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

#include <lhsrhs.hh>

Inheritance diagram for Laplace:

Collaboration diagram for Laplace:

Public Member Functions
virtual Laplace *	clone () const
	Virtual constructor.
	Laplace (const concepts::Formula< Real > &frm)
	Constructor. Takes a function as parameter `frm`.
	Laplace (const concepts::DynArray< Real > &A_M)
	Constructor.
virtual void	operator() (const concepts::Element< Real > &elmX, const concepts::Element< Real > &elmY, concepts::ElementMatrix< Real > &em)
void	operator() (const TriangleP2 &elmX, const TriangleP2 &elmY, concepts::ElementMatrix< Real > &em)
	Computes the element stiffness matrix for a triangle with quadratic shape functions.
void	operator() (const linearFEM::Triangle &elmX, const linearFEM::Triangle &elmY, concepts::ElementMatrix< Real > &em)
	Computes the element stiffness matrix for a triangle with linear shape functions.
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`.
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`.
Static Public Attributes
static const concepts::Real2d	coord_ [4]
	Integration points (3rd order)
static const Real	weights_ [4]
	Integration weights (3rd order)
Protected Member Functions
virtual std::ostream &	info (std::ostream &os) const
	Returns information in an output stream.
Private Attributes
const concepts::DynArray< Real > *	A_M_
std::auto_ptr< const concepts::Formula< Real > >	frm_
	Formula.

Detailed Description

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

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

$\int_K A^M_\alpha(x) \nabla \phi_i \cdot \nabla \phi_j \, dx$

for the element shape functions $\phi_i$ .

Author:: Philipp Frauenfelder, 2002

Definition at line 33 of file lhsrhs.hh.

Constructor & Destructor Documentation

Laplace::Laplace ( const concepts::DynArray< Real > & A_M ) [inline]

Constructor.

Takes a function $A^M_\alpha(x)$ evaluated in all cells as parameter A_M.

Definition at line 38 of file lhsrhs.hh.

Laplace::Laplace ( const concepts::Formula< Real > & frm ) [inline]

Constructor. Takes a function as parameter frm.

Definition at line 40 of file lhsrhs.hh.

Member Function Documentation

virtual Laplace* Laplace::clone ( ) const [virtual]

Virtual constructor.

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

Implements concepts::Cloneable.

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.

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

Computes the element stiffness matrix for a triangle with linear shape functions.

The stiffness matrix is precomputed in case A_M was given in the constructor since the element map is constant. Otherwise, it is integrated numerically with 3rd order rule.

void Laplace::operator()	(	const TriangleP2 &	elmX,
		const TriangleP2 &	elmY,
		concepts::ElementMatrix< Real > &	em
	)

Computes the element stiffness matrix for a triangle with quadratic shape functions.

The stiffness matrix is integrated numerically with 3rd order rule.

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

Member Data Documentation

const concepts::DynArray<Real>* Laplace::A_M_ [private]

Definition at line 67 of file lhsrhs.hh.

const concepts::Real2d Laplace::coord_[4] [static]

Integration points (3rd order)

Definition at line 63 of file lhsrhs.hh.

std::auto_ptr<const concepts::Formula<Real> > Laplace::frm_ [private]

Formula.

Definition at line 69 of file lhsrhs.hh.

const Real Laplace::weights_[4] [static]

Integration weights (3rd order)

Definition at line 61 of file lhsrhs.hh.

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

app-radu/lhsrhs.hh

Public Member Functions

Static Public Attributes

Protected Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation