A "square matrix" operator for the associated FE space and BLFIntegrators The sum of all the BLFIntegrators can be used form the matrix M. This class also supports other assembly levels specified via the SetAssemblyLevel() function. More...

#include <bilinearform.hpp>

Inheritance diagram for mfem::BilinearForm:

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Collaboration diagram for mfem::BilinearForm:

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

	BilinearForm (FiniteElementSpace f, BilinearForm bf, int ps=0)
	Create a BilinearForm on the FiniteElementSpace f, using the same integrators as the BilinearForm bf. More...

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

void	SetAssemblyLevel (AssemblyLevel assembly_level)
	Set the desired assembly level. More...

AssemblyLevel	GetAssemblyLevel () const
	Returns the assembly level. More...

Hybridization *	GetHybridization () const

void	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. More...

bool	StaticCondensationIsEnabled () const
	Check if static condensation was actually enabled by a previous call to EnableStaticCondensation(). More...

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)
	Enable hybridization. More...

void	UsePrecomputedSparsity (int ps=1)
	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. More...

void	UseSparsity (int I, int J, bool isSorted)
	Use the given CSR sparsity pattern to allocate the internal SparseMatrix. More...

void	UseSparsity (SparseMatrix &A)
	Use the sparsity of A to allocate the internal SparseMatrix. More...

void	AllocateMatrix ()
	Pre-allocate the internal SparseMatrix before assembly. More...

Array< BilinearFormIntegrator * > *	GetDBFI ()
	Access all the integrators added with AddDomainIntegrator(). More...

Array< BilinearFormIntegrator * > *	GetBBFI ()
	Access all the integrators added with AddBoundaryIntegrator(). More...

Array< Array< int > * > *	GetBBFI_Marker ()
	Access all boundary markers added with AddBoundaryIntegrator(). If no marker was specified when the integrator was added, the corresponding pointer (to Array<int>) will be NULL. More...

Array< BilinearFormIntegrator * > *	GetFBFI ()
	Access all integrators added with AddInteriorFaceIntegrator(). More...

Array< BilinearFormIntegrator * > *	GetBFBFI ()
	Access all integrators added with AddBdrFaceIntegrator(). More...

Array< Array< int > * > *	GetBFBFI_Marker ()
	Access all boundary markers added with AddBdrFaceIntegrator(). If no marker was specified when the integrator was added, the corresponding pointer (to Array<int>) will be NULL. More...

const double &	operator() (int i, int j)
	Returns a reference to: \( M_{ij} \). More...

virtual double &	Elem (int i, int j)
	Returns a reference to: \( M_{ij} \). More...

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

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

void	FullMult (const Vector &x, Vector &y) const
	Matrix vector multiplication with the original uneliminated matrix. The original matrix is \( M + M_e \) so we have: \( y = M x + M_e x \). More...

virtual void	AddMult (const Vector &x, Vector &y, const double a=1.0) const
	Add the matrix vector multiple to a vector: \( y += a M x \). More...

void	FullAddMult (const Vector &x, Vector &y) const
	Add the original uneliminated matrix vector multiple to a vector. The original matrix is \( M + Me \) so we have: \( y += M x + M_e x \). More...

virtual void	AddMultTranspose (const Vector &x, Vector &y, const double a=1.0) const
	Add the matrix transpose vector multiplication: \( y += a M^T x \). More...

void	FullAddMultTranspose (const Vector &x, Vector &y) const
	Add the original uneliminated matrix transpose vector multiple to a vector. The original matrix is \( M + M_e \) so we have: \( y += M^T x + {M_e}^T x \). More...

virtual void	MultTranspose (const Vector &x, Vector &y) const
	Matrix transpose vector multiplication: \( y = M^T x \). More...

double	InnerProduct (const Vector &x, const Vector &y) const
	Compute \( y^T M x \). More...

virtual MatrixInverse *	Inverse () const
	Returns a pointer to (approximation) of the matrix inverse: \( M^{-1} \). More...

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

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

SparseMatrix &	SpMat ()
	Returns a reference to the sparse matrix: \( M \). More...

SparseMatrix *	LoseMat ()
	Nullifies the internal matrix \( M \) and returns a pointer to it. Used for transfering ownership. More...

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

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

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

void	AddDomainIntegrator (BilinearFormIntegrator *bfi, Array< int > &elem_marker)

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

void	AddBoundaryIntegrator (BilinearFormIntegrator *bfi, Array< int > &bdr_marker)
	Adds new Boundary Integrator, restricted to specific boundary attributes. More...

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

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

void	AddBdrFaceIntegrator (BilinearFormIntegrator *bfi, Array< int > &bdr_marker)
	Adds new boundary Face Integrator, restricted to specific boundary attributes. More...

void	operator= (const double a)
	Sets all sparse values of \( M \) and \( M_e \) to 'a'. More...

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

virtual void	AssembleDiagonal (Vector &diag) const
	Assemble the diagonal of the bilinear form into diag. Note that diag is a tdof Vector. More...

virtual const Operator *	GetProlongation () const
	Get the finite element space prolongation operator. More...

virtual const Operator *	GetRestriction () const
	Get the finite element space restriction operator. More...

virtual const Operator *	GetOutputProlongation () const
	Get the output finite element space prolongation matrix. More...

virtual const Operator *	GetOutputRestrictionTranspose () const
	Returns the output fe space restriction matrix, transposed. More...

virtual const Operator *	GetOutputRestriction () const
	Get the output finite element space restriction matrix. More...

virtual void	FormLinearSystem (const Array< int > &ess_tdof_list, Vector &x, Vector &b, OperatorHandle &A, Vector &X, Vector &B, int copy_interior=0)
	Form the linear system A X = B, corresponding to this bilinear form and the linear form b(.). More...

template<typename OpType >
void	FormLinearSystem (const Array< int > &ess_tdof_list, Vector &x, Vector &b, OpType &A, Vector &X, Vector &B, int copy_interior=0)
	Form the linear system A X = B, corresponding to this bilinear form and the linear form b(.). More...

virtual void	FormSystemMatrix (const Array< int > &ess_tdof_list, OperatorHandle &A)
	Form the linear system matrix A, see FormLinearSystem() for details. More...

template<typename OpType >
void	FormSystemMatrix (const Array< int > &ess_tdof_list, OpType &A)
	Form the linear system matrix A, see FormLinearSystem() for details. More...

virtual void	RecoverFEMSolution (const Vector &X, const Vector &b, Vector &x)
	Recover the solution of a linear system formed with FormLinearSystem(). More...

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)
	Compute the element matrix of the given element. More...

void	ComputeBdrElementMatrix (int i, DenseMatrix &elmat)
	Compute the boundary element matrix of the given boundary element. More...

void	AssembleElementMatrix (int i, const DenseMatrix &elmat, int skip_zeros=1)
	Assemble the given element matrix. More...

void	AssembleElementMatrix (int i, const DenseMatrix &elmat, Array< int > &vdofs, int skip_zeros=1)
	Assemble the given element matrix. More...

void	AssembleBdrElementMatrix (int i, const DenseMatrix &elmat, int skip_zeros=1)
	Assemble the given boundary element matrix. More...

void	AssembleBdrElementMatrix (int i, const DenseMatrix &elmat, Array< int > &vdofs, int skip_zeros=1)
	Assemble the given boundary element matrix. More...

void	EliminateEssentialBC (const Array< int > &bdr_attr_is_ess, const Vector &sol, Vector &rhs, DiagonalPolicy dpolicy=DIAG_ONE)
	Eliminate essential boundary DOFs from the system. More...

void	EliminateEssentialBC (const Array< int > &bdr_attr_is_ess, DiagonalPolicy dpolicy=DIAG_ONE)
	Eliminate essential boundary DOFs from the system matrix. More...

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

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

void	EliminateVDofs (const Array< int > &vdofs, DiagonalPolicy dpolicy=DIAG_ONE)
	Eliminate the given vdofs, storing the eliminated part internally in \( M_e \). More...

void	EliminateEssentialBCFromDofs (const Array< int > &ess_dofs, const Vector &sol, Vector &rhs, DiagonalPolicy dpolicy=DIAG_ONE)
	Similar to EliminateVDofs(const Array<int> &, const Vector &, Vector &, DiagonalPolicy) but here ess_dofs is a marker (boolean) array on all vector-dofs (ess_dofs[i] < 0 is true). More...

void	EliminateEssentialBCFromDofs (const Array< int > &ess_dofs, DiagonalPolicy dpolicy=DIAG_ONE)
	Similar to EliminateVDofs(const Array<int> &, DiagonalPolicy) but here ess_dofs is a marker (boolean) array on all vector-dofs (ess_dofs[i] < 0 is true). More...

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

void	EliminateVDofsInRHS (const Array< int > &vdofs, const Vector &x, Vector &b)
	Use the stored eliminated part of the matrix (see EliminateVDofs(const Array<int> &, DiagonalPolicy)) to modify the r.h.s. b; vdofs is a list of DOFs (non-directional, i.e. >= 0). More...

double	FullInnerProduct (const Vector &x, const Vector &y) const
	Compute inner product for full uneliminated matrix \( y^T M x + y^T M_e x \). More...

virtual void	Update (FiniteElementSpace *nfes=NULL)
	Update the FiniteElementSpace and delete all data associated with the old one. More...

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

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

const FiniteElementSpace *	FESpace () const
	Read-only access to the associated FiniteElementSpace. More...

void	SetDiagonalPolicy (DiagonalPolicy policy)
	Sets diagonal policy used upon construction of the linear system. More...

void	UseExternalIntegrators ()
	Indicate that integrators are not owned by 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...

bool	IsSquare () const
	Returns whether the matrix is a square matrix. More...

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

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

Public Member Functions inherited from mfem::Operator
void	InitTVectors (const Operator Po, const Operator Ri, const Operator *Pi, Vector &x, Vector &b, Vector &X, Vector &B) const
	Initializes memory for true vectors of linear system. More...

	Operator (int s=0)
	Construct a square Operator with given size s (default 0). More...

	Operator (int h, int w)
	Construct an Operator with the given height (output size) and width (input size). More...

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

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

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

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

virtual MemoryClass	GetMemoryClass () const
	Return the MemoryClass preferred by the Operator. More...

virtual Operator &	GetGradient (const Vector &x) const
	Evaluate the gradient operator at the point x. The default behavior in class Operator is to generate an error. More...

void	FormLinearSystem (const Array< int > &ess_tdof_list, Vector &x, Vector &b, Operator *&A, Vector &X, Vector &B, int copy_interior=0)
	Form a constrained linear system using a matrix-free approach. More...

void	FormRectangularLinearSystem (const Array< int > &trial_tdof_list, const Array< int > &test_tdof_list, Vector &x, Vector &b, Operator *&A, Vector &X, Vector &B)
	Form a column-constrained linear system using a matrix-free approach. More...

void	FormSystemOperator (const Array< int > &ess_tdof_list, Operator *&A)
	Return in A a parallel (on truedofs) version of this square operator. More...

void	FormRectangularSystemOperator (const Array< int > &trial_tdof_list, const Array< int > &test_tdof_list, Operator *&A)
	Return in A a parallel (on truedofs) version of this rectangular operator (including constraints). More...

void	FormDiscreteOperator (Operator *&A)
	Return in A a parallel (on truedofs) version of this rectangular operator. 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 ()
	Virtual destructor. More...

Type	GetType () const
	Return the type ID of the Operator class. More...

Protected Member Functions
void	AllocMat ()

void	ConformingAssemble ()

	BilinearForm ()

Protected Member Functions inherited from mfem::Operator
void	FormConstrainedSystemOperator (const Array< int > &ess_tdof_list, ConstrainedOperator *&Aout)
	see FormSystemOperator() More...

void	FormRectangularConstrainedSystemOperator (const Array< int > &trial_tdof_list, const Array< int > &test_tdof_list, RectangularConstrainedOperator *&Aout)
	see FormRectangularSystemOperator() More...

Operator *	SetupRAP (const Operator Pi, const Operator Po)
	Returns RAP Operator of this, using input/output Prolongation matrices Pi corresponds to "P", Po corresponds to "Rt". More...

Protected Attributes
SparseMatrix *	mat
	Sparse matrix \( M \) to be associated with the form. Owned. More...

SparseMatrix *	mat_e
	Sparse Matrix \( M_e \) used to store the eliminations from the b.c. Owned. \( M + M_e = M_{original} \). More...

FiniteElementSpace *	fes
	FE space on which the form lives. Not owned. More...

AssemblyLevel	assembly
	The assembly level of the form (full, partial, etc.) More...

int	batch
	Element batch size used in the form action (1, 8, num_elems, etc.) More...

BilinearFormExtension *	ext
	Extension for supporting Full Assembly (FA), Element Assembly (EA), Partial Assembly (PA), or Matrix Free assembly (MF). More...

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

int	extern_bfs
	Indicates the BilinearFormIntegrators stored in domain_integs, boundary_integs, interior_face_integs, and boundary_face_integs are owned by another BilinearForm. More...

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

Array< Array< int > * >	domain_integs_marker

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

Array< Array< int > * >	boundary_integs_marker
	Entries are not owned. More...

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

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

Array< Array< int > * >	boundary_face_integs_marker
	Entries are not owned. More...

DenseMatrix	elemmat

Array< int >	vdofs

DenseTensor *	element_matrices
	Owned. More...

StaticCondensation *	static_cond
	Owned. More...

Hybridization *	hybridization
	Owned. More...

