mfem::DiscreteLinearOperator Class Reference

#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. More...
void	AddDomainInterpolator (DiscreteInterpolator *di)
	Adds a domain interpolator. Assumes ownership of di. More...
void	AddTraceFaceInterpolator (DiscreteInterpolator *di)
	Adds a trace face interpolator. Assumes ownership of di. More...
Array< BilinearFormIntegrator * > *	GetDI ()
	Access all interpolators added with AddDomainInterpolator(). More...
void	SetAssemblyLevel (AssemblyLevel assembly_level)
	Set the desired assembly level. The default is AssemblyLevel::FULL. More...
virtual void	Assemble (int skip_zeros=1)
	Construct the internal matrix representation of the discrete linear operator. More...
virtual const Operator *	GetOutputRestrictionTranspose () const
	Get the output finite element space restriction matrix in transposed form. More...
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. More...
	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. 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 a reference to: \( M_{ij} \). More...
virtual void	Mult (const Vector &x, Vector &y) const
	Matrix multiplication: \( y = M x \). More...
virtual void	AddMult (const Vector &x, Vector &y, const double a=1.0) const
	Operator application: y+=A(x) (default) or y+=a*A(x). More...
virtual void	MultTranspose (const Vector &x, Vector &y) const
	Action of the transpose operator: y=A^t(x). The default behavior in class Operator is to generate an error. More...
virtual void	AddMultTranspose (const Vector &x, Vector &y, const double a=1.0) const
	Operator transpose application: y+=A^t(x) (default) or y+=a*A^t(x). More...
virtual MatrixInverse *	Inverse () const
	Returns a pointer to (an approximation) of the matrix inverse. More...
virtual void	Finalize (int skip_zeros=1)
	Finalizes the matrix initialization. More...
void	GetBlocks (Array2D< SparseMatrix *> &blocks) const
const SparseMatrix &	SpMat () const
	Returns a const reference to the sparse matrix: \( M \). 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 transferring ownership. More...
void	AddDomainIntegrator (BilinearFormIntegrator *bfi)
	Adds a domain integrator. Assumes ownership of bfi. More...
void	AddBoundaryIntegrator (BilinearFormIntegrator *bfi)
	Adds a boundary integrator. Assumes ownership of bfi. More...
void	AddBoundaryIntegrator (BilinearFormIntegrator *bfi, Array< int > &bdr_marker)
	Adds a boundary integrator. Assumes ownership of bfi. More...
void	AddTraceFaceIntegrator (BilinearFormIntegrator *bfi)
	Add a trace face integrator. Assumes ownership of bfi. More...
void	AddBdrTraceFaceIntegrator (BilinearFormIntegrator *bfi)
	Adds a boundary trace face integrator. Assumes ownership of bfi. More...
void	AddBdrTraceFaceIntegrator (BilinearFormIntegrator *bfi, Array< int > &bdr_marker)
	Adds a boundary trace face integrator. Assumes ownership of bfi. More...
Array< BilinearFormIntegrator * > *	GetDBFI ()
	Access all integrators added with AddDomainIntegrator(). More...
Array< BilinearFormIntegrator * > *	GetBBFI ()
	Access all 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 * > *	GetTFBFI ()
	Access all integrators added with AddTraceFaceIntegrator(). More...
Array< BilinearFormIntegrator * > *	GetBTFBFI ()
	Access all integrators added with AddBdrTraceFaceIntegrator(). More...
Array< Array< int > * > *	GetBTFBFI_Marker ()
	Access all boundary markers added with AddBdrTraceFaceIntegrator(). If no marker was specified when the integrator was added, the corresponding pointer (to Array<int>) will be NULL. More...
void	operator= (const double a)
	Sets all sparse values of \( M \) to a. More...
void	SetAssemblyLevel (AssemblyLevel assembly_level)
	Set the desired assembly level. The default is AssemblyLevel::LEGACY. More...
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. More...
virtual const Operator *	GetProlongation () const
	Get the input finite element space prolongation matrix. More...
virtual const Operator *	GetRestriction () const
	Get the input finite element space restriction matrix. More...
virtual const Operator *	GetOutputProlongation () const
	Get the test finite element space prolongation matrix. More...
virtual const Operator *	GetOutputRestriction () const
	Get the test finite element space restriction matrix. More...
void	ConformingAssemble ()
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 > &trial_vdofs, Array< int > &test_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 > &trial_vdofs, Array< int > &test_vdofs, int skip_zeros=1)
	Assemble the given boundary element matrix. More...
void	EliminateTrialDofs (const Array< int > &bdr_attr_is_ess, const Vector &sol, Vector &rhs)
void	EliminateEssentialBCFromTrialDofs (const Array< int > &marked_vdofs, const Vector &sol, Vector &rhs)
virtual void	EliminateTestDofs (const Array< int > &bdr_attr_is_ess)
