MFEM v4.7.0
Finite element discretization library
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mfem::MatrixFreeAuxiliarySpace Class Reference

Auxiliary space solvers for MatrixFreeAMS preconditioner. More...

#include <auxiliary.hpp>

Inheritance diagram for mfem::MatrixFreeAuxiliarySpace:
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Collaboration diagram for mfem::MatrixFreeAuxiliarySpace:
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Public Member Functions

 MatrixFreeAuxiliarySpace (ParMesh &mesh_lor, Coefficient *alpha_coeff, Coefficient *beta_coeff, MatrixCoefficient *beta_mcoeff, Array< int > &ess_bdr, Operator &curlcurl_oper, Operator &pi, #ifdef MFEM_USE_AMGX bool useAmgX_, #endif int cg_iterations=0)
 Pi space constructor.
 
 MatrixFreeAuxiliarySpace (ParMesh &mesh_lor, Coefficient *beta_coeff, MatrixCoefficient *beta_mcoeff, Array< int > &ess_bdr, Operator &curlcurl_oper, Operator &g, #ifdef MFEM_USE_AMGX bool useAmgX_, #endif int cg_iterations=1)
 G space constructor.
 
 ~MatrixFreeAuxiliarySpace ()
 
void Mult (const Vector &x, Vector &y) const
 Operator application: y=A(x).
 
void SetOperator (const Operator &op)
 Set/update the solver for the given operator.
 
- 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 OperatorGetGradient (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 OperatorGetProlongation () const
 Prolongation operator from linear algebra (linear system) vectors, to input vectors for the operator. NULL means identity.
 
virtual const OperatorGetRestriction () const
 Restriction operator from input vectors for the operator to linear algebra (linear system) vectors. NULL means identity.
 
virtual const OperatorGetOutputProlongation () const
 Prolongation operator from linear algebra (linear system) vectors, to output vectors for the operator. NULL means identity.
 
virtual const OperatorGetOutputRestrictionTranspose () const
 Transpose of GetOutputRestriction, directly available in this form to facilitate matrix-free RAP-type operators.
 
virtual const OperatorGetOutputRestriction () 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 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 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()
 
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".
 
- 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

Auxiliary space solvers for MatrixFreeAMS preconditioner.

Given an operator A and a transfer G, create a solver that approximates (G^T A G)^{-1}. Used for two different auxiliary spaces in the AMS cycle.

The produced solver is based on a low-order refined discretization for the high-order H1 problem.

Definition at line 38 of file auxiliary.hpp.

Constructor & Destructor Documentation

◆ MatrixFreeAuxiliarySpace() [1/2]

mfem::MatrixFreeAuxiliarySpace::MatrixFreeAuxiliarySpace ( ParMesh & mesh_lor,
Coefficient * alpha_coeff,
Coefficient * beta_coeff,
MatrixCoefficient * beta_mcoeff,
Array< int > & ess_bdr,
Operator & curlcurl_oper,
Operator & pi,
#ifdef MFEM_USE_AMGX bool useAmgX_,
#endif int cg_iterations = 0 )

Pi space constructor.

In the AMS framework this auxiliary space has two coefficients.

Parameters
mesh_lorLow-order refined auxiliary mesh
alpha_coeffCoefficient on curl-curl term (1 if null)
beta_coeffCoefficient on mass term (1 if null)
beta_mcoeffMatrix coefficient on mass term
ess_bdrAttributes for essential boundaries
curlcurl_operHigh-order operator for the system
piIdentity interpolation operator
useAmgX_Use AmgX instead of hypre for auxiliary solves
cg_iterationsNumber of CG iterations used to invert auxiliary system, choosing 0 means to use a single V-cycle

Definition at line 120 of file auxiliary.cpp.

◆ MatrixFreeAuxiliarySpace() [2/2]

mfem::MatrixFreeAuxiliarySpace::MatrixFreeAuxiliarySpace ( ParMesh & mesh_lor,
Coefficient * beta_coeff,
MatrixCoefficient * beta_mcoeff,
Array< int > & ess_bdr,
Operator & curlcurl_oper,
Operator & g,
#ifdef MFEM_USE_AMGX bool useAmgX_,
#endif int cg_iterations = 1 )

G space constructor.

This has one coefficient in the AMS framework.

Parameters
mesh_lorLow-order refined auxiliary mesh
beta_coeffCoefficient on mass term (1 if null)
beta_mcoeffMatrix coefficient on mass term
ess_bdrAttributes for essential boundaries
curlcurl_operHigh-order operator for the system
gGradient interpolation operator
useAmgX_Use AmgX instead of hypre for auxiliary solves
cg_iterationsNumber of CG iterations used to invert auxiliary system, choosing 0 means to use a single V-cycle

Definition at line 203 of file auxiliary.cpp.

◆ ~MatrixFreeAuxiliarySpace()

mfem::MatrixFreeAuxiliarySpace::~MatrixFreeAuxiliarySpace ( )

Definition at line 413 of file auxiliary.cpp.

Member Function Documentation

◆ Mult()

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

Operator application: y=A(x).

Implements mfem::Operator.

Definition at line 399 of file auxiliary.cpp.

◆ SetOperator()

void mfem::MatrixFreeAuxiliarySpace::SetOperator ( const Operator & op)
inlinevirtual

Set/update the solver for the given operator.

Implements mfem::Solver.

Definition at line 92 of file auxiliary.hpp.


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