#include <bilinearform.hpp>

Inheritance diagram for mfem::DiscreteLinearOperator:

Collaboration diagram for mfem::DiscreteLinearOperator:

Public Member Functions
	DiscreteLinearOperator (FiniteElementSpace domain_fes, FiniteElementSpace range_fes)
	Construct a DiscreteLinearOperator on the given FiniteElementSpaces domain_fes and range_fes.

void	AddDomainInterpolator (DiscreteInterpolator *di)
	Adds a domain interpolator. Assumes ownership of di.

void	AddDomainInterpolator (DiscreteInterpolator *di, Array< int > &elem_marker)

void	AddTraceFaceInterpolator (DiscreteInterpolator *di)
	Adds a trace face interpolator. Assumes ownership of di.

Array< BilinearFormIntegrator * > *	GetDI ()
	Access all interpolators added with AddDomainInterpolator().

Array< Array< int > * > *	GetDI_Marker ()

void	SetAssemblyLevel (AssemblyLevel assembly_level)
	Set the desired assembly level. The default is AssemblyLevel::FULL.

virtual void	Assemble (int skip_zeros=1)
	Construct the internal matrix representation of the discrete linear operator.

const Operator *	GetOutputRestrictionTranspose () const override
	Get the output finite element space restriction matrix in transposed form.

Public Member Functions inherited from mfem::MixedBilinearForm
	MixedBilinearForm (FiniteElementSpace tr_fes, FiniteElementSpace te_fes)
	Construct a MixedBilinearForm on the given trial, tr_fes, and test, te_fes, FiniteElementSpaces.

	MixedBilinearForm (FiniteElementSpace tr_fes, FiniteElementSpace te_fes, MixedBilinearForm *mbf)
	Create a MixedBilinearForm on the given trial, tr_fes, and test, te_fes, FiniteElementSpaces, using the same integrators as the MixedBilinearForm mbf.

real_t &	Elem (int i, int j) override
	Returns a reference to: \( M_{ij} \).

const real_t &	Elem (int i, int j) const override
	Returns a reference to: \( M_{ij} \).

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

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

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

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

MatrixInverse *	Inverse () const override
	Returns a pointer to (approximation) of the matrix inverse: \( M^{-1} \) (currently unimplemented and returns NULL)

void	Finalize (int skip_zeros=1) override
	Finalizes the matrix initialization if the AssemblyLevel is AssemblyLevel::LEGACY.

void	GetBlocks (Array2D< SparseMatrix * > &blocks) const
	Extract the associated matrix as SparseMatrix blocks. The number of block rows and columns is given by the vector dimensions (vdim) of the test and trial spaces, respectively.

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

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

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

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

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

void	AddDomainIntegrator (BilinearFormIntegrator *bfi)
	Adds a domain integrator. Assumes ownership of bfi.

void	AddDomainIntegrator (BilinearFormIntegrator *bfi, Array< int > &elem_marker)
	Adds a domain integrator. Assumes ownership of bfi.

void	AddBoundaryIntegrator (BilinearFormIntegrator *bfi)
	Adds a boundary integrator. Assumes ownership of bfi.

void	AddBoundaryIntegrator (BilinearFormIntegrator *bfi, Array< int > &bdr_marker)
	Adds a boundary integrator. Assumes ownership of bfi.

void	AddInteriorFaceIntegrator (BilinearFormIntegrator *bfi)
	Adds an interior face integrator. Assumes ownership of bfi.

void	AddBdrFaceIntegrator (BilinearFormIntegrator *bfi)
	Adds a boundary face integrator. Assumes ownership of bfi.

void	AddBdrFaceIntegrator (BilinearFormIntegrator *bfi, Array< int > &bdr_marker)
	Adds a boundary face integrator. Assumes ownership of bfi.

void	AddTraceFaceIntegrator (BilinearFormIntegrator *bfi)
	Add a trace face integrator. Assumes ownership of bfi.

void	AddBdrTraceFaceIntegrator (BilinearFormIntegrator *bfi)
	Adds a boundary trace face integrator. Assumes ownership of bfi.

void	AddBdrTraceFaceIntegrator (BilinearFormIntegrator *bfi, Array< int > &bdr_marker)
	Adds a boundary trace face integrator. Assumes ownership of bfi.

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

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

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

Array< Array< int > * > *	GetBBFI_Marker ()
	Access all boundary markers added with AddBoundaryIntegrator().