virtual void	FormRectangularSystemMatrix (const Array< int > &trial_tdof_list, const Array< int > &test_tdof_list, OperatorHandle &A)
	Return in A that is column-constrained. More...
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. See FormRectangularSystemMatrix() for details. More...
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(.). More...
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(.). More...
void	Update ()
FiniteElementSpace *	TrialFESpace ()
	Return the trial FE space associated with the BilinearForm. More...
const FiniteElementSpace *	TrialFESpace () const
	Read-only access to the associated trial FiniteElementSpace. More...
FiniteElementSpace *	TestFESpace ()
	Return the test FE space associated with the BilinearForm. More...
const FiniteElementSpace *	TestFESpace () const
	Read-only access to the associated test FiniteElementSpace. More...
virtual	~MixedBilinearForm ()
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 void	ArrayMult (const Array< const Vector *> &X, Array< Vector *> &Y) const
	Operator application on a matrix: Y=A(X). More...
virtual void	ArrayMultTranspose (const Array< const Vector *> &X, Array< Vector *> &Y) const
	Action of the transpose operator on a matrix: Y=A^t(X). More...
virtual void	ArrayAddMult (const Array< const Vector *> &X, Array< Vector *> &Y, const double a=1.0) const
	Operator application on a matrix: Y+=A(X) (default) or Y+=a*A(X). More...
virtual void	ArrayAddMultTranspose (const Array< const Vector *> &X, Array< Vector *> &Y, const double a=1.0) const
	Operator transpose application on a matrix: Y+=A^t(X) (default) or Y+=a*A^t(X). 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...
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. 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...
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(). 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, int m=0) const
	Prints operator with input size n and output size m in Matlab format. More...
virtual void	PrintMatlab (std::ostream &out) const
	Prints operator in Matlab format. More...
virtual	~Operator ()
	Virtual destructor. More...
Type	GetType () const
	Return the type ID of the Operator class. 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,   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() 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 inherited from mfem::MixedBilinearForm
SparseMatrix *	mat
	Owned. More...
SparseMatrix *	mat_e
	Owned. More...
FiniteElementSpace *	trial_fes
	Not owned. More...
FiniteElementSpace *	test_fes
	Not owned. More...
AssemblyLevel	assembly
	The form assembly level (full, partial, etc.) More...
MixedBilinearFormExtension *	ext
int	extern_bfs
	Indicates the BilinearFormIntegrators stored in domain_integs, boundary_integs, trace_face_integs and boundary_trace_face_integs are owned by another MixedBilinearForm. More...
Array< BilinearFormIntegrator * >	domain_integs
	Domain integrators. More...
Array< BilinearFormIntegrator * >	boundary_integs
	Boundary integrators. More...
Array< Array< int > * >	boundary_integs_marker
	Entries are not owned. More...
Array< BilinearFormIntegrator * >	trace_face_integs
	Trace face (skeleton) integrators. More...
Array< BilinearFormIntegrator * >	boundary_trace_face_integs
	Boundary trace face (skeleton) integrators. More...
Array< Array< int > * >	boundary_trace_face_integs_marker
	Entries are not owned. More...
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. More...
int	width
	Dimension of the input / number of columns in the matrix. More...

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 1047 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 1061 of file bilinearform.hpp.

Member Function Documentation

AddDomainInterpolator()

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

inline

Adds a domain interpolator. Assumes ownership of di.

Definition at line 1066 of file bilinearform.hpp.

AddTraceFaceInterpolator()

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

inline

Adds a trace face interpolator. Assumes ownership of di.

Definition at line 1070 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 1936 of file bilinearform.cpp.

GetDI()

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

inline

Access all interpolators added with AddDomainInterpolator().

Definition at line 1074 of file bilinearform.hpp.

GetOutputRestrictionTranspose()

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

inlinevirtual

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

Reimplemented from mfem::Operator.

Definition at line 1086 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 1909 of file bilinearform.cpp.

---

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

• fem/bilinearform.hpp
• fem/bilinearform.cpp