Discrete equivalent of the Laplacian in 2D for linear FEM. More...

#include <bilinearForm2D.hh>

Inheritance diagram for linearFEM::Laplace2d:

Collaboration diagram for linearFEM::Laplace2d:

Public Member Functions
virtual Laplace2d *	clone () const
	Virtual constructor.
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)
	Evaluates the bilinear form for all shape functions on `elmX` and `elmY` and stores the result in the matrix `em`.
virtual void	operator() (const Element< typename Realtype< Real >::type > &elmX, const Element< typename Realtype< Real >::type > &elmY, ElementMatrix< Real > &em)=0
	Evaluates the bilinear form for all shape functions on `elmX` and `elmY` and stores the result in the matrix `em`.
void	operator() (const linearFEM::Quad &elmX, const linearFEM::Quad &elmY, concepts::ElementMatrix< Real > &em)
	Computes the element stiffness matrix for a quadrilateral.
void	operator() (const linearFEM::Triangle &elmX, const linearFEM::Triangle &elmY, concepts::ElementMatrix< Real > &em)
	Computes the element stiffness matrix for a triangle.
virtual void	operator() (const concepts::Element< Real > &elmX, const concepts::Element< Real > &elmY, concepts::ElementMatrix< Real > &em)
Protected Member Functions
virtual std::ostream &	info (std::ostream &os) const
	Returns information in an output stream.
Private Attributes
concepts::Array< concepts::Real2d >	shpfct_
	Storage area for values of derivatives of shape functions.

Detailed Description

Discrete equivalent of the Laplacian in 2D for linear FEM.

This bilinear form computes the stiffness matrix resulting from the discretization of the Laplacian (with integration by parts):

$\int_K \nabla \phi_i \cdot \nabla \phi_j \, dx$

for the element shape functions $\phi_i$ .

Author:: Philipp Frauenfelder, 2002

Definition at line 27 of file bilinearForm2D.hh.

Member Function Documentation

virtual Laplace2d* linearFEM::Laplace2d::clone ( ) const [inline, virtual]

Virtual constructor.

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

Implements concepts::Cloneable.

Definition at line 45 of file bilinearForm2D.hh.

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

Returns information in an output stream.

Reimplemented from concepts::OutputOperator.

Reimplemented in hp2D::DiffussionReaction, TraceMass, hp2D::DivDiv< Weight >, hp2D::RotRot, hp2Dedge::RotRot, hp2Dedge::Identity, hp2Dedge::Graduv, hp2Dedge::EdgeIdentity, hp3D::Laplace, hp3D::Identity, hp3D::DivDiv< Weight >, hp3D::Hook, and hp3D::RotRot.

virtual void concepts::BilinearForm< Real , typename Realtype<Real >::type >::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
	)		`[inline, virtual, inherited]`

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 53 of file bilinearForm.hh.

Here is the call graph for this function:

virtual void concepts::BilinearForm< Real , typename Realtype<Real >::type >::operator()	(	const Element< typename Realtype<Real >::type > &	elmX,
		const Element< typename Realtype<Real >::type > &	elmY,
		ElementMatrix< Real > &	em
	)		`[pure virtual, inherited]`

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

void linearFEM::Laplace2d::operator()	(	const linearFEM::Quad &	elmX,
		const linearFEM::Quad &	elmY,
		concepts::ElementMatrix< Real > &	em
	)

Computes the element stiffness matrix for a quadrilateral.

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

void linearFEM::Laplace2d::operator()	(	const linearFEM::Triangle &	elmX,
		const linearFEM::Triangle &	elmY,
		concepts::ElementMatrix< Real > &	em
	)

Computes the element stiffness matrix for a triangle.

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

virtual void linearFEM::Laplace2d::operator()	(	const concepts::Element< Real > &	elmX,
		const concepts::Element< Real > &	elmY,
		concepts::ElementMatrix< Real > &	em
	)		`[virtual]`

Member Data Documentation

concepts::Array<concepts::Real2d> linearFEM::Laplace2d::shpfct_ [private]

Storage area for values of derivatives of shape functions.

Definition at line 48 of file bilinearForm2D.hh.

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

linearFEM/bilinearForm2D.hh

Public Member Functions

Protected Member Functions

Private Attributes

Detailed Description

Member Function Documentation

Member Data Documentation