#include <ref_element.hh>

Collaboration diagram for RefElement< dim >:

[legend]

Public Types
typedef arma::vec::fixed< dim >	LocalPoint

typedef Armor::ArmaVec< double, dim+1 >	BaryPoint

typedef Armor::ArmaVec< double, dim >	FaceBaryPoint

typedef std::vector< BaryPoint >	BarycentricUnitVec

typedef const std::vector< LocalPoint > &	CentersList

Public Member Functions
	DECLARE_EXCEPTION (ExcInvalidPermutation,<< "Side permutation not found.\n")

const std::vector< std::vector< std::vector< unsigned int > > >	nodes_of_subelements

const std::vector< std::vector< std::vector< unsigned int > > >	nodes_of_subelements

const std::vector< std::vector< std::vector< unsigned int > > >	nodes_of_subelements

const std::vector< std::vector< std::vector< unsigned int > > >	nodes_of_subelements

vec::fixed< 1 >	normal_vector (unsigned int sid)

vec::fixed< 2 >	normal_vector (unsigned int sid)

vec::fixed< 3 >	normal_vector (unsigned int sid)

auto	clip (const BaryPoint &barycentric) -> BaryPoint

double	side_measure (unsigned int sid)

double	side_measure (unsigned int sid)

double	side_measure (unsigned int sid)

unsigned int	line_between_faces (unsigned int f1, unsigned int f2)

const std::vector< std::vector< std::vector< unsigned int > > >	nodes_of_subelements

const std::vector< std::vector< std::vector< unsigned int > > >	nodes_of_subelements

const std::vector< std::vector< std::vector< unsigned int > > >	nodes_of_subelements

const std::vector< std::vector< std::vector< unsigned int > > >	nodes_of_subelements

template<unsigned int subdim>
auto	interpolate (arma::vec::fixed< subdim+1 > coord, int sub_simplex_idx) -> BaryPoint

unsigned int	count ()

unsigned int	count ()

unsigned int	count ()

unsigned int	count ()

unsigned int	count ()

unsigned int	count ()

unsigned int	count ()

unsigned int	count ()

unsigned int	count ()

unsigned int	count ()

unsigned int	count ()

unsigned int	count ()

unsigned int	count ()

unsigned int	count ()

unsigned int	count ()

unsigned int	count ()

template<template< unsigned int OutDim, unsigned int InDim > class TInteraction, unsigned int OutDim, unsigned int InDim>
const IdxVector<(InDim >OutDim ? InDim+1 :dim-InDim) >	interact (TInteraction< OutDim, InDim > interaction, bool inv)

Static Public Member Functions
static LocalPoint	node_coords (unsigned int nid)

static LocalPoint	normal_vector (unsigned int sid)

static BaryPoint	clip (const BaryPoint &barycentric)

static unsigned int	normal_orientation (unsigned int sid)

static double	side_measure (unsigned int sid)

static unsigned int	oposite_node (unsigned int sid)

static unsigned int	line_between_faces (unsigned int f1, unsigned int f2)

static BaryPoint	local_to_bary (const LocalPoint &lp)
	Converts from local to barycentric coordinates. More...

static LocalPoint	bary_to_local (const BaryPoint &bp)
	Converts from barycentric to local coordinates. More...

static BarycentricUnitVec	make_bary_unit_vec ()

static FaceBaryPoint	barycentric_on_face (const BaryPoint &barycentric, unsigned int i_face)

static CentersList	centers_of_subelements (unsigned int sub_dim)

static std::pair< unsigned int, unsigned int >	zeros_positions (const BaryPoint &barycentric, double tolerance=std::numeric_limits< double >::epsilon() *2)

template<unsigned int subdim>
static unsigned int	topology_idx (unsigned int zeros_positions)

template<unsigned int subdim>
static unsigned int	count ()

template<unsigned int subdim>
static arma::mat::fixed< dim+1, subdim+1 >	bary_coords (unsigned int sid)

template<unsigned int subdim>
static BaryPoint	interpolate (arma::vec::fixed< subdim+1 > coord, int sub_simplex_idx)

static BaryPoint	line_barycentric_interpolation (BaryPoint first_coords, BaryPoint second_coords, double first_theta, double second_theta, double theta)

template<template< unsigned int OutDim, unsigned int InDim > class TInteraction, unsigned int OutDim, unsigned int InDim>
static const IdxVector<(InDim >OutDim ? InDim+1 :dim-InDim) >	interact (TInteraction< OutDim, InDim > interaction, bool inv=false)

Static Public Attributes
static const unsigned int	n_sides = dim + 1
	Number of sides. More...

static const unsigned int	n_nodes = dim + 1
	Number of nodes. More...

static const unsigned int	n_nodes_per_side = dim
	Number of nodes on one side. More...

static const unsigned int	n_lines_per_node = dim
	Number of lines with one common node. More...

static const unsigned int	n_nodes_per_line = 2
	Number of nodes in one line. More...

static const unsigned int	n_sides_per_line = 2
	Number of sides with one common line. `dim` == 3. More...

static const unsigned int	n_sides_per_node = dim
	Number of sides with one common line. More...

