#include <solvers.hpp>

Inheritance diagram for mfem::BlockILU:

Collaboration diagram for mfem::BlockILU:

Public Types
enum class	Reordering { MINIMUM_DISCARDED_FILL , NONE }
	The reordering method used by the BlockILU factorization. More...

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...

Public Member Functions
	BlockILU (int block_size_, Reordering reordering_=Reordering::MINIMUM_DISCARDED_FILL, int k_fill_=0)

	BlockILU (const Operator &op, int block_size_=1, Reordering reordering_=Reordering::MINIMUM_DISCARDED_FILL, int k_fill_=0)

void	SetOperator (const Operator &op)

void	Mult (const Vector &b, Vector &x) const
	Solve the system `LUx = b`, where `L` and `U` are the block ILU factors.

int *	GetBlockI ()

int *	GetBlockJ ()

real_t *	GetBlockData ()

Public Member Functions inherited from mfem::Solver
	Solver (int s=0, bool iter_mode=false)
	Initialize a square Solver with size s.

	Solver (int h, int w, bool iter_mode=false)
	Initialize a Solver with height h and width w.

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	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.

virtual void	AddMult (const Vector &x, Vector &y, const real_t a=1.0) const
	Operator application: `y+=A(x)` (default) or `y+=a*A(x)`.

virtual void	AddMultTranspose (const Vector &x, Vector &y, const real_t a=1.0) const
	Operator transpose application: `y+=A^t(x)` (default) or `y+=a*A^t(x)`.

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.

virtual const Operator *	GetProlongation () const
	Prolongation operator from linear algebra (linear system) vectors, to input vectors for the operator. `NULL` means identity.

virtual const Operator *	GetRestriction () const
	Restriction operator from input vectors for the operator to linear algebra (linear system) vectors. `NULL` means identity.

virtual const Operator *	GetOutputProlongation () const
	Prolongation operator from linear algebra (linear system) vectors, to output vectors for the operator. `NULL` means identity.

virtual const Operator *	GetOutputRestrictionTranspose () const
	Transpose of GetOutputRestriction, directly available in this form to facilitate matrix-free RAP-type operators.

virtual const Operator *	GetOutputRestriction () const
	Restriction operator from output vectors for the operator to linear algebra (linear system) vectors. `NULL` means identity.

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 Attributes inherited from mfem::Solver
bool	iterative_mode
	If true, use the second argument of Mult() as an initial guess.

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::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

Block ILU solver: Performs a block ILU(k) approximate factorization with specified block size. Currently only k=0 is supported. This is useful as a preconditioner for DG-type discretizations, where the system matrix has a natural (elemental) block structure.

In the case of DG discretizations, the block size should usually be set to either ndofs_per_element or vdim*ndofs_per_element (if the finite element space has Ordering::byVDIM). The block size must evenly divide the size of the matrix.

Renumbering the blocks is also supported by specifying a reordering method. Currently greedy minimum discarded fill ordering and no reordering are supported. Renumbering the blocks can lead to a much better approximate factorization.

Definition at line 988 of file solvers.hpp.

Member Enumeration Documentation

◆ Reordering

enum class mfem::BlockILU::Reordering

strong

The reordering method used by the BlockILU factorization.

Enumerator
MINIMUM_DISCARDED_FILL
NONE

Definition at line 993 of file solvers.hpp.

Constructor & Destructor Documentation

◆ BlockILU() [1/2]

mfem::BlockILU::BlockILU	(	int	block_size_,
		Reordering	reordering_ = Reordering::MINIMUM_DISCARDED_FILL,
		int	k_fill_ = 0 )

Create an "empty" BlockILU solver. SetOperator must be called later to actually form the factorization

Definition at line 2749 of file solvers.cpp.

◆ BlockILU() [2/2]

mfem::BlockILU::BlockILU	(	const Operator &	op,
		int	block_size_ = 1,
		Reordering	reordering_ = Reordering::MINIMUM_DISCARDED_FILL,
		int	k_fill_ = 0 )

Create a block ILU approximate factorization for the matrix op. op should be of type either SparseMatrix or HypreParMatrix. In the case that op is a HypreParMatrix, the ILU factorization is performed on the diagonal blocks of the parallel decomposition.

Definition at line 2758 of file solvers.cpp.

Member Function Documentation

◆ GetBlockData()

real_t * mfem::BlockILU::GetBlockData ( )

inline

Get the data array for the block CSR representation of the factorization. Similar to SparseMatrix::GetData(). Mostly used for testing.

Definition at line 1037 of file solvers.hpp.

◆ GetBlockI()

int * mfem::BlockILU::GetBlockI ( )

inline

Get the I array for the block CSR representation of the factorization. Similar to SparseMatrix::GetI(). Mostly used for testing.

Definition at line 1027 of file solvers.hpp.

◆ GetBlockJ()

int * mfem::BlockILU::GetBlockJ ( )

inline

Get the J array for the block CSR representation of the factorization. Similar to SparseMatrix::GetJ(). Mostly used for testing.

Definition at line 1032 of file solvers.hpp.

◆ Mult()

void mfem::BlockILU::Mult	(	const Vector &	b,
		Vector &	x ) const

virtual

Solve the system LUx = b, where L and U are the block ILU factors.

Implements mfem::Operator.

Definition at line 2998 of file solvers.cpp.

◆ SetOperator()

void mfem::BlockILU::SetOperator ( const Operator & op )

virtual

Perform the block ILU factorization for the matrix op. As in the constructor, op must either be a SparseMatrix or HypreParMatrix

Implements mfem::Solver.

Definition at line 2767 of file solvers.cpp.

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

linalg/solvers.hpp
linalg/solvers.cpp

Public Types

Public Member Functions

Additional Inherited Members

Detailed Description

Member Enumeration Documentation

◆ Reordering

Constructor & Destructor Documentation

◆ BlockILU() [1/2]

◆ BlockILU() [2/2]

Member Function Documentation

◆ GetBlockData()

◆ GetBlockI()

◆ GetBlockJ()

◆ Mult()

◆ SetOperator()