MFEM  v4.5.2
Finite element discretization library
Public Types | Public Member Functions | List of all members
mfem::BlockILU Class Reference

#include <solvers.hpp>

Inheritance diagram for mfem::BlockILU:
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Collaboration diagram for mfem::BlockILU:
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Public Types

enum  Reordering { Reordering::MINIMUM_DISCARDED_FILL, Reordering::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. More...
 
int * GetBlockI ()
 
int * GetBlockJ ()
 
double * GetBlockData ()
 
- Public Member Functions inherited from mfem::Solver
 Solver (int s=0, bool iter_mode=false)
 Initialize a square Solver with size s. More...
 
 Solver (int h, int w, bool iter_mode=false)
 Initialize a Solver with height h and width w. 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 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 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 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 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 OperatorGetGradient (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...
 
virtual const OperatorGetProlongation () const
 Prolongation operator from linear algebra (linear system) vectors, to input vectors for the operator. NULL means identity. More...
 
virtual const OperatorGetRestriction () const
 Restriction operator from input vectors for the operator to linear algebra (linear system) vectors. NULL means identity. More...
 
virtual const OperatorGetOutputProlongation () const
 Prolongation operator from linear algebra (linear system) vectors, to output vectors for the operator. NULL means identity. More...
 
virtual const OperatorGetOutputRestrictionTranspose () const
 Transpose of GetOutputRestriction, directly available in this form to facilitate matrix-free RAP-type operators. More...
 
virtual const OperatorGetOutputRestriction () const
 Restriction operator from output vectors for the operator to linear algebra (linear system) vectors. NULL means identity. 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 Attributes inherited from mfem::Solver
bool iterative_mode
 If true, use the second argument of Mult() as an initial guess. 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...
 
OperatorSetupRAP (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::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

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 946 of file solvers.hpp.

Member Enumeration Documentation

◆ Reordering

The reordering method used by the BlockILU factorization.

Enumerator
MINIMUM_DISCARDED_FILL 
NONE 

Definition at line 951 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 2745 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 2754 of file solvers.cpp.

Member Function Documentation

◆ GetBlockData()

double* 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 995 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 985 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 990 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 2994 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 2763 of file solvers.cpp.


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