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

#include <bilinearForm2D.hh>

Inheritance diagram for linearFEM::Identity2d:

Public Member Functions
virtual Identity2d *	clone () 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()

virtual std::ostream& concepts::BilinearForm< Real , typename Realtype<Real >::type >::info ( std::ostream & os ) const

protectedvirtualinherited

Returns information in an output stream.

Reimplemented from concepts::OutputOperator.

Reimplemented in hp3D::RotRot, hp3D::Hook, hp3D::DivDiv< Weight >, hp3D::Identity< F >, hp3D::Laplace< F >, hp3D::BilinearFormTwoPartDeriv< F >, hp2Dedge::EdgeIdentity, hp2Dedge::Rotuv, hp2Dedge::RotRot< F >, hp2Dedge::IdentityMatrix< F >, hp2Dedge::Identity< F >, hp2Dedge::GraduvMatrix< F >, hp2Dedge::Graduv< F >, hp2D::RotRot, hp2D::DivDiv< Weight >, hp2D::BilinearFormTwoPartDeriv< F >, hp2D::BilinearFormOnePartDeriv< F >, hp2D::LaplaceMatrix< F >, and hp2D::Laplace< F >.

◆ 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

elmX	Left element (test functions)
elmY	Right element (trial functions)
em	Return 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

elmX	Left element
elmY	Right element
em	Return element matrix
ep	Element 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:

linearFEM/bilinearForm2D.hh

linearFEM::Identity2d Class Referenceabstract

Public Member Functions

Protected Member Functions

Private Attributes