DiagonalPolicy	diag_policy

int	precompute_sparsity

Protected Attributes inherited from mfem::Operator
int	height
	Dimension of the output / number of rows in the matrix. More...

int	width
	Dimension of the input / number of columns in the matrix. More...

Additional Inherited Members
Public Types inherited from mfem::Operator
enum	DiagonalPolicy { DIAG_ZERO, DIAG_ONE, DIAG_KEEP }
	Defines operator diagonal policy upon elimination of rows and/or columns. More...

enum	Type { ANY_TYPE, MFEM_SPARSEMAT, Hypre_ParCSR, PETSC_MATAIJ, PETSC_MATIS, PETSC_MATSHELL, PETSC_MATNEST, PETSC_MATHYPRE, PETSC_MATGENERIC, Complex_Operator, MFEM_ComplexSparseMat, Complex_Hypre_ParCSR }
	Enumeration defining IDs for some classes derived from Operator. More...

Detailed Description

A "square matrix" operator for the associated FE space and BLFIntegrators The sum of all the BLFIntegrators can be used form the matrix M. This class also supports other assembly levels specified via the SetAssemblyLevel() function.

Definition at line 59 of file bilinearform.hpp.

Constructor & Destructor Documentation

mfem::BilinearForm::BilinearForm ( )

inlineprotected

Definition at line 131 of file bilinearform.hpp.

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

Creates bilinear form associated with FE space *f.

The pointer f is not owned by the newly constructed object.

Definition at line 66 of file bilinearform.cpp.

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

Create a BilinearForm on the FiniteElementSpace f, using the same integrators as the BilinearForm bf.

The pointer f is not owned by the newly constructed object.

The integrators in bf are copied as pointers and they are not owned by the newly constructed BilinearForm.

The optional parameter ps is used to initialize the internal flag precompute_sparsity, see UsePrecomputedSparsity() for details.

Definition at line 84 of file bilinearform.cpp.

mfem::BilinearForm::~BilinearForm ( )

virtual

Destroys bilinear form.

Definition at line 1102 of file bilinearform.cpp.

Member Function Documentation

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

Adds new boundary Face Integrator. Assumes ownership of bfi.

Definition at line 266 of file bilinearform.cpp.

void mfem::BilinearForm::AddBdrFaceIntegrator	(	BilinearFormIntegrator *	bfi,
		Array< int > &	bdr_marker
	)

Adds new boundary Face Integrator, restricted to specific boundary attributes.

Assumes ownership of bfi. The array bdr_marker is stored internally as a pointer to the given Array<int> object.

Definition at line 273 of file bilinearform.cpp.

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

Adds new Boundary Integrator. Assumes ownership of bfi.

Definition at line 248 of file bilinearform.cpp.

void mfem::BilinearForm::AddBoundaryIntegrator	(	BilinearFormIntegrator *	bfi,
		Array< int > &	bdr_marker
	)

Adds new Boundary Integrator, restricted to specific boundary attributes.

Assumes ownership of bfi. The array bdr_marker is stored internally as a pointer to the given Array<int> object.

Definition at line 254 of file bilinearform.cpp.

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

Adds new Domain Integrator. Assumes ownership of bfi.

Definition at line 235 of file bilinearform.cpp.

void mfem::BilinearForm::AddDomainIntegrator	(	BilinearFormIntegrator *	bfi,
		Array< int > &	elem_marker
	)

Adds new Domain Integrator restricted to certain elements specified by the elem_attr_marker.

Definition at line 241 of file bilinearform.cpp.

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

Adds new interior Face Integrator. Assumes ownership of bfi.

Definition at line 261 of file bilinearform.cpp.

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

inlinevirtual

Add the matrix vector multiple to a vector: \( y += a M x \).

Definition at line 274 of file bilinearform.hpp.

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

inlinevirtual

Add the matrix transpose vector multiplication: \( y += a M^T x \).

Definition at line 284 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 232 of file bilinearform.hpp.

void mfem::BilinearForm::AllocMat ( )

protected

Definition at line 21 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 385 of file bilinearform.cpp.

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

Assemble the given boundary element matrix.

The boundary element matrix elmat is assembled for the boundary element i, i.e. added to the system matrix. The flag skip_zeros skips the zero elements of the matrix, unless they are breaking the symmetry of the system matrix.

Definition at line 357 of file bilinearform.cpp.

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

Assemble the given boundary element matrix.

The boundary element matrix elmat is assembled for the boundary element i, i.e. added to the system matrix. The vdofs of the element are returned in vdofs. The flag skip_zeros skips the zero elements of the matrix, unless they are breaking the symmetry of the system matrix.

