Tetrahedral element with linear shapefunctions. More...

#include <element.hh>

Inheritance diagram for linDG3D::FvdgP1TetElem:

Public Types
typedef Real	type

Public Member Functions
virtual const concepts::Tetrahedron3d &	cell () const
	Returns the geometrical cell of this element. More...

virtual const Cell &	cell () const=0
	Returns the cell on which the element is built. More...

concepts::Real3d	edgeCenter (uint edgeIdx) const
	Returns the real world coordinates of the center of the edge with index `edgeIdx`. More...

Real3d	elemMap (const Real coord_local) const

Real3d	elemMap (const Real2d &coord_local) const

Real3d	elemMap (const Real3d &coord_local) const

	FvdgP1TetElem (const concepts::Tetrahedron3d &cell, uint idx[])
	Constructor. More...

const concepts::ElementGraphics< Real > *	graphics () const
	Returns the graphics object for the element. More...

Real	shapeFct (const uint fctIdx, const concepts::Real3d xi) const
	Shape function. More...

Real	shapeFctEdgeCenter (const uint fctIdx, const uint edgeIdx) const
	Shapefunction at edge center. More...

concepts::Real3d	shapeFctGradient (const uint fctIdx) const
	Gradient of shape function. More...

Real	shapeFctVertex (const uint fctIdx, const uint vtxIdx) const
	Shapefunction at vertex. More...

Real	solution (const concepts::Vector< Real > &sol, const concepts::Real3d xi) const
	Returns the value of the solution `sol` at the reference element coordinate `xi`. More...

Real	solutionEdgeCenter (const concepts::Vector< Real > &sol, const uint edgeIdx) const
	Returns the value of the solution `sol` at the center of edge `edgeIdx` of this tetrahedron. More...

Real	solutionVertex (const concepts::Vector< Real > &sol, const uint vertexIdx) const
	Returns the value of the solution `sol` at vertex `vertexIdx` of this tetrahedron. More...

const concepts::Tetrahedron &	support () const
	Returns the topological support of this element. More...

const concepts::TMatrixBase< Real > &	T () const
	Returns the T matrix of this element. More...

virtual const TMatrixBase< Real > &	T () const=0
	Returns the T matrix of the element. More...

const concepts::Real3d	vertex (const uint i) const
	Returns the vertex with local index `i` in this element. More...

Protected Member Functions
virtual std::ostream &	info (std::ostream &os) const
	Returns cell and T matrix of this element. More...

Protected Attributes
const concepts::Tetrahedron3d &	cell_

std::unique_ptr< concepts::TMatrixBase< Real > >	T_

Static Protected Attributes
static Real	eta_ [6][3]

static std::unique_ptr< FvdgP1TetGraphics >	graphics_
	Graphics object of the element. More...

static uint	nonVanishingNbr_ [6]
	Number of non vanishing shape function at edge centers. More...

static Real	nonVanishingSign_ [6]
	Value of non vanishing shape function at edge centers. More...

static Real	shapeFctEdgeCenter_ [6][4]
	Values of shape functions at edge centers. More...

static Real	shapeFctGradient_ [3][4]
	Values of shape function gradients. More...

static Real	shapeFctVertex_ [4][4]
	Values of shape functions at vertices. More...

Detailed Description

Tetrahedral element with linear shapefunctions.

Author: Christoph Winkelmann, 2002

Definition at line 179 of file element.hh.

Member Typedef Documentation

◆ type

typedef Real concepts::ElementWithCell< Real >::type

inherited

Definition at line 81 of file element.hh.

Constructor & Destructor Documentation

◆ FvdgP1TetElem()

linDG3D::FvdgP1TetElem::FvdgP1TetElem	(	const concepts::Tetrahedron3d &	cell,
		uint	idx[]
	)

Constructor.

Creates a T matrix of type TIndex from idx.

Parameters

cell	The Cell the element lives on
idx	Describes the map local / global dof

Member Function Documentation

◆ cell() [1/2]

virtual const concepts::Tetrahedron3d& linDG3D::FvdgElement::cell ( ) const

inlinevirtualinherited

Returns the geometrical cell of this element.