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

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

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.

Array< BilinearFormIntegrator * > *	GetTFBFI ()
	Access all integrators added with AddTraceFaceIntegrator().

Array< BilinearFormIntegrator * > *	GetBTFBFI ()
	Access all integrators added with AddBdrTraceFaceIntegrator().

Array< Array< int > * > *	GetBTFBFI_Marker ()
	Access all boundary markers added with AddBdrTraceFaceIntegrator()

void	operator= (const real_t a)
	Sets all sparse values of \( M \) to a.

void	SetAssemblyLevel (AssemblyLevel assembly_level)
	Set the desired assembly level. The default is AssemblyLevel::LEGACY.

void	Assemble (int skip_zeros=1)

void	AssembleDiagonal_ADAt (const Vector &D, Vector &diag) const
	Assemble the diagonal of ADA^T into diag, where A is this mixed bilinear form and D is a diagonal.

const Operator *	GetProlongation () const override
	Get the input finite element space prolongation matrix.

const Operator *	GetRestriction () const override
	Get the input finite element space restriction matrix.

const Operator *	GetOutputProlongation () const override
	Get the test finite element space prolongation matrix.

const Operator *	GetOutputRestriction () const override
	Get the test finite element space restriction matrix.

void	ConformingAssemble ()
	For partially conforming trial and/or test FE spaces, complete the assembly process by performing \( P2^t A P1 \) where \( A \) is the internal sparse matrix; \( P1 \) and \( P2 \) are the conforming prolongation matrices of the trial and test FE spaces, respectively. After this call the MixedBilinearForm becomes an operator on the conforming FE spaces.

void	ComputeElementMatrix (int i, DenseMatrix &elmat) const
	Compute the element matrix of the given element.

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

void	ComputeTraceFaceMatrix (int i, DenseMatrix &elmat) const
	Compute the trace face matrix of the given face element.

void	ComputeBdrTraceFaceMatrix (int i, DenseMatrix &elmat) const
	Compute the boundary trace face matrix of the given boundary element.

void	ComputeFaceMatrix (int i, DenseMatrix &elmat) const
	Compute the face matrix of the given face element.

void	ComputeBdrFaceMatrix (int i, DenseMatrix &elmat) const
	Compute the boundary face matrix of the given boundary element.

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

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

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

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

void	EliminateTrialEssentialBC (const Array< int > &bdr_attr_is_ess, const Vector &sol, Vector &rhs)
	Eliminate essential boundary trial DOFs from the system.

void	EliminateTrialEssentialBC (const Array< int > &bdr_attr_is_ess)
	Eliminate essential boundary trial DOFs from the system matrix.

MFEM_DEPRECATED void	EliminateTrialDofs (const Array< int > &bdr_attr_is_ess, const Vector &sol, Vector &rhs)
	(DEPRECATED) Eliminate essential boundary trial DOFs from the system.

void	EliminateTrialVDofs (const Array< int > &vdofs, const Vector &sol, Vector &rhs)
	Eliminate the given trial vdofs. NOTE: here, vdofs is a list of DOFs.

void	EliminateTrialVDofs (const Array< int > &vdofs)
	Eliminate the given trial vdofs, storing the eliminated part internally in \( M_e \).

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

void	EliminateEssentialBCFromTrialDofs (const Array< int > &marked_vdofs, const Vector &sol, Vector &rhs)
	Similar to EliminateTrialVDofs(const Array<int> &, const Vector &, Vector &) but here ess_dofs is a marker (boolean) array on all vector-dofs (ess_dofs[i] < 0 is true).

void	EliminateTestEssentialBC (const Array< int > &bdr_attr_is_ess)
	Eliminate essential boundary test DOFs from the system matrix.

virtual MFEM_DEPRECATED void	EliminateTestDofs (const Array< int > &bdr_attr_is_ess)
	(DEPRECATED) Eliminate essential boundary test DOFs from the system.

void	EliminateTestVDofs (const Array< int > &vdofs)
	Eliminate the given test vdofs. NOTE: here, vdofs is a list of DOFs.

virtual void	FormRectangularSystemMatrix (const Array< int > &trial_tdof_list, const Array< int > &test_tdof_list, OperatorHandle &A)
	Return in A that is column-constrained.