Definition at line 363 of file bilinearform.cpp.

void mfem::BilinearForm::AssembleDiagonal ( Vector & diag ) const

virtual

Assemble the diagonal of the bilinear form into diag. Note that diag is a tdof Vector.

When the AssemblyLevel is not LEGACY, and the mesh has hanging nodes, this method returns |P^T| d_l, where d_l is the diagonal of the form before applying conforming assembly, P^T is the transpose of the conforming prolongation, and |.| denotes the entry-wise absolute value. In general, this is just an approximation of the exact diagonal for this case.

Reimplemented from mfem::Operator.

Reimplemented in mfem::ParBilinearForm.

Definition at line 664 of file bilinearform.cpp.

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

Assemble the given element matrix.

The element matrix elmat is assembled for the element i, i.e. added to the system matrix. The flag skip_zeros skips the zero elements of the matrix, unless they are breaking the symmetry of the system matrix.

Definition at line 329 of file bilinearform.cpp.

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

Assemble the given element matrix.

The element matrix elmat is assembled for the element i, i.e. added to the system matrix. The vdofs of the element are returned in vdofs. The flag skip_zeros skips the zero elements of the matrix, unless they are breaking the symmetry of the system matrix.

Definition at line 335 of file bilinearform.cpp.

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

Compute the boundary element matrix of the given boundary element.

Definition at line 308 of file bilinearform.cpp.

void mfem::BilinearForm::ComputeElementMatrices ( )

Compute and store internally all element matrices.

Definition at line 863 of file bilinearform.cpp.

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

Compute the element matrix of the given element.

The element matrix is computed by calling the domain integrators or the one stored internally by a prior call of ComputeElementMatrices() is returned when available.

Definition at line 280 of file bilinearform.cpp.

void mfem::BilinearForm::ConformingAssemble ( )

protected

Definition at line 629 of file bilinearform.cpp.

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

virtual

Returns a reference to: \( M_{ij} \).

Implements mfem::Matrix.

Definition at line 209 of file bilinearform.cpp.

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

virtual

Returns constant reference to: \( M_{ij} \).

Implements mfem::Matrix.

Definition at line 214 of file bilinearform.cpp.

void mfem::BilinearForm::EliminateEssentialBC	(	const Array< int > &	bdr_attr_is_ess,
		const Vector &	sol,
		Vector &	rhs,
		DiagonalPolicy	dpolicy = `DIAG_ONE`
	)

Eliminate essential boundary DOFs from the system.

The array bdr_attr_is_ess marks boundary attributes that constitute the essential part of the boundary. By default, the diagonal at the essential DOFs is set to 1.0. This behavior is controlled by the argument dpolicy.

Definition at line 905 of file bilinearform.cpp.

void mfem::BilinearForm::EliminateEssentialBC	(	const Array< int > &	bdr_attr_is_ess,
		DiagonalPolicy	dpolicy = `DIAG_ONE`
	)

Eliminate essential boundary DOFs from the system matrix.

Definition at line 923 of file bilinearform.cpp.

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

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

Definition at line 940 of file bilinearform.cpp.

void mfem::BilinearForm::EliminateEssentialBCFromDofs	(	const Array< int > &	ess_dofs,
		const Vector &	sol,
		Vector &	rhs,
		DiagonalPolicy	dpolicy = `DIAG_ONE`
	)

Similar to EliminateVDofs(const Array<int> &, const Vector &, Vector &, DiagonalPolicy) but here ess_dofs is a marker (boolean) array on all vector-dofs (ess_dofs[i] < 0 is true).

Definition at line 997 of file bilinearform.cpp.

void mfem::BilinearForm::EliminateEssentialBCFromDofs	(	const Array< int > &	ess_dofs,
		DiagonalPolicy	dpolicy = `DIAG_ONE`
	)

Similar to EliminateVDofs(const Array<int> &, DiagonalPolicy) but here ess_dofs is a marker (boolean) array on all vector-dofs (ess_dofs[i] < 0 is true).

Definition at line 1012 of file bilinearform.cpp.

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

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

Definition at line 1024 of file bilinearform.cpp.

void mfem::BilinearForm::EliminateVDofs	(	const Array< int > &	vdofs,
		const Vector &	sol,
		Vector &	rhs,
		DiagonalPolicy	dpolicy = `DIAG_ONE`
	)

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

In this case the eliminations are applied to the internal \( M \) and rhs without storing the elimination matrix \( M_e \).

Definition at line 957 of file bilinearform.cpp.

void mfem::BilinearForm::EliminateVDofs	(	const Array< int > &	vdofs,
		DiagonalPolicy	dpolicy = `DIAG_ONE`
	)

Eliminate the given vdofs, storing the eliminated part internally in \( M_e \).

