MFEM  v4.5.1
Finite element discretization library
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mfem::MatrixFreeAMS Class Reference

An auxiliary Maxwell solver for a high-order curl-curl system without high-order assembly. More...

#include <auxiliary.hpp>

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

 MatrixFreeAMS (ParBilinearForm &aform, Operator &oper, ParFiniteElementSpace &nd_fespace, Coefficient *alpha_coeff, Coefficient *beta_coeff, MatrixCoefficient *beta_mcoeff, Array< int > &ess_bdr,#ifdef MFEM_USE_AMGX bool useAmgX=false,#endif int inner_pi_its=0, int inner_g_its=1, Solver *nd_smoother=NULL)
 Construct matrix-free AMS preconditioner. More...
 
 ~MatrixFreeAMS ()
 
void SetOperator (const Operator &op)
 Set/update the solver for the given operator. More...
 
void Mult (const Vector &x, Vector &y) const
 Operator application: y=A(x). More...
 
- 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 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 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. 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

An auxiliary Maxwell solver for a high-order curl-curl system without high-order assembly.

The auxiliary space solves are done using a low-order refined approach, but all the interpolation operators, residuals, etc. are done in a matrix-free manner.

See Barker and Kolev, Matrix-free preconditioning for high-order H(curl) discretizations (https://doi.org/10.1002/nla.2348)

Definition at line 168 of file auxiliary.hpp.

Constructor & Destructor Documentation

mfem::MatrixFreeAMS::MatrixFreeAMS ( ParBilinearForm aform,
Operator oper,
ParFiniteElementSpace nd_fespace,
Coefficient alpha_coeff,
Coefficient beta_coeff,
MatrixCoefficient beta_mcoeff,
Array< int > &  ess_bdr,
#ifdef MFEM_USE_AMGX bool  useAmgX = false,
#endif int  inner_pi_its = 0,
int  inner_g_its = 1,
Solver nd_smoother = NULL 
)

Construct matrix-free AMS preconditioner.

Parameters
aformBilinearForm for curl-curl problem, generally will have a CurlCurlIntegrator and possibly a VectorFEMassIntegrator.
operOperator to precondition.
nd_fespaceUnderlying Nedelec finite element space.
alpha_coeffCoefficient on curl-curl term in Maxwell problem (can be null, in which case constant 1 is assumed)
beta_coeff(scalar) coefficient on mass term in Maxwell problem
beta_mcoeff(matrix) coefficient on mass term
ess_bdrBoundary attributes that are marked essential. In contrast to other MFEM cases, these are attributes not dofs, because we need to apply these boundary conditions to different bilinear forms.
useAmgXUse AmgX (instead of hypre) for LOR problems
inner_pi_itsNumber of CG iterations on auxiliary pi space, may need more for difficult coefficients
inner_g_itsNumber of CG iterations on auxiliary g space, may need more for difficult coefficients
nd_smootherOptional user-provided smoother for Nedelec space, this object takes ownership and will delete.

Definition at line 426 of file auxiliary.cpp.

mfem::MatrixFreeAMS::~MatrixFreeAMS ( )

Definition at line 499 of file auxiliary.cpp.

Member Function Documentation

void mfem::MatrixFreeAMS::Mult ( const Vector x,
Vector y 
) const
inlinevirtual

Operator application: y=A(x).

Implements mfem::Operator.

Definition at line 208 of file auxiliary.hpp.

void mfem::MatrixFreeAMS::SetOperator ( const Operator op)
inlinevirtual

Set/update the solver for the given operator.

Implements mfem::Solver.

Definition at line 206 of file auxiliary.hpp.


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