static const unsigned int	n_lines_per_side = (unsigned int)((dim * (dim - 1)) / 2)
	Number of lines on boundary of one side. More...

static const unsigned int	n_lines = (unsigned int)((dim * (dim + 1)) / 2)
	Number of lines, i.e. `object` of dimension `dim-2` on the boundary of the reference element. More...

static const std::vector< std::vector< std::vector< unsigned int > > >	nodes_of_subelements

Private Member Functions
const std::vector< IdxVector< 2 > >	line_nodes_

const std::vector< IdxVector< 2 > >	line_nodes_

const std::vector< IdxVector< 2 > >	line_nodes_

const std::vector< IdxVector< 1 > >	node_lines_

const std::vector< IdxVector< 2 > >	node_lines_

const std::vector< IdxVector< 3 > >	side_nodes_

const std::vector< IdxVector< 3 > >	side_lines_

const IdxVector< 1 >	topology_zeros_ []

const IdxVector< 2 >	topology_zeros_ []

const IdxVector< 3 >	topology_zeros_ []

const IdxVector< 6 >	topology_zeros_ []

const IdxVector< 1 >	topology_zeros_ []

const IdxVector< 2 >	topology_zeros_ []

const IdxVector< 3 >	topology_zeros_ []

const IdxVector< 6 >	topology_zeros_ []

const std::vector< IdxVector< 2 > >	line_nodes_

const std::vector< IdxVector< 2 > >	line_nodes_

const std::vector< IdxVector< 2 > >	line_nodes_

const std::vector< IdxVector< 1 > >	node_lines_

const std::vector< IdxVector< 2 > >	node_lines_

const std::vector< IdxVector< 3 > >	node_lines_

const std::vector< IdxVector< 3 > >	side_nodes_

const std::vector< IdxVector< 3 > >	node_sides_

const std::vector< IdxVector< 2 > >	line_sides_

const std::vector< IdxVector< 3 > >	side_lines_

const IdxVector< 1 >	topology_zeros_ []

const IdxVector< 2 >	topology_zeros_ []

const IdxVector< 3 >	topology_zeros_ []

const IdxVector< 6 >	topology_zeros_ []

const IdxVector< 1 >	interact_ (unsigned int i, bool inv)
	This function is for "side_nodes" - for given side, give me nodes (0->0, 1->1). More...

const IdxVector< 2 >	interact_ (unsigned int i, bool inv)
	For line i {0}, give me indices of its nodes. More...

const IdxVector< 2 >	interact_ (unsigned int i, bool inv)
	For line i {0,1,2}, give me indices of its nodes. More...

const IdxVector< 2 >	interact_ (unsigned int i, bool inv)
	For line i {0,1,2,3,4,5}, give me indices of its nodes. More...

const IdxVector< 1 >	interact_ (unsigned int i, bool inv)
	For node i {0,1}, give me indices of lines. More...

const IdxVector< 2 >	interact_ (unsigned int i, bool inv)
	For node i {0,1,2}, give me indices of lines. More...

const IdxVector< 3 >	interact_ (unsigned int i, bool inv)
	For node i {0,1,2,3}, give me indices of lines. More...

const IdxVector< 3 >	interact_ (unsigned int i, bool inv)
	For side i {0,1,2}, give me indices of its nodes. More...

const IdxVector< 3 >	interact_ (unsigned int i, bool inv)
	For node i {0,1,2,3}, give me indices of sides. More...

const IdxVector< 2 >	interact_ (unsigned int i, bool inv)
	For line i {0,1,2,3}, give me indices of sides. More...

const IdxVector< 3 >	interact_ (unsigned int i, bool inv)
	For side i {0,1,2}, give me indices of its lines. More...

Static Private Member Functions
template<unsigned int OutDim, unsigned int InDim>
static const IdxVector<(InDim >OutDim ? InDim+1 :dim-InDim) >	interact_ (unsigned int index, bool inv=false)
	Internal part of the interact function. More...

Static Private Attributes
static const std::vector< IdxVector< n_nodes_per_line > >	line_nodes_
	[n_lines] For given line, returns its nodes indices. More...

static const std::vector< IdxVector< n_lines_per_node > >	node_lines_
	[n_nodes] For given node, returns lines indices. More...

static const std::vector< IdxVector< n_nodes_per_side > >	side_nodes_
	[n_sides] For given side, returns nodes indices. For `dim` == 3. More...

static const std::vector< IdxVector< n_sides_per_node > >	node_sides_
	[n_nodes] For given node, returns sides indices. For `dim` == 3. More...

static const std::vector< IdxVector< n_sides_per_line > >	line_sides_
	[n_lines] For given line, returns sides indices. For `dim` == 3. More...

static const std::vector< IdxVector< n_lines_per_side > >	side_lines_
	[n_sides] For given side, returns lines indices. For `dim` == 3. More...

static const IdxVector<(n_lines > n_nodes) ? n_lines :n_nodes >	topology_zeros_ [dim+1]

Detailed Description

template<unsigned int dim>
class RefElement< dim >

Definition at line 339 of file ref_element.hh.

Member Typedef Documentation

◆ BarycentricUnitVec

template<unsigned int dim>

typedef std::vector<BaryPoint> RefElement< dim >::BarycentricUnitVec

Definition at line 428 of file ref_element.hh.