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 975 of file bilinearform.cpp.

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

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

Definition at line 1036 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 166 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 143 of file bilinearform.cpp.

FiniteElementSpace* mfem::BilinearForm::FESpace ( )

inline

Return the FE space associated with the BilinearForm.

Definition at line 605 of file bilinearform.hpp.

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

inline

Read-only access to the associated FiniteElementSpace.

Definition at line 607 of file bilinearform.hpp.

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

virtual

Finalizes the matrix initialization.

Reimplemented from mfem::Matrix.

Definition at line 224 of file bilinearform.cpp.

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

virtual

Form the linear system A X = B, corresponding to this bilinear form and the linear form b(.).

This method applies any necessary transformations to the linear system such as: eliminating boundary conditions; applying conforming constraints for non-conforming AMR; parallel assembly; 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.

Reimplemented in mfem::ParBilinearForm.

Definition at line 693 of file bilinearform.cpp.

template<typename OpType >

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

inline

Form the linear system A X = B, corresponding to this bilinear form and the linear form b(.).

Version of the method FormLinearSystem() where the system matrix is returned in the variable A, of type OpType, holding a reference to the system matrix (created with the method OpType::MakeRef()). The reference will be invalidated when SetOperatorType(), Update(), or the destructor is called.

Definition at line 451 of file bilinearform.hpp.

void mfem::BilinearForm::FormSystemMatrix	(	const Array< int > &	ess_tdof_list,
		OperatorHandle &	A
	)

virtual

Form the linear system matrix A, see FormLinearSystem() for details.

Reimplemented in mfem::ParBilinearForm.

Definition at line 762 of file bilinearform.cpp.

template<typename OpType >

void mfem::BilinearForm::FormSystemMatrix	(	const Array< int > &	ess_tdof_list,
		OpType &	A
	)

inline

Form the linear system matrix A, see FormLinearSystem() for details.

Version of the method FormSystemMatrix() where the system matrix is returned in the variable A, of type OpType, holding a reference to the system matrix (created with the method OpType::MakeRef()). The reference will be invalidated when SetOperatorType(), Update(), or the destructor is called.

Definition at line 473 of file bilinearform.hpp.

void mfem::BilinearForm::FreeElementMatrices ( )

inline

Free the memory used by the element matrices.

Definition at line 493 of file bilinearform.hpp.

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

inline

Add the original uneliminated matrix vector multiple to a vector. The original matrix is \( M + Me \) so we have: \( y += M x + M_e x \).

Definition at line 280 of file bilinearform.hpp.

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

inline

Add the original uneliminated matrix transpose vector multiple to a vector. The original matrix is \( M + M_e \) so we have: \( y += M^T x + {M_e}^T x \).

Definition at line 291 of file bilinearform.hpp.

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

inline

Compute inner product for full uneliminated matrix \( y^T M x + y^T M_e x \).

Definition at line 594 of file bilinearform.hpp.

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

inline

Matrix vector multiplication with the original uneliminated matrix. The original matrix is \( M + M_e \) so we have: \( y = M x + M_e x \).

Definition at line 270 of file bilinearform.hpp.

AssemblyLevel mfem::BilinearForm::GetAssemblyLevel ( ) const

inline

Returns the assembly level.

Definition at line 183 of file bilinearform.hpp.

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

inline

Access all the integrators added with AddBoundaryIntegrator().

Definition at line 238 of file bilinearform.hpp.

Array<Array<int>*>* mfem::BilinearForm::GetBBFI_Marker ( )

inline

Access all boundary markers added with AddBoundaryIntegrator(). If no marker was specified when the integrator was added, the corresponding pointer (to Array<int>) will be NULL.

Definition at line 242 of file bilinearform.hpp.

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

inline

Access all integrators added with AddBdrFaceIntegrator().

Definition at line 248 of file bilinearform.hpp.

Array<Array<int>*>* mfem::BilinearForm::GetBFBFI_Marker ( )

inline

Access all boundary markers added with AddBdrFaceIntegrator(). If no marker was specified when the integrator was added, the corresponding pointer (to Array<int>) will be NULL.

Definition at line 252 of file bilinearform.hpp.

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

inline

Access all the integrators added with AddDomainIntegrator().

Definition at line 235 of file bilinearform.hpp.

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

inline

Access all integrators added with AddInteriorFaceIntegrator().

Definition at line 245 of file bilinearform.hpp.

MFEM_DEPRECATED FiniteElementSpace* mfem::BilinearForm::GetFES ( )

inline

(DEPRECATED) Return the FE space associated with the BilinearForm.

Deprecated:: Use FESpace() instead.

Definition at line 602 of file bilinearform.hpp.

Hybridization* mfem::BilinearForm::GetHybridization ( ) const

inline

Definition at line 185 of file bilinearform.hpp.

virtual const Operator* mfem::BilinearForm::GetOutputProlongation ( ) const

inlinevirtual

Get the output finite element space prolongation matrix.

Reimplemented from mfem::Operator.

Definition at line 400 of file bilinearform.hpp.

virtual const Operator* mfem::BilinearForm::GetOutputRestriction ( ) const

inlinevirtual

Get the output finite element space restriction matrix.

Reimplemented from mfem::Operator.

Definition at line 410 of file bilinearform.hpp.

virtual const Operator* mfem::BilinearForm::GetOutputRestrictionTranspose ( ) const

inlinevirtual

Returns the output fe space restriction matrix, transposed.

Logically, this is the transpose of GetOutputRestriction, but in practice it is convenient to have it in transposed form for construction of RAP operators in matrix-free methods.

Reimplemented from mfem::Operator.

Definition at line 407 of file bilinearform.hpp.

virtual const Operator* mfem::BilinearForm::GetProlongation ( ) const

inlinevirtual

Get the finite element space prolongation operator.

Reimplemented from mfem::Operator.

Reimplemented in mfem::ParBilinearForm.

Definition at line 394 of file bilinearform.hpp.

virtual const Operator* mfem::BilinearForm::GetRestriction ( ) const

inlinevirtual

Get the finite element space restriction operator.

Reimplemented from mfem::Operator.

Reimplemented in mfem::ParBilinearForm.

Definition at line 397 of file bilinearform.hpp.

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

inline

Compute \( y^T M x \).

Definition at line 299 of file bilinearform.hpp.

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

virtual

Returns a pointer to (approximation) of the matrix inverse: \( M^{-1} \).

Implements mfem::Matrix.

Definition at line 219 of file bilinearform.cpp.

SparseMatrix* mfem::BilinearForm::LoseMat ( )

inline

Nullifies the internal matrix \( M \) and returns a pointer to it. Used for transfering ownership.

Definition at line 324 of file bilinearform.hpp.

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

virtual

Matrix vector multiplication: \( y = M x \).

Implements mfem::Operator.

Definition at line 1043 of file bilinearform.cpp.

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

inlinevirtual

Matrix transpose vector multiplication: \( y = M^T x \).

Reimplemented from mfem::Operator.

Definition at line 295 of file bilinearform.hpp.

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

inline

Returns a reference to: \( M_{ij} \).

Definition at line 256 of file bilinearform.hpp.

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

inline

Sets all sparse values of \( M \) and \( M_e \) to 'a'.

Definition at line 373 of file bilinearform.hpp.

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

virtual

Recover the solution of a linear system formed with FormLinearSystem().

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.

Reimplemented from mfem::Operator.

Reimplemented in mfem::ParBilinearForm.

Definition at line 805 of file bilinearform.cpp.

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

inline

Return the trace FE space associated with static condensation.

Definition at line 198 of file bilinearform.hpp.

void mfem::BilinearForm::SetAssemblyLevel ( AssemblyLevel assembly_level )

Set the desired assembly level.

Valid choices are:

This method must be called before assembly.

Definition at line 115 of file bilinearform.cpp.

void mfem::BilinearForm::SetDiagonalPolicy ( DiagonalPolicy policy )

Sets diagonal policy used upon construction of the linear system.

Policies include:

DIAG_ZERO (Set the diagonal values to zero)
DIAG_ONE (Set the diagonal values to one)
DIAG_KEEP (Keep the diagonal values)

Definition at line 1097 of file bilinearform.cpp.

int mfem::BilinearForm::Size ( ) const

inline

Get the size of the BilinearForm as a square matrix.

Definition at line 168 of file bilinearform.hpp.

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

inline

Returns a const reference to the sparse matrix.

Definition at line 309 of file bilinearform.hpp.

SparseMatrix& mfem::BilinearForm::SpMat ( )

inline

Returns a reference to the sparse matrix: \( M \).

Definition at line 316 of file bilinearform.hpp.

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

inline

Returns a const reference to the sparse matrix of eliminated b.c.: \( M_e \).

Definition at line 327 of file bilinearform.hpp.

SparseMatrix& mfem::BilinearForm::SpMatElim ( )

inline

Returns a reference to the sparse matrix of eliminated b.c.: \( M_e \).

Definition at line 334 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 195 of file bilinearform.hpp.

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

virtual

Update the FiniteElementSpace and delete all data associated with the old one.

Reimplemented in mfem::ParBilinearForm.

Definition at line 1055 of file bilinearform.cpp.

void mfem::BilinearForm::UseExternalIntegrators ( )

inline

Indicate that integrators are not owned by the BilinearForm.

Definition at line 619 of file bilinearform.hpp.

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 212 of file bilinearform.hpp.

void mfem::BilinearForm::UseSparsity	(	int *	I,
		int *	J,
		bool	isSorted
	)

Use the given CSR sparsity pattern to allocate the internal SparseMatrix.

The I and J arrays must define a square graph with size equal to GetVSize() of the associated FiniteElementSpace.
This method should be called after enabling static condensation or hybridization, if used.
In the case of static condensation, I and J are not used.
The ownership of the arrays I and J remains with the caller.

Definition at line 183 of file bilinearform.cpp.

void mfem::BilinearForm::UseSparsity ( SparseMatrix & A )

Use the sparsity of A to allocate the internal SparseMatrix.

Definition at line 199 of file bilinearform.cpp.

Member Data Documentation

AssemblyLevel mfem::BilinearForm::assembly

protected

The assembly level of the form (full, partial, etc.)

Definition at line 76 of file bilinearform.hpp.

int mfem::BilinearForm::batch

protected

Element batch size used in the form action (1, 8, num_elems, etc.)

Definition at line 78 of file bilinearform.hpp.

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

protected

Set of boundary face Integrators to be applied.

Definition at line 108 of file bilinearform.hpp.

Array<Array<int>*> mfem::BilinearForm::boundary_face_integs_marker

protected

Entries are not owned.

Definition at line 109 of file bilinearform.hpp.

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

protected

Set of Boundary Integrators to be applied.

Definition at line 101 of file bilinearform.hpp.

Array<Array<int>*> mfem::BilinearForm::boundary_integs_marker

protected

Entries are not owned.

Definition at line 102 of file bilinearform.hpp.

DiagonalPolicy mfem::BilinearForm::diag_policy

protected

This data member allows one to specify what should be done to the diagonal matrix entries and corresponding RHS values upon elimination of the constrained DoFs.

Definition at line 122 of file bilinearform.hpp.

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

protected

Set of Domain Integrators to be applied.

Definition at line 93 of file bilinearform.hpp.

Array<Array<int>*> mfem::BilinearForm::domain_integs_marker

protected

Element attribute marker (should be of length mesh->attributes) Includes all by default. 0 - ignore attribute 1 - include attribute

Definition at line 98 of file bilinearform.hpp.

DenseTensor* mfem::BilinearForm::element_matrices

protected

Owned.

Definition at line 114 of file bilinearform.hpp.

DenseMatrix mfem::BilinearForm::elemmat

protected

Definition at line 111 of file bilinearform.hpp.

BilinearFormExtension* mfem::BilinearForm::ext

protected

Extension for supporting Full Assembly (FA), Element Assembly (EA), Partial Assembly (PA), or Matrix Free assembly (MF).

Definition at line 81 of file bilinearform.hpp.

int mfem::BilinearForm::extern_bfs

protected

Indicates the BilinearFormIntegrators stored in domain_integs, boundary_integs, interior_face_integs, and boundary_face_integs are owned by another BilinearForm.

Definition at line 90 of file bilinearform.hpp.

FiniteElementSpace* mfem::BilinearForm::fes

protected

FE space on which the form lives. Not owned.

Definition at line 73 of file bilinearform.hpp.

Hybridization* mfem::BilinearForm::hybridization

protected

Owned.

Definition at line 117 of file bilinearform.hpp.

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

protected

Set of interior face Integrators to be applied.

Definition at line 105 of file bilinearform.hpp.

SparseMatrix* mfem::BilinearForm::mat

protected

Sparse matrix \( M \) to be associated with the form. Owned.

Definition at line 65 of file bilinearform.hpp.

SparseMatrix* mfem::BilinearForm::mat_e

protected

Sparse Matrix \( M_e \) used to store the eliminations from the b.c. Owned. \( M + M_e = M_{original} \).

Definition at line 70 of file bilinearform.hpp.

int mfem::BilinearForm::precompute_sparsity

protected

Definition at line 124 of file bilinearform.hpp.

long mfem::BilinearForm::sequence

protected

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

Definition at line 85 of file bilinearform.hpp.

StaticCondensation* mfem::BilinearForm::static_cond

protected

Owned.

Definition at line 116 of file bilinearform.hpp.

Array<int> mfem::BilinearForm::vdofs

protected

Definition at line 112 of file bilinearform.hpp.

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

fem/bilinearform.hpp
fem/bilinearform.cpp

Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation