int space_dimT, typename pt_coord_t = double, typename ConstructorVecT = SmallVec<space_dimT, unsigned int>, typename hyEdge_index_t = unsigned int>

Point<space_dimT, pt_coord_t> Geometry::UnitCube< hyEdge_dimT, space_dimT, pt_coord_t, ConstructorVecT, hyEdge_index_t >::hyEdge::inner_normal ( const unsigned int index ) const

inline

Return inner normal of given index.

Return outer unit normal with respect to the hypernode which is spanned by all vectors spanning the phyiscal element, but the vector of the given index. The vector has to be in the span of the columns of the local transformation matrix. This is an element of the same dimension as the full space.

◆ lexicographic()

template<unsigned int hyEdge_dimT, unsigned int space_dimT, typename pt_coord_t = double, typename ConstructorVecT = SmallVec<space_dimT, unsigned int>, typename hyEdge_index_t = unsigned int>

template<unsigned int n_sub_points, typename one_dim_float_t >

Point<space_dimT, pt_coord_t> Geometry::UnitCube< hyEdge_dimT, space_dimT, pt_coord_t, ConstructorVecT, hyEdge_index_t >::hyEdge::lexicographic	(	unsigned int	index,
		const SmallVec< n_sub_points, one_dim_float_t > &	points_1d
	)		const

inline

Return lexicographically ordered equidistant tensorial point of given index.

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◆ local_normal()

template<unsigned int hyEdge_dimT, unsigned int space_dimT, typename pt_coord_t = double, typename ConstructorVecT = SmallVec<space_dimT, unsigned int>, typename hyEdge_index_t = unsigned int>

Point<hyEdge_dimT, pt_coord_t> Geometry::UnitCube< hyEdge_dimT, space_dimT, pt_coord_t, ConstructorVecT, hyEdge_index_t >::hyEdge::local_normal ( const unsigned int index ) const

inline

Return local normal of given index.

Return outer unit normal with respect to the hypernode which is spanned by the vectors spanning the phyiscal element, orthogonally projected to a hyEdge_dimT dimensional space, but the vector of the given index. This is an element of the same dimension as the reference element.

◆ map_ref_to_phys() [1/2]

template<unsigned int hyEdge_dimT, unsigned int space_dimT, typename pt_coord_t = double, typename ConstructorVecT = SmallVec<space_dimT, unsigned int>, typename hyEdge_index_t = unsigned int>

template<unsigned int n_vec>

SmallMat<space_dimT, n_vec, pt_coord_t> Geometry::UnitCube< hyEdge_dimT, space_dimT, pt_coord_t, ConstructorVecT, hyEdge_index_t >::hyEdge::map_ref_to_phys ( const SmallMat< hyEdge_dimT, n_vec, pt_coord_t > & points ) const

inline

Map n_vec points from reference to physical element.

Parameters

points Matrix whose columns consist of the points to be mapped.

Return values

phy_points Matrix whose columns consist of the mapped points.

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◆ map_ref_to_phys() [2/2]

template<unsigned int hyEdge_dimT, unsigned int space_dimT, typename pt_coord_t = double, typename ConstructorVecT = SmallVec<space_dimT, unsigned int>, typename hyEdge_index_t = unsigned int>

template<unsigned int n_vec>

SmallMat<space_dimT, n_vec, pt_coord_t>& Geometry::UnitCube< hyEdge_dimT, space_dimT, pt_coord_t, ConstructorVecT, hyEdge_index_t >::hyEdge::map_ref_to_phys ( SmallMat< space_dimT, n_vec, pt_coord_t > & points ) const

inline

Map n_vec points from reference to physical element.

Parameters

points Matrix whose columns consist of the points to be mapped.

Return values

points Matrix whose columns consist of the mapped points.

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◆ mat_q()

template<unsigned int hyEdge_dimT, unsigned int space_dimT, typename pt_coord_t = double, typename ConstructorVecT = SmallVec<space_dimT, unsigned int>, typename hyEdge_index_t = unsigned int>

const SmallSquareMat<space_dimT, pt_coord_t> Geometry::UnitCube< hyEdge_dimT, space_dimT, pt_coord_t, ConstructorVecT, hyEdge_index_t >::hyEdge::mat_q ( ) const

inline

Return matrix Q of the QR decomposition of the linear transoformation.

◆ mat_r()

template<unsigned int hyEdge_dimT, unsigned int space_dimT, typename pt_coord_t = double, typename ConstructorVecT = SmallVec<space_dimT, unsigned int>, typename hyEdge_index_t = unsigned int>

const SmallSquareMat<hyEdge_dimT, pt_coord_t> Geometry::UnitCube< hyEdge_dimT, space_dimT, pt_coord_t, ConstructorVecT, hyEdge_index_t >::hyEdge::mat_r ( ) const

inline

Return reduced matrix R of the QR decomposition of the linear transoformation.