◆ BaryPoint

template<unsigned int dim>

typedef Armor::ArmaVec<double, dim+1> RefElement< dim >::BaryPoint

Barycentric coordinates.

e.g. coordinates (a,b,c) on triangle with vertices X, Y, Z represents a point: a*X+b*Y+c*Z

Definition at line 349 of file ref_element.hh.

◆ CentersList

template<unsigned int dim>

typedef const std::vector<LocalPoint>& RefElement< dim >::CentersList

Definition at line 443 of file ref_element.hh.

◆ FaceBaryPoint

template<unsigned int dim>

typedef Armor::ArmaVec<double, dim> RefElement< dim >::FaceBaryPoint

Definition at line 350 of file ref_element.hh.

◆ LocalPoint

template<unsigned int dim>

typedef arma::vec::fixed<dim> RefElement< dim >::LocalPoint

Definition at line 342 of file ref_element.hh.

Member Function Documentation

◆ bary_coords()

template<unsigned int dim>

template<unsigned int subdim>

arma::mat::fixed< dim+1, subdim+1 > RefElement< dim >::bary_coords ( unsigned int sid )

inlinestatic

Parameters

sid - index of a sub-simplex in a simplex return an array of barycentric coordinates on <dim> simplex from <subdim> simplex for example: simplex<3> - ABCD and its subsubsimplex<1> AD (line index: 3) AD has barycoords for A (1,0), for D (0,1), but A in ABCD is (1,0,0,0) and D is (0,0,0,1) this method creates array ((1,0,0,0),(0,0,0,1))

Definition at line 604 of file ref_element.hh.

◆ bary_to_local()

template<unsigned int dim>

auto RefElement< dim >::bary_to_local ( const BaryPoint & bp )

static

Converts from barycentric to local coordinates.

Parameters

bp	point in barycentric coordinates

Returns: point in local coordinates

Definition at line 201 of file ref_element.cc.

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◆ barycentric_on_face()

template<unsigned int dim>

auto RefElement< dim >::barycentric_on_face	(	const BaryPoint &	barycentric,
		unsigned int	i_face
	)

static

For given barycentric coordinates on the ref element returns barycentric coordinates on the ref. element of given face. Assumes that the input point is on the face. Barycentric order: (complanatory, local_coords )

Definition at line 279 of file ref_element.cc.

◆ centers_of_subelements()

template<unsigned int dim>

auto RefElement< dim >::centers_of_subelements ( unsigned int sub_dim )

static

Definition at line 366 of file ref_element.cc.

◆ clip() [1/2]

template<unsigned int dim>

auto RefElement< dim >::clip ( const BaryPoint & barycentric )

static

If the given barycentric coordinate is in the ref. element, return unchanged. If the given barycentric coordinate is out of the ref. element, project it on the surface of the ref. element.

Definition at line 332 of file ref_element.cc.

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◆ clip() [2/2]

auto RefElement< 0 >::clip ( const BaryPoint & barycentric ) -> BaryPoint

Definition at line 312 of file ref_element.cc.

◆ count() [1/17]

template<unsigned int dim>

template<unsigned int subdim>

static unsigned int RefElement< dim >::count ( )

static

Function returns number of subdim-simplices inside dim-simplex. The aim is covering all the n_**** members with a single function. TODO: think of generalization for n_****_per_**** members, like function interact: template<unsigned int subdimA, unsigned int subdimB> static unsigned int count();

◆ count() [2/17]

unsigned int RefElement< 3 >::count< 0 > ( )

inline

Definition at line 641 of file ref_element.hh.

◆ count() [3/17]

unsigned int RefElement< 3 >::count< 1 > ( )

inline

Definition at line 643 of file ref_element.hh.

◆ count() [4/17]

unsigned int RefElement< 3 >::count< 2 > ( )

inline

Definition at line 645 of file ref_element.hh.

◆ count() [5/17]

unsigned int RefElement< 3 >::count< 3 > ( )

inline

Definition at line 647 of file ref_element.hh.

◆ count() [6/17]

unsigned int RefElement< 2 >::count< 0 > ( )

inline

Definition at line 649 of file ref_element.hh.

◆ count() [7/17]

unsigned int RefElement< 2 >::count< 1 > ( )

inline

Definition at line 651 of file ref_element.hh.

◆ count() [8/17]

unsigned int RefElement< 2 >::count< 2 > ( )

inline

Definition at line 653 of file ref_element.hh.

◆ count() [9/17]

unsigned int RefElement< 2 >::count< 3 > ( )

inline

Definition at line 655 of file ref_element.hh.

◆ count() [10/17]

unsigned int RefElement< 1 >::count< 0 > ( )

inline

Definition at line 657 of file ref_element.hh.

◆ count() [11/17]

unsigned int RefElement< 1 >::count< 1 > ( )

inline

Definition at line 659 of file ref_element.hh.

◆ count() [12/17]

unsigned int RefElement< 1 >::count< 2 > ( )

inline

Definition at line 661 of file ref_element.hh.

◆ count() [13/17]

unsigned int RefElement< 1 >::count< 3 > ( )

inline

Definition at line 663 of file ref_element.hh.

