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

#include <bilinearForm2D.hh>

Inheritance diagram for linearFEM::Laplace2d:

Public Member Functions
virtual Laplace2d *	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 stiffness matrix for a quadrilateral. More...

void	operator() (const linearFEM::Triangle &elmX, const linearFEM::Triangle &elmY, concepts::ElementMatrix< Real > &em) const
	Computes the element stiffness 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< concepts::Real2d >	shpfct_
	Storage area for values of derivatives of shape functions. More...

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 30 of file bilinearForm2D.hh.

Member Function Documentation

◆ clone() [1/2]

virtual Laplace2d* linearFEM::Laplace2d::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 48 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::Laplace2d::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::Laplace2d::operator()	(	const linearFEM::Quad &	elmX,
		const linearFEM::Quad &	elmY,
		concepts::ElementMatrix< Real > &	em
	)		const

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.

◆ operator()() [5/5]

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

Computes the element stiffness matrix for a triangle.

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

Member Data Documentation

◆ shpfct_

concepts::Array<concepts::Real2d> linearFEM::Laplace2d::shpfct_

mutableprivate

Storage area for values of derivatives of shape functions.

Definition at line 51 of file bilinearForm2D.hh.

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

linearFEM/bilinearForm2D.hh

linearFEM::Laplace2d Class Referenceabstract

Public Member Functions

Protected Member Functions

Private Attributes