template<typename OpType >
void	FormRectangularSystemMatrix (const Array< int > &trial_tdof_list, const Array< int > &test_tdof_list, OpType &A)
	Form the column-constrained linear system matrix A.

virtual void	FormRectangularLinearSystem (const Array< int > &trial_tdof_list, const Array< int > &test_tdof_list, Vector &x, Vector &b, OperatorHandle &A, Vector &X, Vector &B)
	Form the linear system A X = B, corresponding to this mixed bilinear form and the linear form b(.).

template<typename OpType >
void	FormRectangularLinearSystem (const Array< int > &trial_tdof_list, const Array< int > &test_tdof_list, Vector &x, Vector &b, OpType &A, Vector &X, Vector &B)
	Form the linear system A X = B, corresponding to this bilinear form and the linear form b(.).

void	Update ()
	Must be called after making changes to trial_fes or test_fes.

FiniteElementSpace *	TrialFESpace ()
	Return the trial FE space associated with the BilinearForm.

const FiniteElementSpace *	TrialFESpace () const
	Read-only access to the associated trial FiniteElementSpace.

FiniteElementSpace *	TestFESpace ()
	Return the test FE space associated with the BilinearForm.

const FiniteElementSpace *	TestFESpace () const
	Read-only access to the associated test FiniteElementSpace.

void	Print (std::ostream &os=mfem::out, int width_=4) const override
	Prints operator to stream os.

virtual	~MixedBilinearForm ()
	Deletes internal matrices, bilinear integrators, and the BilinearFormExtension.

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

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

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

virtual	~Matrix ()
	Destroys matrix.

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.

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

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

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

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

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

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

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

virtual void	ArrayMult (const Array< const Vector * > &X, Array< Vector * > &Y) const
	Operator application on a matrix: `Y=A(X)`.

virtual void	ArrayMultTranspose (const Array< const Vector * > &X, Array< Vector * > &Y) const
	Action of the transpose operator on a matrix: `Y=A^t(X)`.

virtual void	ArrayAddMult (const Array< const Vector * > &X, Array< Vector * > &Y, const real_t a=1.0) const
	Operator application on a matrix: `Y+=A(X)` (default) or `Y+=a*A(X)`.

virtual void	ArrayAddMultTranspose (const Array< const Vector * > &X, Array< Vector * > &Y, const real_t a=1.0) const
	Operator transpose application on a matrix: `Y+=A^t(X)` (default) or `Y+=a*A^t(X)`.

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.

virtual void	AssembleDiagonal (Vector &diag) const
	Computes the diagonal entries into diag. Typically, this operation only makes sense for linear Operators. In some cases, only an approximation of the diagonal is computed.

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.

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.

virtual void	RecoverFEMSolution (const Vector &X, const Vector &b, Vector &x)
	Reconstruct a solution vector x (e.g. a GridFunction) from the solution X of a constrained linear system obtained from Operator::FormLinearSystem() or Operator::FormRectangularLinearSystem().

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

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).

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

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

virtual void	PrintMatlab (std::ostream &out) const
	Prints operator in Matlab format.

virtual	~Operator ()
	Virtual destructor.

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

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 , Complex_DenseMat , MFEM_Block_Matrix , MFEM_Block_Operator }
	Enumeration defining IDs for some classes derived from Operator. More...

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

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

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".

Protected Attributes inherited from mfem::MixedBilinearForm
SparseMatrix *	mat
	Owned.

SparseMatrix *	mat_e
	Owned.

FiniteElementSpace *	trial_fes
	Not owned.

FiniteElementSpace *	test_fes
	Not owned.

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

std::unique_ptr< MixedBilinearFormExtension >	ext

int	extern_bfs
	Indicates the BilinearFormIntegrators stored in MixedBilinearForm::domain_integs, MixedBilinearForm::boundary_integs, MixedBilinearForm::trace_face_integs and MixedBilinearForm::boundary_trace_face_integs are owned by another MixedBilinearForm.

Array< BilinearFormIntegrator * >	domain_integs
	Domain integrators.

Array< Array< int > * >	domain_integs_marker
	Entries are not owned.

Array< BilinearFormIntegrator * >	boundary_integs
	Boundary integrators.

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

Array< BilinearFormIntegrator * >	interior_face_integs
	Interior face integrators.

Array< BilinearFormIntegrator * >	boundary_face_integs
	Boundary face integrators.

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

Array< BilinearFormIntegrator * >	trace_face_integs
	Trace face (skeleton) integrators.

Array< BilinearFormIntegrator * >	boundary_trace_face_integs
	Boundary trace face (skeleton) integrators.

Array< Array< int > * >	boundary_trace_face_integs_marker
	Entries are not owned.

DenseMatrix	elemmat

Array< int >	trial_vdofs

Array< int >	test_vdofs

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

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

Detailed Description

Class for constructing the matrix representation of a linear operator, v = L u, from one FiniteElementSpace (domain) to another FiniteElementSpace (range). The constructed matrix A is such that

V = A U

where U and V are the vectors of degrees of freedom representing the functions u and v, respectively. The dimensions of A are

number of rows of A = dimension of the range space and
number of cols of A = dimension of the domain space.

This class is very similar to MixedBilinearForm. One difference is that the linear operator L is defined using a special kind of BilinearFormIntegrator (we reuse its functionality instead of defining a new class). The other difference with the MixedBilinearForm class is that the "assembly" process overwrites the global matrix entries using the local element matrices instead of adding them.

Note that if we define the bilinear form b(u,v) := (Lu,v) using an inner product in the range space, then its matrix representation, B, is

B = M A, (since V^t B U = b(u,v) = (Lu,v) = V^t M A U)

where M denotes the mass matrix for the inner product in the range space: V1^t M V2 = (v1,v2). Similarly, if c(u,w) := (Lu,Lw) then

C = A^t M A.

Definition at line 1253 of file bilinearform.hpp.

Constructor & Destructor Documentation

◆ DiscreteLinearOperator()

mfem::DiscreteLinearOperator::DiscreteLinearOperator	(	FiniteElementSpace *	domain_fes,
		FiniteElementSpace *	range_fes )

inline

Construct a DiscreteLinearOperator on the given FiniteElementSpaces domain_fes and range_fes.

The pointers domain_fes and range_fes are not owned by the newly constructed object.

Definition at line 1267 of file bilinearform.hpp.

Member Function Documentation

◆ AddDomainInterpolator() [1/2]

void mfem::DiscreteLinearOperator::AddDomainInterpolator ( DiscreteInterpolator * di )

inline

Adds a domain interpolator. Assumes ownership of di.

Definition at line 1272 of file bilinearform.hpp.

◆ AddDomainInterpolator() [2/2]

void mfem::DiscreteLinearOperator::AddDomainInterpolator	(	DiscreteInterpolator *	di,
		Array< int > &	elem_marker )

inline

Definition at line 1274 of file bilinearform.hpp.

◆ AddTraceFaceInterpolator()

void mfem::DiscreteLinearOperator::AddTraceFaceInterpolator ( DiscreteInterpolator * di )

inline

Adds a trace face interpolator. Assumes ownership of di.

Definition at line 1279 of file bilinearform.hpp.

◆ Assemble()

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

virtual

Construct the internal matrix representation of the discrete linear operator.

Definition at line 2401 of file bilinearform.cpp.

◆ GetDI()

Array< BilinearFormIntegrator * > * mfem::DiscreteLinearOperator::GetDI ( )

inline

Access all interpolators added with AddDomainInterpolator().

Definition at line 1283 of file bilinearform.hpp.

◆ GetDI_Marker()

Array< Array< int > * > * mfem::DiscreteLinearOperator::GetDI_Marker ( )

inline

Definition at line 1284 of file bilinearform.hpp.

◆ GetOutputRestrictionTranspose()

const Operator * mfem::DiscreteLinearOperator::GetOutputRestrictionTranspose ( ) const

inlineoverridevirtual

Get the output finite element space restriction matrix in transposed form.

Reimplemented from mfem::Operator.

Definition at line 1296 of file bilinearform.hpp.

◆ SetAssemblyLevel()

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

Set the desired assembly level. The default is AssemblyLevel::FULL.

This method must be called before assembly.

Definition at line 2374 of file bilinearform.cpp.

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

fem/bilinearform.hpp
fem/bilinearform.cpp

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ DiscreteLinearOperator()

Member Function Documentation

◆ AddDomainInterpolator() [1/2]

◆ AddDomainInterpolator() [2/2]

◆ AddTraceFaceInterpolator()

◆ Assemble()

◆ GetDI()

◆ GetDI_Marker()

◆ GetOutputRestrictionTranspose()

◆ SetAssemblyLevel()