◆ count() [14/17]

unsigned int RefElement< 0 >::count< 0 > ( )

inline

Definition at line 665 of file ref_element.hh.

◆ count() [15/17]

unsigned int RefElement< 0 >::count< 1 > ( )

inline

Definition at line 667 of file ref_element.hh.

◆ count() [16/17]

unsigned int RefElement< 0 >::count< 2 > ( )

inline

Definition at line 669 of file ref_element.hh.

◆ count() [17/17]

unsigned int RefElement< 0 >::count< 3 > ( )

inline

Definition at line 671 of file ref_element.hh.

◆ DECLARE_EXCEPTION()

template<unsigned int dim>

RefElement< dim >::DECLARE_EXCEPTION	(	ExcInvalidPermutation	,
		<< "Side permutation not found.\n"
	)

◆ interact() [1/2]

template<unsigned int dim>

template<template< unsigned int OutDim, unsigned int InDim > class TInteraction, unsigned int OutDim, unsigned int InDim>

const IdxVector< (InDim>OutDim ? InDim+1 : dim-InDim) > RefElement< dim >::interact	(	TInteraction< OutDim, InDim >	interaction,
		bool	inv
	)

inline

Definition at line 753 of file ref_element.hh.

◆ interact() [2/2]

template<unsigned int dim>

template<template< unsigned int OutDim, unsigned int InDim > class TInteraction, unsigned int OutDim, unsigned int InDim>

static const IdxVector< (InDim>OutDim ? InDim+1 : dim-InDim) > RefElement< dim >::interact	(	TInteraction< OutDim, InDim >	interaction,
		bool	inv = `false`
	)

static

Usage: RefElement<3>::interact(Interaction<2,0>(1)) (means: In tetrahedron <3>, give indices of sides <2>, connected by node <0> with index 1) RefElement<3>::interact(Interaction<2,0>(1))[1] (as above, but give only the side with index 1)

Template usage: RefElement<dim>::interact(Interaction<OutDim, InDim>(i))[j] (means: on dim-dimensional reference element, go on InDim-dimensional subelement with index i, which connects OutDim-dimnesional subelements and select the one with index j)

This method serves as an interface to topology information of the reference element. It returns indices of OutDim-dimensional object of InDim-dimnesional object of given index in dim-dimnesional reference element.

Template Parameters

interaction	- auxilliary object carying the index and the template arguments OutDim and InDim
OutDim	- output dimension (give me node-0, line-1, side-2), <= dim
InDim	- input dimension (for node-0, line-1, side-2), <= dim

Returns: vector of indices of OutDim-dimensional subelements represented by IdxVector object.

possible calls: dim OutDim InDim return 1,2,3 0 1 InDim+1 - give me indices of nodes of line of given index 3 0 2 InDim+1 - give me indices of nodes of a side (triangle) of given index 3 1 2 InDim+1 - give me indices of lines of side (triangle) of given index

1,2,3 1 0 dim-InDim - give me indices of lines with common node of given index 3 2 0 dim-InDim - give me indices of sides (triangles) with common node of given index 3 2 1 dim-InDim - give me indices of sides (triangles) with common line of given index

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◆ interact_() [1/12]

const IdxVector<(InDim > OutDim InDim :dim) InDim RefElement< dim >::interact_	(	unsigned int	i,
		bool	inv
	)

inlineprivate

This function is for "side_nodes" - for given side, give me nodes (0->0, 1->1).

Definition at line 687 of file ref_element.hh.

◆ interact_() [2/12]

const IdxVector< 2 > RefElement< 1 >::interact_< 0, 1 >	(	unsigned int	i,
		bool	inv
	)

inlineprivate

For line i {0}, give me indices of its nodes.

Definition at line 692 of file ref_element.hh.

◆ interact_() [3/12]

const IdxVector< 2 > RefElement< 2 >::interact_< 0, 1 >	(	unsigned int	i,
		bool	inv
	)

inlineprivate

For line i {0,1,2}, give me indices of its nodes.

Definition at line 697 of file ref_element.hh.

◆ interact_() [4/12]

const IdxVector< 2 > RefElement< 3 >::interact_< 0, 1 >	(	unsigned int	i,
		bool	inv
	)

inlineprivate

For line i {0,1,2,3,4,5}, give me indices of its nodes.

Definition at line 702 of file ref_element.hh.

◆ interact_() [5/12]

const IdxVector< 1 > RefElement< 1 >::interact_< 1, 0 >	(	unsigned int	i,
		bool	inv
	)

inlineprivate

For node i {0,1}, give me indices of lines.

Definition at line 707 of file ref_element.hh.

◆ interact_() [6/12]

const IdxVector< 2 > RefElement< 2 >::interact_< 1, 0 >	(	unsigned int	i,
		bool	inv
	)

inlineprivate

For node i {0,1,2}, give me indices of lines.

Definition at line 712 of file ref_element.hh.

◆ interact_() [7/12]

const IdxVector< 3 > RefElement< 3 >::interact_< 1, 0 >	(	unsigned int	i,
		bool	inv
	)

inlineprivate

For node i {0,1,2,3}, give me indices of lines.

Definition at line 717 of file ref_element.hh.