◆ outer_normal()

template<unsigned int hyEdge_dimT, unsigned int space_dimT, typename pt_coord_t = double, typename ConstructorVecT = SmallVec<space_dimT, unsigned int>, typename hyEdge_index_t = unsigned int>

Point<space_dimT, pt_coord_t> Geometry::UnitCube< hyEdge_dimT, space_dimT, pt_coord_t, ConstructorVecT, hyEdge_index_t >::hyEdge::outer_normal ( const unsigned int index ) const

inline

Return outer normal of given index.

Return unit normal with respect to the hyperedge within the full space.

◆ space_dim()

template<unsigned int hyEdge_dimT, unsigned int space_dimT, typename pt_coord_t = double, typename ConstructorVecT = SmallVec<space_dimT, unsigned int>, typename hyEdge_index_t = unsigned int>

static constexpr unsigned int Geometry::UnitCube< hyEdge_dimT, space_dimT, pt_coord_t, ConstructorVecT, hyEdge_index_t >::hyEdge::space_dim ( )

inlinestaticconstexpr

Return dimension of the surrounding space.

◆ span_vec()

template<unsigned int hyEdge_dimT, unsigned int space_dimT, typename pt_coord_t = double, typename ConstructorVecT = SmallVec<space_dimT, unsigned int>, typename hyEdge_index_t = unsigned int>

SmallVec<space_dimT, pt_coord_t> Geometry::UnitCube< hyEdge_dimT, space_dimT, pt_coord_t, ConstructorVecT, hyEdge_index_t >::hyEdge::span_vec ( const unsigned int index ) const

inline

Return matrix column of the affine-linear transformation.

Parameters

index Index of the matrix column to be returned.

Return values

column The specified matrix column.

Member Data Documentation

◆ char_length

template<unsigned int hyEdge_dimT, unsigned int space_dimT, typename pt_coord_t = double, typename ConstructorVecT = SmallVec<space_dimT, unsigned int>, typename hyEdge_index_t = unsigned int>

SmallVec<hyEdge_dimT, pt_coord_t> Geometry::UnitCube< hyEdge_dimT, space_dimT, pt_coord_t, ConstructorVecT, hyEdge_index_t >::hyEdge::char_length

private

Lengths of the orthotope's lines which are parallel to the dim_indices axes.

◆ dim_indices

template<unsigned int hyEdge_dimT, unsigned int space_dimT, typename pt_coord_t = double, typename ConstructorVecT = SmallVec<space_dimT, unsigned int>, typename hyEdge_index_t = unsigned int>

SmallVec<hyEdge_dimT, unsigned int> Geometry::UnitCube< hyEdge_dimT, space_dimT, pt_coord_t, ConstructorVecT, hyEdge_index_t >::hyEdge::dim_indices

private

The dimensions in wihch the orthotope evolves.

◆ translation

template<unsigned int hyEdge_dimT, unsigned int space_dimT, typename pt_coord_t = double, typename ConstructorVecT = SmallVec<space_dimT, unsigned int>, typename hyEdge_index_t = unsigned int>

Point<space_dimT, pt_coord_t> Geometry::UnitCube< hyEdge_dimT, space_dimT, pt_coord_t, ConstructorVecT, hyEdge_index_t >::hyEdge::translation

private

Translation vector of the origin.

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

/home/runner/work/HyperHDG/HyperHDG/include/HyperHDG/geometry/unit_cube.hxx

Public Member Functions

Static Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

template<unsigned int hyEdge_dimT, unsigned int space_dimT, typename pt_coord_t = double, typename ConstructorVecT = SmallVec<space_dimT, unsigned int>, typename hyEdge_index_t = unsigned int> class Geometry::UnitCube< hyEdge_dimT, space_dimT, pt_coord_t, ConstructorVecT, hyEdge_index_t >::hyEdge

Constructor & Destructor Documentation

◆ hyEdge()

Member Function Documentation

◆ adapt_data()

◆ area()

◆ boundary_lexicographic()

◆ face_area()

◆ face_barycenter()

◆ fill_data()

◆ hyEdge_dim()

◆ inner_normal()

◆ lexicographic()

◆ local_normal()

◆ map_ref_to_phys() [1/2]

◆ map_ref_to_phys() [2/2]

◆ mat_q()

◆ mat_r()

◆ outer_normal()

◆ space_dim()

◆ span_vec()

Member Data Documentation

◆ char_length

◆ dim_indices

◆ translation

template<unsigned int hyEdge_dimT, unsigned int space_dimT, typename pt_coord_t = double, typename ConstructorVecT = SmallVec<space_dimT, unsigned int>, typename hyEdge_index_t = unsigned int>
class Geometry::UnitCube< hyEdge_dimT, space_dimT, pt_coord_t, ConstructorVecT, hyEdge_index_t >::hyEdge