Line element with linear shape function in 1D. More...

#include <element1D.hh>

Inheritance diagram for linearFEM::Line:
linearFEM::Element concepts::ElementWithCell< Real >

Public Types

typedef Real type
 

Public Member Functions

virtual const concepts::Edge1dcell () const
 Returns the cell of this element. More...
 
virtual const Cell & cell () const=0
 Returns the cell on which the element is built. More...
 
Real3d elemMap (const Real coord_local) const
 
Real3d elemMap (const Real2d &coord_local) const
 
Real3d elemMap (const Real3d &coord_local) const
 
virtual const concepts::ElementGraphics< Real > * graphics () const
 
 Line (const concepts::Edge1d &cell, concepts::TColumn< Real > *T0, concepts::TColumn< Real > *T1=0)
 Constructor. More...
 
 Line (const concepts::Edge1d &cell, uint idx[])
 Constructor. More...
 
Real shapefct (const uint i, const Real xi) const
 Computes the value of the ith shape function in the point xi. More...
 
Real shapefctD (const uint i) const
 Returns the derivative of the ith shape function. More...
 
virtual const concepts::Edgesupport () const
 Returns the support of this element. More...
 
virtual 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...
 

Protected Member Functions

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

Protected Attributes

std::unique_ptr< concepts::TMatrixBase< Real > > T_
 T matrix of this element. More...
 

Private Attributes

const concepts::Edge1dcell_
 Cell of the element. More...
 

Static Private Attributes

static std::unique_ptr< LineGraphicsgraphics_
 

Detailed Description

Line element with linear shape function in 1D.

The cell which is contained in this element is responsible for the topology (connectivity) and the geometry. The shape functions can be evaluated with the shapefct and shapefctD members. The information in the T matrix is generated in the space and stored here.

Author
Philipp Frauenfelder, 2002
Examples
linearFEM1d-simple.cc, and linearFEM1d.cc.

Definition at line 34 of file element1D.hh.

Member Typedef Documentation

◆ type

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

Definition at line 81 of file element.hh.

Constructor & Destructor Documentation

◆ Line() [1/2]

linearFEM::Line::Line ( const concepts::Edge1d cell,
uint  idx[] 
)
inline

Constructor.

Creates a T matrix out of idx.

See also
concepts::TIndex
Parameters
cellCell of the element
idxDescribes the map local / global dof

Definition at line 41 of file element1D.hh.

◆ Line() [2/2]

linearFEM::Line::Line ( const concepts::Edge1d cell,
concepts::TColumn< Real > *  T0,
concepts::TColumn< Real > *  T1 = 0 
)
inline

Constructor.

Creates a T matrix out of T0 and T1

See also
concepts::TMatrix
Parameters
cellCell of the element
T0Contains T columns
T1Contains T columns

Definition at line 49 of file element1D.hh.

Member Function Documentation

◆ cell() [1/2]

virtual const concepts::Edge1d& linearFEM::Line::cell ( ) const
inlinevirtual

Returns the cell of this element.

Implements linearFEM::Element.

Examples
linearFEM1d-simple.cc, and linearFEM1d.cc.

Definition at line 53 of file element1D.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 >.

◆ 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()

virtual const concepts::ElementGraphics<Real>* linearFEM::Line::graphics ( ) const
virtual

◆ info()

virtual std::ostream& linearFEM::Line::info ( std::ostream &  os) const
protectedvirtual

◆ shapefct()

Real linearFEM::Line::shapefct ( const uint  i,
const Real  xi 
) const

Computes the value of the ith shape function in the point xi.

Precondition
xi >= -1 and xi <= 1
Parameters
iIndex of the shape fct. (0, 1, 2)
xiCoordinate
Examples
linearFEM1d-simple.cc, and linearFEM1d.cc.

◆ shapefctD()

Real linearFEM::Line::shapefctD ( const uint  i) const

Returns the derivative of the ith shape function.

The shape functions are linear and the derivative is constant. Therefore, no coordinates are necessary.

Parameters
iIndex of the shape fct. (0, 1)

◆ support()

virtual const concepts::Edge& linearFEM::Line::support ( ) const
inlinevirtual

Returns the support of this element.

Implements linearFEM::Element.

Definition at line 52 of file element1D.hh.

◆ T() [1/2]

virtual const concepts::TMatrixBase<Real>& linearFEM::Element::T ( ) const
inlinevirtualinherited

Returns the T matrix of this element.

Definition at line 47 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 >.

Member Data Documentation

◆ cell_

const concepts::Edge1d& linearFEM::Line::cell_
private

Cell of the element.

Definition at line 71 of file element1D.hh.

◆ graphics_

std::unique_ptr<LineGraphics> linearFEM::Line::graphics_
staticprivate

Definition at line 72 of file element1D.hh.

◆ T_

std::unique_ptr<concepts::TMatrixBase<Real> > linearFEM::Element::T_
protectedinherited

T matrix of this element.

Definition at line 50 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
© 2020 Eidgenössische Technische Hochschule Zürich