◆ interact_() [8/12]

const IdxVector< 3 > RefElement< 3 >::interact_< 0, 2 >	(	unsigned int	i,
		bool	inv
	)

inlineprivate

For side i {0,1,2}, give me indices of its nodes.

Definition at line 722 of file ref_element.hh.

◆ interact_() [9/12]

const IdxVector< 3 > RefElement< 3 >::interact_< 2, 0 >	(	unsigned int	i,
		bool	inv
	)

inlineprivate

For node i {0,1,2,3}, give me indices of sides.

Definition at line 727 of file ref_element.hh.

◆ interact_() [10/12]

const IdxVector< 2 > RefElement< 3 >::interact_< 2, 1 >	(	unsigned int	i,
		bool	inv
	)

inlineprivate

For line i {0,1,2,3}, give me indices of sides.

Definition at line 732 of file ref_element.hh.

◆ interact_() [11/12]

const IdxVector< 3 > RefElement< 3 >::interact_< 1, 2 >	(	unsigned int	i,
		bool	inv
	)

inlineprivate

For side i {0,1,2}, give me indices of its lines.

Definition at line 737 of file ref_element.hh.

◆ interact_() [12/12]

template<unsigned int dim>

template<unsigned int OutDim, unsigned int InDim>

static const IdxVector< (InDim>OutDim ? InDim+1 : dim-InDim) > RefElement< dim >::interact_	(	unsigned int	index,
		bool	inv = `false`
	)

staticprivate

Internal part of the interact function.

◆ interpolate() [1/2]

template<unsigned int dim>

template<unsigned int subdim>

static BaryPoint RefElement< dim >::interpolate	(	arma::vec::fixed< subdim+1 >	coord,
		int	sub_simplex_idx
	)

static

Interpolate barycentric coords to a higher dimension of a simplex.

Parameters

coord	- barycentric coords of a point on a sub-simplex
sub_simplex_idx	- id of sub-simplex on a simplex

◆ interpolate() [2/2]

template<unsigned int dim>

template<unsigned int subdim>

auto RefElement< dim >::interpolate	(	arma::vec::fixed< subdim+1 >	coord,
		int	sub_simplex_idx
	)		-> BaryPoint

Definition at line 635 of file ref_element.hh.

◆ line_barycentric_interpolation()

template<unsigned int dim>

arma::vec::fixed< dim+1 > RefElement< dim >::line_barycentric_interpolation	(	BaryPoint	first_coords,
		BaryPoint	second_coords,
		double	first_theta,
		double	second_theta,
		double	theta
	)

static

Basic line interpolation.

Basic line interpolation

Definition at line 437 of file ref_element.cc.

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◆ line_between_faces() [1/2]

unsigned int RefElement< 3 >::line_between_faces	(	unsigned int	f1,
		unsigned int	f2
	)

Definition at line 423 of file ref_element.cc.

◆ line_between_faces() [2/2]

template<unsigned int dim>

static unsigned int RefElement< dim >::line_between_faces	(	unsigned int	f1,
		unsigned int	f2
	)

static

Return index of 1D line, shared by two faces f1 and f2 of the reference tetrahedron. Implemented only for dim == 3.

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◆ line_nodes_() [1/6]

const std::vector< IdxVector< 2 > > RefElement< 1 >::line_nodes_

private

Definition at line 45 of file ref_element.cc.

◆ line_nodes_() [2/6]

const std::vector< IdxVector< 2 > > RefElement< 2 >::line_nodes_

private

Definition at line 48 of file ref_element.cc.

◆ line_nodes_() [3/6]

const std::vector< IdxVector< 2 > > RefElement< 3 >::line_nodes_

private

Definition at line 53 of file ref_element.cc.

◆ line_nodes_() [4/6]

const std::vector< IdxVector< 2 > > RefElement< 1 >::line_nodes_

private

Definition at line 560 of file ref_element.hh.

◆ line_nodes_() [5/6]

const std::vector< IdxVector< 2 > > RefElement< 2 >::line_nodes_

private

Definition at line 561 of file ref_element.hh.

◆ line_nodes_() [6/6]

const std::vector< IdxVector< 2 > > RefElement< 3 >::line_nodes_

private

Definition at line 562 of file ref_element.hh.

◆ line_sides_()

const std::vector< IdxVector< 2 > > RefElement< 3 >::line_sides_

private

Definition at line 569 of file ref_element.hh.

◆ local_to_bary()

template<unsigned int dim>

auto RefElement< dim >::local_to_bary ( const LocalPoint & lp )

static

Converts from local to barycentric coordinates.

Parameters

lp	point in local coordinates (x,y)

Returns: point in barycentric coordinates (1-x-y, x, y)

Definition at line 187 of file ref_element.cc.

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◆ make_bary_unit_vec()

template<unsigned int dim>

auto RefElement< dim >::make_bary_unit_vec

static

Used in the clip method.

Definition at line 318 of file ref_element.cc.

◆ node_coords()

template<unsigned int dim>

arma::vec::fixed< dim > RefElement< dim >::node_coords ( unsigned int nid )

inlinestatic

Return coordinates of given node.

See also: the class documentation RefElement

Parameters

nid	Node number. NOTE: Implementation is dependent on current node and side numbering.

Definition at line 619 of file ref_element.hh.

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◆ node_lines_() [1/5]

const std::vector< IdxVector< 1 > > RefElement< 1 >::node_lines_

private

Definition at line 62 of file ref_element.cc.

◆ node_lines_() [2/5]

const std::vector< IdxVector< 2 > > RefElement< 2 >::node_lines_

private

Definition at line 66 of file ref_element.cc.

◆ node_lines_() [3/5]

const std::vector< IdxVector< 1 > > RefElement< 1 >::node_lines_

private

Definition at line 563 of file ref_element.hh.

◆ node_lines_() [4/5]

const std::vector< IdxVector< 2 > > RefElement< 2 >::node_lines_

private

Definition at line 564 of file ref_element.hh.

◆ node_lines_() [5/5]

const std::vector< IdxVector< 3 > > RefElement< 3 >::node_lines_

private

Definition at line 566 of file ref_element.hh.

◆ node_sides_()

const std::vector< IdxVector< 3 > > RefElement< 3 >::node_sides_

private

Definition at line 568 of file ref_element.hh.

◆ nodes_of_subelements() [1/8]

const std::vector< std::vector< std::vector< unsigned int > > > RefElement< 0 >::nodes_of_subelements

Definition at line 163 of file ref_element.cc.

◆ nodes_of_subelements() [2/8]

const std::vector< std::vector< std::vector< unsigned int > > > RefElement< 1 >::nodes_of_subelements

Definition at line 167 of file ref_element.cc.

◆ nodes_of_subelements() [3/8]

const std::vector< std::vector< std::vector< unsigned int > > > RefElement< 2 >::nodes_of_subelements

Definition at line 172 of file ref_element.cc.

◆ nodes_of_subelements() [4/8]

const std::vector< std::vector< std::vector< unsigned int > > > RefElement< 3 >::nodes_of_subelements

Definition at line 178 of file ref_element.cc.

◆ nodes_of_subelements() [5/8]

const std::vector< std::vector< std::vector< unsigned int > > > RefElement< 0 >::nodes_of_subelements

Definition at line 587 of file ref_element.hh.

◆ nodes_of_subelements() [6/8]

const std::vector< std::vector< std::vector< unsigned int > > > RefElement< 1 >::nodes_of_subelements

Definition at line 588 of file ref_element.hh.

◆ nodes_of_subelements() [7/8]

const std::vector< std::vector< std::vector< unsigned int > > > RefElement< 2 >::nodes_of_subelements

Definition at line 589 of file ref_element.hh.

◆ nodes_of_subelements() [8/8]

const std::vector< std::vector< std::vector< unsigned int > > > RefElement< 3 >::nodes_of_subelements

Definition at line 590 of file ref_element.hh.

◆ normal_orientation()

template<unsigned int dim>

unsigned int RefElement< dim >::normal_orientation ( unsigned int sid )

static

Returns orientation of the normal of side sid. 0 -> OUT, 1 -> IN. NOTE: Implementation is dependent on current node and side numbering.

Definition at line 216 of file ref_element.cc.

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◆ normal_vector() [1/4]

vec::fixed< 1 > RefElement< 1 >::normal_vector ( unsigned int sid )

Definition at line 225 of file ref_element.cc.

◆ normal_vector() [2/4]

vec::fixed< 2 > RefElement< 2 >::normal_vector ( unsigned int sid )

Definition at line 233 of file ref_element.cc.

◆ normal_vector() [3/4]

vec::fixed< 3 > RefElement< 3 >::normal_vector ( unsigned int sid )

Definition at line 255 of file ref_element.cc.

◆ normal_vector() [4/4]

template<unsigned int dim>

static LocalPoint RefElement< dim >::normal_vector ( unsigned int sid )

static

Compute normal vector to a given side.

Parameters

sid	Side number.

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◆ oposite_node()

template<unsigned int dim>

unsigned int RefElement< dim >::oposite_node ( unsigned int sid )

inlinestatic

Returns index of the node that is oposite to side of given index sid. Note: It is dependent on current node and side numbering.

Parameters

sid	Side number. NOTE: Implementation is dependent on current node and side numbering.

Definition at line 209 of file ref_element.cc.

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◆ side_lines_() [1/2]

const std::vector< IdxVector< 3 > > RefElement< 3 >::side_lines_

private

Definition at line 97 of file ref_element.cc.

◆ side_lines_() [2/2]

const std::vector< IdxVector< 3 > > RefElement< 3 >::side_lines_

private

Definition at line 570 of file ref_element.hh.

◆ side_measure() [1/4]

double RefElement< 1 >::side_measure ( unsigned int sid )

Definition at line 394 of file ref_element.cc.

◆ side_measure() [2/4]

double RefElement< 2 >::side_measure ( unsigned int sid )

Definition at line 403 of file ref_element.cc.

◆ side_measure() [3/4]

double RefElement< 3 >::side_measure ( unsigned int sid )

Definition at line 412 of file ref_element.cc.

◆ side_measure() [4/4]

template<unsigned int dim>

static double RefElement< dim >::side_measure ( unsigned int sid )

static

◆ side_nodes_() [1/2]

const std::vector< IdxVector< 3 > > RefElement< 3 >::side_nodes_

private

Definition at line 76 of file ref_element.cc.

◆ side_nodes_() [2/2]

const std::vector< IdxVector< 3 > > RefElement< 3 >::side_nodes_

private

Definition at line 567 of file ref_element.hh.

◆ topology_idx()

template<unsigned int dim>

template<unsigned int subdim>

unsigned int RefElement< dim >::topology_idx ( unsigned int zeros_positions )

static

According to positions of zeros in barycentric coordinates, it gives the index of subdim-simplex in the reference element. Number of zeros must be equal to (3-subdim). e.g.: if 1 zeros, return index of side (subdim 2) if 2 zeros, return index of edge (subdim 1) if 3 zeros, return index of vertex (subdim 0)

Definition at line 676 of file ref_element.hh.

◆ topology_zeros_() [1/12]

const IdxVector< 1 > RefElement< 0 >::topology_zeros_

private

Definition at line 104 of file ref_element.cc.

◆ topology_zeros_() [2/12]

const IdxVector< 2 > RefElement< 1 >::topology_zeros_

private

Definition at line 109 of file ref_element.cc.

◆ topology_zeros_() [3/12]

const IdxVector< 3 > RefElement< 2 >::topology_zeros_

private

Definition at line 117 of file ref_element.cc.

◆ topology_zeros_() [4/12]

const IdxVector< 6 > RefElement< 3 >::topology_zeros_

private

Definition at line 129 of file ref_element.cc.

◆ topology_zeros_() [5/12]

const IdxVector< 1 > RefElement< 0 >::topology_zeros_

private

Definition at line 554 of file ref_element.hh.

◆ topology_zeros_() [6/12]

const IdxVector< 2 > RefElement< 1 >::topology_zeros_

private

Definition at line 555 of file ref_element.hh.

◆ topology_zeros_() [7/12]

const IdxVector< 3 > RefElement< 2 >::topology_zeros_

private

Definition at line 556 of file ref_element.hh.

◆ topology_zeros_() [8/12]

const IdxVector< 6 > RefElement< 3 >::topology_zeros_

private

Definition at line 557 of file ref_element.hh.

◆ topology_zeros_() [9/12]

const IdxVector< 1 > RefElement< 0 >::topology_zeros_

private

Definition at line 573 of file ref_element.hh.

◆ topology_zeros_() [10/12]

const IdxVector< 2 > RefElement< 1 >::topology_zeros_

private

Definition at line 574 of file ref_element.hh.

◆ topology_zeros_() [11/12]

const IdxVector< 3 > RefElement< 2 >::topology_zeros_

private

Definition at line 575 of file ref_element.hh.

◆ topology_zeros_() [12/12]

const IdxVector< 6 > RefElement< 3 >::topology_zeros_

private

Definition at line 576 of file ref_element.hh.

◆ zeros_positions()

template<unsigned int dim>

std::pair< unsigned int, unsigned int > RefElement< dim >::zeros_positions	(	const BaryPoint &	barycentric,
		double	tolerance = `std::numeric_limits<double>::epsilon()*2`
	)

static

Return (1) number of zeros and (2) positions of zeros in barycentric coordinates. tolerance serves for testing zero values of barycentric coordinates.

Definition at line 294 of file ref_element.cc.

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Member Data Documentation

◆ line_nodes_

template<unsigned int dim>

const std::vector<IdxVector<n_nodes_per_line> > RefElement< dim >::line_nodes_

staticprivate

[n_lines] For given line, returns its nodes indices.

Definition at line 533 of file ref_element.hh.

◆ line_sides_

template<unsigned int dim>

const std::vector<IdxVector<n_sides_per_line> > RefElement< dim >::line_sides_

staticprivate

[n_lines] For given line, returns sides indices. For dim == 3.

Definition at line 537 of file ref_element.hh.

◆ n_lines

template<unsigned int dim>

const unsigned int RefElement< dim >::n_lines = (unsigned int)((dim * (dim + 1)) / 2)

static

Number of lines, i.e. object of dimension dim-2 on the boundary of the reference element.

Definition at line 410 of file ref_element.hh.

◆ n_lines_per_node

template<unsigned int dim>

const unsigned int RefElement< dim >::n_lines_per_node = dim

static

Number of lines with one common node.

Definition at line 401 of file ref_element.hh.

◆ n_lines_per_side

template<unsigned int dim>

const unsigned int RefElement< dim >::n_lines_per_side = (unsigned int)((dim * (dim - 1)) / 2)

static

Number of lines on boundary of one side.

Definition at line 407 of file ref_element.hh.

◆ n_nodes

template<unsigned int dim>

const unsigned int RefElement< dim >::n_nodes = dim + 1

static

Number of nodes.

Definition at line 399 of file ref_element.hh.

◆ n_nodes_per_line

template<unsigned int dim>

const unsigned int RefElement< dim >::n_nodes_per_line = 2

static

Number of nodes in one line.

Definition at line 402 of file ref_element.hh.

◆ n_nodes_per_side

template<unsigned int dim>

const unsigned int RefElement< dim >::n_nodes_per_side = dim

static

Number of nodes on one side.

Definition at line 400 of file ref_element.hh.

◆ n_sides

template<unsigned int dim>

const unsigned int RefElement< dim >::n_sides = dim + 1

static

Number of sides.

Definition at line 398 of file ref_element.hh.

◆ n_sides_per_line

template<unsigned int dim>

const unsigned int RefElement< dim >::n_sides_per_line = 2

static

Number of sides with one common line. dim == 3.

Definition at line 403 of file ref_element.hh.

◆ n_sides_per_node

template<unsigned int dim>

const unsigned int RefElement< dim >::n_sides_per_node = dim

static

Number of sides with one common line.

Definition at line 404 of file ref_element.hh.

◆ node_lines_

template<unsigned int dim>

const std::vector<IdxVector<n_lines_per_node> > RefElement< dim >::node_lines_

staticprivate

[n_nodes] For given node, returns lines indices.

Definition at line 534 of file ref_element.hh.

◆ node_sides_

template<unsigned int dim>

const std::vector<IdxVector<n_sides_per_node> > RefElement< dim >::node_sides_

staticprivate

[n_nodes] For given node, returns sides indices. For dim == 3.

Definition at line 536 of file ref_element.hh.

◆ nodes_of_subelements

template<unsigned int dim>

const std::vector< std::vector< std::vector<unsigned int> > > RefElement< dim >::nodes_of_subelements

static

Definition at line 413 of file ref_element.hh.

◆ side_lines_

template<unsigned int dim>

const std::vector<IdxVector<n_lines_per_side> > RefElement< dim >::side_lines_

staticprivate

[n_sides] For given side, returns lines indices. For dim == 3.

Definition at line 538 of file ref_element.hh.

◆ side_nodes_

template<unsigned int dim>

const std::vector<IdxVector<n_nodes_per_side> > RefElement< dim >::side_nodes_

staticprivate

[n_sides] For given side, returns nodes indices. For dim == 3.

Definition at line 535 of file ref_element.hh.

◆ topology_zeros_

template<unsigned int dim>

const IdxVector<(n_lines > n_nodes) ? n_lines : n_nodes> RefElement< dim >::topology_zeros_[dim+1]

staticprivate

Consider an n-face (node, edge, face, bulk) with dimension subdim and index within subdimension idx. Barycentric coordinates of all points on the n-face have unique pattern of zero coordinates.

topology_zeros_[subdim][idx] is a bitfield with '1' where the pattern have zeros.

Definition at line 548 of file ref_element.hh.

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

/home/runner/work/flow123d/flow123d/src/mesh/ref_element.hh
/home/runner/work/flow123d/flow123d/src/mesh/ref_element.cc

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Private Member Functions

Static Private Member Functions

Static Private Attributes

Detailed Description

template<unsigned int dim> class RefElement< dim >

Member Typedef Documentation

◆ BarycentricUnitVec

◆ BaryPoint

◆ CentersList

◆ FaceBaryPoint

◆ LocalPoint

Member Function Documentation

◆ bary_coords()

◆ bary_to_local()

◆ barycentric_on_face()

◆ centers_of_subelements()

◆ clip() [1/2]

◆ clip() [2/2]

◆ count() [1/17]

◆ count() [2/17]

◆ count() [3/17]

◆ count() [4/17]

◆ count() [5/17]

◆ count() [6/17]

◆ count() [7/17]

◆ count() [8/17]

◆ count() [9/17]

◆ count() [10/17]

◆ count() [11/17]

◆ count() [12/17]

◆ count() [13/17]

◆ count() [14/17]

◆ count() [15/17]

◆ count() [16/17]

◆ count() [17/17]

◆ DECLARE_EXCEPTION()

◆ interact() [1/2]

◆ interact() [2/2]

◆ interact_() [1/12]

◆ interact_() [2/12]

◆ interact_() [3/12]

◆ interact_() [4/12]

◆ interact_() [5/12]

◆ interact_() [6/12]

◆ interact_() [7/12]

◆ interact_() [8/12]

◆ interact_() [9/12]

◆ interact_() [10/12]

◆ interact_() [11/12]

◆ interact_() [12/12]

◆ interpolate() [1/2]

◆ interpolate() [2/2]

◆ line_barycentric_interpolation()

◆ line_between_faces() [1/2]

◆ line_between_faces() [2/2]

◆ line_nodes_() [1/6]

◆ line_nodes_() [2/6]

◆ line_nodes_() [3/6]

◆ line_nodes_() [4/6]

◆ line_nodes_() [5/6]

◆ line_nodes_() [6/6]

◆ line_sides_()

◆ local_to_bary()

◆ make_bary_unit_vec()

◆ node_coords()

◆ node_lines_() [1/5]

◆ node_lines_() [2/5]

◆ node_lines_() [3/5]

◆ node_lines_() [4/5]

◆ node_lines_() [5/5]

◆ node_sides_()

◆ nodes_of_subelements() [1/8]

◆ nodes_of_subelements() [2/8]

◆ nodes_of_subelements() [3/8]

◆ nodes_of_subelements() [4/8]

◆ nodes_of_subelements() [5/8]

template<unsigned int dim>
class RefElement< dim >