#include <bilinearform.hpp>

Inheritance diagram for mfem::BilinearForm:

Collaboration diagram for mfem::BilinearForm:

Public Member Functions
	BilinearForm (FiniteElementSpace *f)
	Creates bilinear form associated with FE space *f. More...

	BilinearForm (FiniteElementSpace f, BilinearForm bf, int ps=0)

int	Size () const
	Get the size of the BilinearForm as a square matrix. More...

void	EnableStaticCondensation ()

bool	StaticCondensationIsEnabled () const

FiniteElementSpace *	SCFESpace () const
	Return the trace FE space associated with static condensation. More...

void	EnableHybridization (FiniteElementSpace constr_space, BilinearFormIntegrator constr_integ, const Array< int > &ess_tdof_list)

void	UsePrecomputedSparsity (int ps=1)

void	AllocateMatrix ()

Array< BilinearFormIntegrator * > *	GetDBFI ()

Array< BilinearFormIntegrator * > *	GetBBFI ()

Array< BilinearFormIntegrator * > *	GetFBFI ()

Array< BilinearFormIntegrator * > *	GetBFBFI ()

const double &	operator() (int i, int j)

virtual double &	Elem (int i, int j)
	Returns reference to a_{ij}. More...

virtual const double &	Elem (int i, int j) const
	Returns constant reference to a_{ij}. More...

virtual void	Mult (const Vector &x, Vector &y) const
	Matrix vector multiplication. More...

void	FullMult (const Vector &x, Vector &y) const

virtual void	AddMult (const Vector &x, Vector &y, const double a=1.0) const

void	FullAddMult (const Vector &x, Vector &y) const

double	InnerProduct (const Vector &x, const Vector &y) const

virtual MatrixInverse *	Inverse () const
	Returns a pointer to (approximation) of the matrix inverse. More...

virtual void	Finalize (int skip_zeros=1)
	Finalizes the matrix initialization. More...

const SparseMatrix &	SpMat () const
	Returns a reference to the sparse matrix. More...

SparseMatrix &	SpMat ()

SparseMatrix *	LoseMat ()

const SparseMatrix &	SpMatElim () const
	Returns a reference to the sparse matrix of eliminated b.c. More...

SparseMatrix &	SpMatElim ()

void	AddDomainIntegrator (BilinearFormIntegrator *bfi)
	Adds new Domain Integrator. More...

void	AddBoundaryIntegrator (BilinearFormIntegrator *bfi)
	Adds new Boundary Integrator. More...

void	AddInteriorFaceIntegrator (BilinearFormIntegrator *bfi)
	Adds new interior Face Integrator. More...

void	AddBdrFaceIntegrator (BilinearFormIntegrator *bfi)
	Adds new boundary Face Integrator. More...

void	operator= (const double a)

void	Assemble (int skip_zeros=1)
	Assembles the form i.e. sums over all domain/bdr integrators. More...

void	FormLinearSystem (Array< int > &ess_tdof_list, Vector &x, Vector &b, SparseMatrix &A, Vector &X, Vector &B, int copy_interior=0)

void	RecoverFEMSolution (const Vector &X, const Vector &b, Vector &x)

void	ComputeElementMatrices ()
	Compute and store internally all element matrices. More...

void	FreeElementMatrices ()
	Free the memory used by the element matrices. More...

void	ComputeElementMatrix (int i, DenseMatrix &elmat)

void	AssembleElementMatrix (int i, const DenseMatrix &elmat, Array< int > &vdofs, int skip_zeros=1)

void	AssembleBdrElementMatrix (int i, const DenseMatrix &elmat, Array< int > &vdofs, int skip_zeros=1)

void	EliminateEssentialBC (Array< int > &bdr_attr_is_ess, Vector &sol, Vector &rhs, int d=0)

void	EliminateEssentialBC (Array< int > &bdr_attr_is_ess, int d=0)

void	EliminateEssentialBCDiag (Array< int > &bdr_attr_is_ess, double value)
	Perform elimination and set the diagonal entry to the given value. More...

void	EliminateVDofs (Array< int > &vdofs, Vector &sol, Vector &rhs, int d=0)
	Eliminate the given vdofs. NOTE: here, vdofs is a list of DOFs. More...

void	EliminateVDofs (Array< int > &vdofs, int d=0)

void	EliminateEssentialBCFromDofs (Array< int > &ess_dofs, Vector &sol, Vector &rhs, int d=0)

void	EliminateEssentialBCFromDofs (Array< int > &ess_dofs, int d=0)

void	EliminateEssentialBCFromDofsDiag (Array< int > &ess_dofs, double value)
	Perform elimination and set the diagonal entry to the given value. More...

void	EliminateVDofsInRHS (Array< int > &vdofs, const Vector &x, Vector &b)

double	FullInnerProduct (const Vector &x, const Vector &y) const

virtual void	Update (FiniteElementSpace *nfes=NULL)

FiniteElementSpace *	GetFES ()
	Return the FE space associated with the BilinearForm. More...

virtual	~BilinearForm ()
	Destroys bilinear form. More...

Public Member Functions inherited from mfem::Matrix
	Matrix (int s)
	Creates a square matrix of size s. More...

	Matrix (int h, int w)
	Creates a matrix of the given height and width. More...

virtual void	Print (std::ostream &out=std::cout, int width_=4) const
	Prints matrix to stream out. More...

virtual	~Matrix ()
	Destroys matrix. More...

Public Member Functions inherited from mfem::Operator
	Operator (int s=0)
	Construct a square Operator with given size s (default 0) More...

	Operator (int h, int w)

int	Height () const
	Get the height (size of output) of the Operator. Synonym with NumRows. More...

int	NumRows () const

int	Width () const
	Get the width (size of input) of the Operator. Synonym with NumCols. More...

int	NumCols () const

virtual void	MultTranspose (const Vector &x, Vector &y) const
	Action of the transpose operator. More...

virtual Operator &	GetGradient (const Vector &x) const
	Evaluate the gradient operator at the point x. More...

void	PrintMatlab (std::ostream &out, int n=0, int m=0) const
	Prints operator with input size n and output size m in matlab format. More...

virtual	~Operator ()

Protected Member Functions
void	AllocMat ()

void	ConformingAssemble ()

	BilinearForm ()

Protected Attributes
SparseMatrix *	mat
	Sparse matrix to be associated with the form. More...

SparseMatrix *	mat_e
	Matrix used to eliminate b.c. More...

FiniteElementSpace *	fes
	FE space on which the form lives. More...

long	sequence

int	extern_bfs

Array< BilinearFormIntegrator * >	dbfi
	Set of Domain Integrators to be applied. More...

Array< BilinearFormIntegrator * >	bbfi
	Set of Boundary Integrators to be applied. More...

Array< BilinearFormIntegrator * >	fbfi
	Set of interior face Integrators to be applied. More...

Array< BilinearFormIntegrator * >	bfbfi
	Set of boundary face Integrators to be applied. More...

DenseMatrix	elemmat

Array< int >	vdofs

DenseTensor *	element_matrices

StaticCondensation *	static_cond

Hybridization *	hybridization

int	precompute_sparsity

Protected Attributes inherited from mfem::Operator
int	height

int	width

Detailed Description

Class for bilinear form - "Matrix" with associated FE space and BLFIntegrators.

Definition at line 29 of file bilinearform.hpp.

Constructor & Destructor Documentation

mfem::BilinearForm::BilinearForm ( )

inlineprotected

Definition at line 74 of file bilinearform.hpp.

mfem::BilinearForm::BilinearForm ( FiniteElementSpace * f )

Creates bilinear form associated with FE space *f.

Definition at line 65 of file bilinearform.cpp.

mfem::BilinearForm::BilinearForm	(	FiniteElementSpace *	f,
		BilinearForm *	bf,
		int	ps = `0`
	)

Definition at line 78 of file bilinearform.cpp.

mfem::BilinearForm::~BilinearForm ( )

virtual

Destroys bilinear form.

Definition at line 807 of file bilinearform.cpp.

Member Function Documentation

void mfem::BilinearForm::AddBdrFaceIntegrator ( BilinearFormIntegrator * bfi )

Adds new boundary Face Integrator.

Definition at line 194 of file bilinearform.cpp.

void mfem::BilinearForm::AddBoundaryIntegrator ( BilinearFormIntegrator * bfi )

Adds new Boundary Integrator.

Definition at line 184 of file bilinearform.cpp.

void mfem::BilinearForm::AddDomainIntegrator ( BilinearFormIntegrator * bfi )

Adds new Domain Integrator.

Definition at line 179 of file bilinearform.cpp.

void mfem::BilinearForm::AddInteriorFaceIntegrator ( BilinearFormIntegrator * bfi )

Adds new interior Face Integrator.

Definition at line 189 of file bilinearform.cpp.

virtual void mfem::BilinearForm::AddMult	(	const Vector &	x,
		Vector &	y,
		const double	a = `1.0`
	)		const

inlinevirtual

Definition at line 144 of file bilinearform.hpp.

void mfem::BilinearForm::AllocateMatrix ( )

inline

Pre-allocate the internal SparseMatrix before assembly. If the flag 'precompute sparsity' is set, the matrix is allocated in CSR format (i.e. finalized) and the entries are initialized with zeros.

Definition at line 120 of file bilinearform.hpp.

void mfem::BilinearForm::AllocMat ( )

protected

Definition at line 20 of file bilinearform.cpp.

void mfem::BilinearForm::Assemble ( int skip_zeros = 1 )

Assembles the form i.e. sums over all domain/bdr integrators.

Definition at line 271 of file bilinearform.cpp.

void mfem::BilinearForm::AssembleBdrElementMatrix	(	int	i,
		const DenseMatrix &	elmat,
		Array< int > &	vdofs,
		int	skip_zeros = `1`
	)

Definition at line 249 of file bilinearform.cpp.

void mfem::BilinearForm::AssembleElementMatrix	(	int	i,
		const DenseMatrix &	elmat,
		Array< int > &	vdofs,
		int	skip_zeros = `1`
	)

Definition at line 227 of file bilinearform.cpp.

void mfem::BilinearForm::ComputeElementMatrices ( )

Compute and store internally all element matrices.

Definition at line 593 of file bilinearform.cpp.

void mfem::BilinearForm::ComputeElementMatrix	(	int	i,
		DenseMatrix &	elmat
	)

Definition at line 199 of file bilinearform.cpp.

void mfem::BilinearForm::ConformingAssemble ( )

protected

Definition at line 415 of file bilinearform.cpp.

double & mfem::BilinearForm::Elem	(	int	i,
		int	j
	)

virtual

Returns reference to a_{ij}.

Implements mfem::Matrix.

Definition at line 151 of file bilinearform.cpp.

const double & mfem::BilinearForm::Elem	(	int	i,
		int	j
	)		const

virtual

Returns constant reference to a_{ij}.

Implements mfem::Matrix.

Definition at line 156 of file bilinearform.cpp.

void mfem::BilinearForm::EliminateEssentialBC	(	Array< int > &	bdr_attr_is_ess,
		Vector &	sol,
		Vector &	rhs,
		int	d = `0`
	)

Eliminate essential boundary DOFs from the system. The array 'bdr_attr_is_ess' marks boundary attributes that constitute the essential part of the boundary. If d == 0, the diagonal at the essential DOFs is set to 1.0, otherwise it is left the same.

Definition at line 635 of file bilinearform.cpp.

void mfem::BilinearForm::EliminateEssentialBC	(	Array< int > &	bdr_attr_is_ess,
		int	d = `0`
	)

Definition at line 652 of file bilinearform.cpp.

void mfem::BilinearForm::EliminateEssentialBCDiag	(	Array< int > &	bdr_attr_is_ess,
		double	value
	)

Perform elimination and set the diagonal entry to the given value.

Definition at line 668 of file bilinearform.cpp.

void mfem::BilinearForm::EliminateEssentialBCFromDofs	(	Array< int > &	ess_dofs,
		Vector &	sol,
		Vector &	rhs,
		int	d = `0`
	)

Similar to EliminateVDofs but here ess_dofs is a marker (boolean) array on all vdofs (ess_dofs[i] < 0 is true).

Definition at line 723 of file bilinearform.cpp.

void mfem::BilinearForm::EliminateEssentialBCFromDofs	(	Array< int > &	ess_dofs,
		int	d = `0`
	)

Similar to EliminateVDofs but here ess_dofs is a marker (boolean) array on all vdofs (ess_dofs[i] < 0 is true).

Definition at line 737 of file bilinearform.cpp.

void mfem::BilinearForm::EliminateEssentialBCFromDofsDiag	(	Array< int > &	ess_dofs,
		double	value
	)

Perform elimination and set the diagonal entry to the given value.

Definition at line 748 of file bilinearform.cpp.

void mfem::BilinearForm::EliminateVDofs	(	Array< int > &	vdofs,
		Vector &	sol,
		Vector &	rhs,
		int	d = `0`
	)

Eliminate the given vdofs. NOTE: here, vdofs is a list of DOFs.

Definition at line 685 of file bilinearform.cpp.

void mfem::BilinearForm::EliminateVDofs	(	Array< int > &	vdofs,
		int	d = `0`
	)

Eliminate the given vdofs storing the eliminated part internally; this method works in conjunction with EliminateVDofsInRHS and allows elimination of boundary conditions in multiple right-hand sides. In this method, vdofs is a list of DOFs.

Definition at line 702 of file bilinearform.cpp.

void mfem::BilinearForm::EliminateVDofsInRHS	(	Array< int > &	vdofs,
		const Vector &	x,
		Vector &	b
	)

Use the stored eliminated part of the matrix (see EliminateVDofs) to modify r.h.s.; vdofs is a list of DOFs (non-directional, i.e. >= 0).

Definition at line 760 of file bilinearform.cpp.

void mfem::BilinearForm::EnableHybridization	(	FiniteElementSpace *	constr_space,
		BilinearFormIntegrator *	constr_integ,
		const Array< int > &	ess_tdof_list
	)

Enable hybridization; for details see the description for class Hybridization in fem/hybridization.hpp. This method should be called before assembly.

Definition at line 141 of file bilinearform.cpp.

void mfem::BilinearForm::EnableStaticCondensation ( )

Enable the use of static condensation. For details see the description for class StaticCondensation in fem/staticcond.hpp This method should be called before assembly. If the number of unknowns after static condensation is not reduced, it is not enabled.

Definition at line 124 of file bilinearform.cpp.

void mfem::BilinearForm::Finalize ( int skip_zeros = 1 )

virtual

Finalizes the matrix initialization.

Reimplemented from mfem::Matrix.

Definition at line 171 of file bilinearform.cpp.

void mfem::BilinearForm::FormLinearSystem	(	Array< int > &	ess_tdof_list,
		Vector &	x,
		Vector &	b,
		SparseMatrix &	A,
		Vector &	X,
		Vector &	B,
		int	copy_interior = `0`
	)

Form the linear system A X = B, corresponding to the current bilinear form and b(.), by applying any necessary transformations such as: eliminating boundary conditions; applying conforming constraints for non-conforming AMR; static condensation; hybridization.

The GridFunction-size vector x must contain the essential b.c. The BilinearForm and the LinearForm-size vector b must be assembled.

The vector X is initialized with a suitable initial guess: when using hybridization, the vector X is set to zero; otherwise, the essential entries of X are set to the corresponding b.c. and all other entries are set to zero (copy_interior == 0) or copied from x (copy_interior != 0).

This method can be called multiple times (with the same ess_tdof_list array) to initialize different right-hand sides and boundary condition values.

After solving the linear system, the finite element solution x can be recovered by calling RecoverFEMSolution (with the same vectors X, b, and x).

NOTE: If there are no transformations, X simply reuses the data of x.

Definition at line 450 of file bilinearform.cpp.

void mfem::BilinearForm::FreeElementMatrices ( )

inline

Free the memory used by the element matrices.

Definition at line 240 of file bilinearform.hpp.

void mfem::BilinearForm::FullAddMult	(	const Vector &	x,
		Vector &	y
	)		const

inline

Definition at line 147 of file bilinearform.hpp.

double mfem::BilinearForm::FullInnerProduct	(	const Vector &	x,
		const Vector &	y
	)		const

inline

Definition at line 284 of file bilinearform.hpp.

void mfem::BilinearForm::FullMult	(	const Vector &	x,
		Vector &	y
	)		const

inline

Definition at line 141 of file bilinearform.hpp.

Array<BilinearFormIntegrator*>* mfem::BilinearForm::GetBBFI ( )

inline

Definition at line 124 of file bilinearform.hpp.

Array<BilinearFormIntegrator*>* mfem::BilinearForm::GetBFBFI ( )

inline

Definition at line 128 of file bilinearform.hpp.

Array<BilinearFormIntegrator*>* mfem::BilinearForm::GetDBFI ( )

inline

Definition at line 122 of file bilinearform.hpp.

Array<BilinearFormIntegrator*>* mfem::BilinearForm::GetFBFI ( )

inline

Definition at line 126 of file bilinearform.hpp.

FiniteElementSpace* mfem::BilinearForm::GetFES ( )

inline

Return the FE space associated with the BilinearForm.

Definition at line 290 of file bilinearform.hpp.

double mfem::BilinearForm::InnerProduct	(	const Vector &	x,
		const Vector &	y
	)		const

inline

Definition at line 150 of file bilinearform.hpp.

MatrixInverse * mfem::BilinearForm::Inverse ( ) const

virtual

Returns a pointer to (approximation) of the matrix inverse.

Implements mfem::Matrix.

Definition at line 166 of file bilinearform.cpp.

SparseMatrix* mfem::BilinearForm::LoseMat ( )

inline

Definition at line 170 of file bilinearform.hpp.

void mfem::BilinearForm::Mult	(	const Vector &	x,
		Vector &	y
	)		const

virtual

Matrix vector multiplication.

Implements mfem::Operator.

Definition at line 161 of file bilinearform.cpp.

const double& mfem::BilinearForm::operator()	(	int	i,
		int	j
	)

inline

Definition at line 130 of file bilinearform.hpp.

void mfem::BilinearForm::operator= ( const double a )

inline

Definition at line 196 of file bilinearform.hpp.

void mfem::BilinearForm::RecoverFEMSolution	(	const Vector &	X,
		const Vector &	b,
		Vector &	x
	)

Call this method after solving a linear system constructed using the FormLinearSystem method to recover the solution as a GridFunction-size vector in x. Use the same arguments as in the FormLinearSystem call.

Definition at line 545 of file bilinearform.cpp.

FiniteElementSpace* mfem::BilinearForm::SCFESpace ( ) const

inline

Return the trace FE space associated with static condensation.

Definition at line 102 of file bilinearform.hpp.

int mfem::BilinearForm::Size ( ) const

inline

Get the size of the BilinearForm as a square matrix.

Definition at line 89 of file bilinearform.hpp.

const SparseMatrix& mfem::BilinearForm::SpMat ( ) const

inline

Returns a reference to the sparse matrix.

Definition at line 160 of file bilinearform.hpp.

SparseMatrix& mfem::BilinearForm::SpMat ( )

inline

Definition at line 165 of file bilinearform.hpp.

const SparseMatrix& mfem::BilinearForm::SpMatElim ( ) const

inline

Returns a reference to the sparse matrix of eliminated b.c.

Definition at line 173 of file bilinearform.hpp.

SparseMatrix& mfem::BilinearForm::SpMatElim ( )

inline

Definition at line 178 of file bilinearform.hpp.

bool mfem::BilinearForm::StaticCondensationIsEnabled ( ) const

inline

Check if static condensation was actually enabled by a previous call to EnableStaticCondensation.

Definition at line 99 of file bilinearform.hpp.

void mfem::BilinearForm::Update ( FiniteElementSpace * nfes = NULL )

virtual

Reimplemented in mfem::ParBilinearForm.

Definition at line 767 of file bilinearform.cpp.

void mfem::BilinearForm::UsePrecomputedSparsity ( int ps = 1 )

inline

For scalar FE spaces, precompute the sparsity pattern of the matrix (assuming dense element matrices) based on the types of integrators present in the bilinear form.

Definition at line 115 of file bilinearform.hpp.

Member Data Documentation

Array<BilinearFormIntegrator*> mfem::BilinearForm::bbfi

protected

Set of Boundary Integrators to be applied.

Definition at line 51 of file bilinearform.hpp.

Array<BilinearFormIntegrator*> mfem::BilinearForm::bfbfi

protected

Set of boundary face Integrators to be applied.

Definition at line 57 of file bilinearform.hpp.

Array<BilinearFormIntegrator*> mfem::BilinearForm::dbfi

protected

Set of Domain Integrators to be applied.

Definition at line 48 of file bilinearform.hpp.

DenseTensor* mfem::BilinearForm::element_matrices

protected

Definition at line 62 of file bilinearform.hpp.

DenseMatrix mfem::BilinearForm::elemmat

protected

Definition at line 59 of file bilinearform.hpp.

int mfem::BilinearForm::extern_bfs

protected

Definition at line 45 of file bilinearform.hpp.

Array<BilinearFormIntegrator*> mfem::BilinearForm::fbfi

protected

Set of interior face Integrators to be applied.

Definition at line 54 of file bilinearform.hpp.

FiniteElementSpace* mfem::BilinearForm::fes

protected

FE space on which the form lives.

Definition at line 39 of file bilinearform.hpp.

Hybridization* mfem::BilinearForm::hybridization

protected

Definition at line 65 of file bilinearform.hpp.

SparseMatrix* mfem::BilinearForm::mat

protected

Sparse matrix to be associated with the form.

Definition at line 33 of file bilinearform.hpp.

SparseMatrix* mfem::BilinearForm::mat_e

protected

Matrix used to eliminate b.c.

Definition at line 36 of file bilinearform.hpp.

int mfem::BilinearForm::precompute_sparsity

protected

Definition at line 67 of file bilinearform.hpp.

long mfem::BilinearForm::sequence

protected

Indicates the Mesh::sequence corresponding to the current state of the BilinearForm.

Definition at line 43 of file bilinearform.hpp.

StaticCondensation* mfem::BilinearForm::static_cond

protected

Definition at line 64 of file bilinearform.hpp.

Array<int> mfem::BilinearForm::vdofs

protected

Definition at line 60 of file bilinearform.hpp.

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

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation