Discrete equivalent for a reaction term in 2D for linear FEM. More...

#include <bilinearForm2D.hh>

Inheritance diagram for linearFEM::Identity2d:
concepts::BilinearForm< Real > concepts::Cloneable concepts::OutputOperator

Public Member Functions

virtual Identity2dclone () const
 Virtual constructor. More...
 
virtual BilinearForm * clone () const=0
 Virtual constructor. More...
 
virtual void operator() (const concepts::Element< Real > &elmX, const concepts::Element< Real > &elmY, concepts::ElementMatrix< Real > &em) const
 
virtual void operator() (const Element< typename Realtype< Real >::type > &elmX, const Element< typename Realtype< Real >::type > &elmY, ElementMatrix< Real > &em) const=0
 Evaluates the bilinear form for all shape functions on elmX and elmY and stores the result in the matrix em. More...
 
virtual void operator() (const Element< typename Realtype< Real >::type > &elmX, const Element< typename Realtype< Real >::type > &elmY, ElementMatrix< Real > &em, const ElementPair< typename Realtype< Real >::type > &ep) const
 Evaluates the bilinear form for all shape functions on elmX and elmY and stores the result in the matrix em. More...
 
void operator() (const linearFEM::Quad &elmX, const linearFEM::Quad &elmY, concepts::ElementMatrix< Real > &em) const
 Computes the element mass matrix for a quadrilateral. More...
 
void operator() (const linearFEM::Triangle &elmX, const linearFEM::Triangle &elmY, concepts::ElementMatrix< Real > &em) const
 Computes the element mass matrix for a triangle. More...
 

Protected Member Functions

virtual std::ostream & info (std::ostream &os) const
 Returns information in an output stream. More...
 

Private Attributes

concepts::Array< Real > shpfct_
 Storage area for values of shape functions. More...
 

Detailed Description

Discrete equivalent for a reaction term in 2D for linear FEM.

This bilinear form computes the mass matrix resulting from the discretization of a reaction term with reaction coefficient 1:

\[ \int_K \phi_i \phi_j \, dx \]

for the element shape functions $\phi_i$.

Author
Philipp Frauenfelder, 2002

Definition at line 63 of file bilinearForm2D.hh.

Member Function Documentation

◆ clone() [1/2]

virtual Identity2d* linearFEM::Identity2d::clone ( ) const
inlinevirtual

Virtual constructor.

Returns a pointer to a copy of itself. The caller is responsible to destroy this copy.

Implements concepts::Cloneable.

Definition at line 81 of file bilinearForm2D.hh.

◆ clone() [2/2]

virtual BilinearForm* concepts::BilinearForm< Real , typename Realtype<Real >::type >::clone ( ) const
pure virtualinherited

Virtual constructor.

Returns a pointer to a copy of itself. The caller is responsible to destroy this copy.

◆ info()

◆ operator()() [1/5]

virtual void linearFEM::Identity2d::operator() ( const concepts::Element< Real > &  elmX,
const concepts::Element< Real > &  elmY,
concepts::ElementMatrix< Real > &  em 
) const
virtual

◆ operator()() [2/5]

virtual void concepts::BilinearForm< Real , typename Realtype<Real >::type >::operator() ( const Element< G > &  elmX,
const Element< G > &  elmY,
ElementMatrix< F > &  em 
) const
pure virtualinherited

Evaluates the bilinear form for all shape functions on elmX and elmY and stores the result in the matrix em.

Postcondition
The returned matrix em has the correct size.
Parameters
elmXLeft element (test functions)
elmYRight element (trial functions)
emReturn element matrix

◆ operator()() [3/5]

virtual void concepts::BilinearForm< Real , typename Realtype<Real >::type >::operator() ( const Element< G > &  elmX,
const Element< G > &  elmY,
ElementMatrix< F > &  em,
const ElementPair< G > &  ep 
) const
inlinevirtualinherited

Evaluates the bilinear form for all shape functions on elmX and elmY and stores the result in the matrix em.

If this method is not reimplemented in a derived class, the default behaviour is to call the application operator without ep.

Postcondition
The returned matrix em has the correct size.
Parameters
elmXLeft element
elmYRight element
emReturn element matrix
epElement pair holding more information on the pair elmX and elmY

Definition at line 57 of file bilinearForm.hh.

◆ operator()() [4/5]

void linearFEM::Identity2d::operator() ( const linearFEM::Quad elmX,
const linearFEM::Quad elmY,
concepts::ElementMatrix< Real > &  em 
) const

Computes the element mass matrix for a quadrilateral.

The mass matrix has to be integrated numericaly since the Jacobian of the element map is not constant.

◆ operator()() [5/5]

void linearFEM::Identity2d::operator() ( const linearFEM::Triangle elmX,
const linearFEM::Triangle elmY,
concepts::ElementMatrix< Real > &  em 
) const

Computes the element mass matrix for a triangle.

The mass matrix is precomputed since the element map is constant.

Member Data Documentation

◆ shpfct_

concepts::Array<Real> linearFEM::Identity2d::shpfct_
mutableprivate

Storage area for values of shape functions.

Definition at line 84 of file bilinearForm2D.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