Definition at line 44 of file element.hh.

◆ cell() [2/2]

virtual const Cell& concepts::ElementWithCell< Real >::cell ( ) const

pure virtualinherited

Returns the cell on which the element is built.

Implemented in hp3D::Element< Real >, hp2D::Element< Real >, and hp1D::BaseElement< Real >.

◆ edgeCenter()

concepts::Real3d linDG3D::FvdgElement::edgeCenter ( uint edgeIdx ) const

inherited

Returns the real world coordinates of the center of the edge with index edgeIdx.

Parameters

edgeIdx Edge index

◆ elemMap() [1/3]

Real3d concepts::ElementWithCell< Real >::elemMap ( const Real coord_local ) const

inlineinherited

Definition at line 86 of file element.hh.

◆ elemMap() [2/3]

Real3d concepts::ElementWithCell< Real >::elemMap ( const Real2d & coord_local ) const

inlineinherited

Definition at line 90 of file element.hh.

◆ elemMap() [3/3]

Real3d concepts::ElementWithCell< Real >::elemMap ( const Real3d & coord_local ) const

inlineinherited

Definition at line 94 of file element.hh.

◆ graphics()

const concepts::ElementGraphics<Real>* linDG3D::FvdgP1TetElem::graphics ( ) const

virtual

Returns the graphics object for the element.

Implements linDG3D::FvdgElement.

◆ info()

virtual std::ostream& linDG3D::FvdgP1TetElem::info ( std::ostream & os ) const

protectedvirtual

Returns cell and T matrix of this element.

Reimplemented from linDG3D::FvdgElement.

◆ shapeFct()

Real linDG3D::FvdgP1TetElem::shapeFct	(	const uint	fctIdx,
		const concepts::Real3d	xi
	)		const

virtual

Shape function.

Returns the value of a shape function

Parameters

fctIdx	number of the shape function
xi	reference coordinate to evaluate the shape function at

Implements linDG3D::FvdgElement.

◆ shapeFctEdgeCenter()

Real linDG3D::FvdgP1TetElem::shapeFctEdgeCenter	(	const uint	fctIdx,
		const uint	edgeIdx
	)		const

inlinevirtual

Shapefunction at edge center.

Returns the value of shape function fctIdx at center of edge edgeIdx of this tetrahedron

Parameters

fctIdx	number of the shape function
edgeIdx	number of edge

Implements linDG3D::FvdgElement.

Definition at line 196 of file element.hh.

◆ shapeFctGradient()

concepts::Real3d linDG3D::FvdgP1TetElem::shapeFctGradient ( const uint fctIdx ) const

virtual

Gradient of shape function.

Returns the gradient of shape function fctIdx

Parameters

fctIdx number of the shape function

Implements linDG3D::FvdgElement.

◆ shapeFctVertex()

Real linDG3D::FvdgP1TetElem::shapeFctVertex	(	const uint	fctIdx,
		const uint	vtxIdx
	)		const

inlinevirtual

Shapefunction at vertex.

Returns the value of shape function fctIdx at vertex vtxIdx of this tetrahedron

Parameters

fctIdx	number of the shape function
vtxIdx	number of vertex

Implements linDG3D::FvdgElement.

Definition at line 206 of file element.hh.

◆ solution()

Real linDG3D::FvdgElement::solution	(	const concepts::Vector< Real > &	sol,
		const concepts::Real3d	xi
	)		const

inherited

Returns the value of the solution sol at the reference element coordinate xi.

Parameters

sol	solution vector
xi	reference element coordinate to get solution at

◆ solutionEdgeCenter()

Real linDG3D::FvdgP1TetElem::solutionEdgeCenter	(	const concepts::Vector< Real > &	sol,
		const uint	edgeIdx
	)		const

virtual

Returns the value of the solution sol at the center of edge edgeIdx of this tetrahedron.

Parameters

sol	solution vector
edgeIdx	number of edge

Implements linDG3D::FvdgElement.

◆ solutionVertex()

Real linDG3D::FvdgP1TetElem::solutionVertex	(	const concepts::Vector< Real > &	sol,
		const uint	vertexIdx
	)		const

virtual

Returns the value of the solution sol at vertex vertexIdx of this tetrahedron.

Parameters

sol	solution vector
vertexIdx	number of vertex

Implements linDG3D::FvdgElement.

◆ support()

const concepts::Tetrahedron& linDG3D::FvdgElement::support ( ) const

inlineinherited

Returns the topological support of this element.

Definition at line 36 of file element.hh.

◆ T() [1/2]

const concepts::TMatrixBase<Real>& linDG3D::FvdgElement::T ( ) const

inlineinherited

Returns the T matrix of this element.

Definition at line 38 of file element.hh.

◆ T() [2/2]

virtual const TMatrixBase<Real >& concepts::ElementWithCell< Real >::T ( ) const

pure virtualinherited

Returns the T matrix of the element.

Implemented in hp3D::Element< Real >, and hp2D::Element< Real >.

◆ vertex()

const concepts::Real3d linDG3D::FvdgElement::vertex ( const uint i ) const

inlineinherited

Returns the vertex with local index i in this element.

Definition at line 40 of file element.hh.

Member Data Documentation

◆ cell_

const concepts::Tetrahedron3d& linDG3D::FvdgElement::cell_

protectedinherited

Definition at line 103 of file element.hh.

◆ eta_

Real linDG3D::FvdgElement::eta_[6][3]

staticprotectedinherited

Definition at line 104 of file element.hh.

◆ graphics_

std::unique_ptr<FvdgP1TetGraphics> linDG3D::FvdgP1TetElem::graphics_

staticprotected

Graphics object of the element.

Definition at line 246 of file element.hh.

◆ nonVanishingNbr_

uint linDG3D::FvdgP1TetElem::nonVanishingNbr_[6]

staticprotected

Number of non vanishing shape function at edge centers.

Definition at line 240 of file element.hh.

◆ nonVanishingSign_

Real linDG3D::FvdgP1TetElem::nonVanishingSign_[6]

staticprotected

Value of non vanishing shape function at edge centers.

Definition at line 242 of file element.hh.

◆ shapeFctEdgeCenter_

Real linDG3D::FvdgP1TetElem::shapeFctEdgeCenter_[6][4]

staticprotected

Values of shape functions at edge centers.

Definition at line 236 of file element.hh.

◆ shapeFctGradient_

Real linDG3D::FvdgP1TetElem::shapeFctGradient_[3][4]

staticprotected

Values of shape function gradients.

Definition at line 238 of file element.hh.

◆ shapeFctVertex_

Real linDG3D::FvdgP1TetElem::shapeFctVertex_[4][4]

staticprotected

Values of shape functions at vertices.

Definition at line 244 of file element.hh.

◆ T_

std::unique_ptr<concepts::TMatrixBase<Real> > linDG3D::FvdgElement::T_

protectedinherited

Definition at line 102 of file element.hh.

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

linDG3D/element.hh

linDG3D::FvdgP1TetElem Class Referenceabstract

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Static Protected Attributes

Detailed Description

Member Typedef Documentation

◆ type

Constructor & Destructor Documentation

◆ FvdgP1TetElem()

Member Function Documentation

◆ cell() [1/2]

◆ cell() [2/2]

◆ edgeCenter()

◆ elemMap() [1/3]

◆ elemMap() [2/3]

◆ elemMap() [3/3]

◆ graphics()

◆ info()

◆ shapeFct()

◆ shapeFctEdgeCenter()

◆ shapeFctGradient()

◆ shapeFctVertex()

◆ solution()

◆ solutionEdgeCenter()

◆ solutionVertex()

◆ support()

◆ T() [1/2]

◆ T() [2/2]

◆ vertex()

Member Data Documentation

◆ cell_

◆ eta_

◆ graphics_

◆ nonVanishingNbr_

◆ nonVanishingSign_

◆ shapeFctEdgeCenter_

◆ shapeFctGradient_

◆ shapeFctVertex_

◆ T_