Tetrahedral element with linear shapefunctions. More...

#include <element.hh>

Inheritance diagram for linDG3D::FvdgP1TetElem:
linDG3D::FvdgElement concepts::ElementWithCell< Real >

Public Types

typedef Real type
 

Public Member Functions

virtual const concepts::Tetrahedron3dcell () 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::Tetrahedronsupport () 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::Tetrahedron3dcell_
 
std::unique_ptr< concepts::TMatrixBase< Real > > T_
 

Static Protected Attributes

static Real eta_ [6][3]
 
static std::unique_ptr< FvdgP1TetGraphicsgraphics_
 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
cellThe Cell the element lives on
idxDescribes 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
edgeIdxEdge 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
fctIdxnumber of the shape function
xireference 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
fctIdxnumber of the shape function
edgeIdxnumber 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
fctIdxnumber 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
fctIdxnumber of the shape function
vtxIdxnumber 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
solsolution vector
xireference 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
solsolution vector
edgeIdxnumber 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
solsolution vector
vertexIdxnumber 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:
Page URL: http://wiki.math.ethz.ch/bin/view/Concepts/WebHome
21 August 2020
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