Solve the H(div) saddle-point system using MINRES with matrix-free block-diagonal preconditioning. More...

#include <hdiv_linear_solver.hpp>

Inheritance diagram for mfem::HdivSaddlePointSolver:

Collaboration diagram for mfem::HdivSaddlePointSolver:

Public Types
enum	Mode { GRAD_DIV , DARCY }
	Which type of saddle-point problem is being solved? 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
	HdivSaddlePointSolver (ParMesh &mesh_, ParFiniteElementSpace &fes_rt_, ParFiniteElementSpace &fes_l2_, Coefficient &L_coeff_, Coefficient &R_coeff_, const Array< int > &ess_rt_dofs_, Mode mode_)
	Creates a solver for the H(div) saddle-point system.

	HdivSaddlePointSolver (ParMesh &mesh_, ParFiniteElementSpace &fes_rt_, ParFiniteElementSpace &fes_l2_, Coefficient &R_coeff_, const Array< int > &ess_rt_dofs_)
	Creates a linear solver for the case when the L2 diagonal block is zero (for Darcy problems).

void	Setup ()
	Build the linear operator and solver. Must be called when the coefficients change.

void	SetBC (const Vector &x_rt)
	Sets the Dirichlet boundary conditions at the RT essential DOFs.

void	Mult (const Vector &b, Vector &x) const override
	Solve the linear system for L2 (scalar) and RT (flux) unknowns.

void	SetOperator (const Operator &op) override
	No-op.

int	GetNumIterations () const
	Get the number of MINRES iterations.

void	EliminateBC (Vector &) const
	Eliminates the BCs (called internally, not public interface).

const Array< int > &	GetOffsets () const
	Return the offsets of the block system.

MINRESSolver &	GetMINRES ()
	Returns the internal MINRES solver.

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

Solve the H(div) saddle-point system using MINRES with matrix-free block-diagonal preconditioning.

See HdivSaddlePointSolver::HdivSaddlePointSolver for the problem description.

Definition at line 27 of file hdiv_linear_solver.hpp.

Member Enumeration Documentation

◆ Mode

enum mfem::HdivSaddlePointSolver::Mode

Which type of saddle-point problem is being solved?

Enumerator
GRAD_DIV	Grad-div problem.
DARCY	Darcy/mixed Poisson problem.

Definition at line 31 of file hdiv_linear_solver.hpp.

Constructor & Destructor Documentation

◆ HdivSaddlePointSolver() [1/2]

mfem::HdivSaddlePointSolver::HdivSaddlePointSolver	(	ParMesh &	mesh_,
		ParFiniteElementSpace &	fes_rt_,
		ParFiniteElementSpace &	fes_l2_,
		Coefficient &	L_coeff_,
		Coefficient &	R_coeff_,
		const Array< int > &	ess_rt_dofs_,
		Mode	mode_ )

Creates a solver for the H(div) saddle-point system.

The associated matrix is given by

[  L    B ]
[ B^T  -R ]

where L is the L2 mass matrix, R is the RT mass matrix, and B is the divergence form (VectorFEDivergenceIntegrator).

Essential boundary conditions in the RT space are given by ess_rt_dofs_. (Rows and columns are eliminated from R and columns are eliminated from B).

The L block has coefficient L_coeff_ and the R block has coefficient R_coeff_.

The parameter mode_ determines whether the block system corresponds to a grad-div problem or a Darcy problem. Specifically, if mode_ is Mode::GRAD_DIV, then the B and B^T blocks are also scaled by L_coeff_, and if mode_ is Mode::DARCY, then the B and B^T blocks are unweighted.

Mode::GRAD_DIV corresponds to the grad-div problem

alpha u - grad ( beta div ( u )) = f,

where alpha is R_coeff_ and beta is L_coeff_.

Mode::DARCY corresponds to the Darcy-type problem

alpha p - div ( beta grad ( p )) = f,

where alpha is L_coeff and beta is R_coeff_. In this case, the coefficient alpha is allowed to be zero.

Definition at line 65 of file hdiv_linear_solver.cpp.

◆ HdivSaddlePointSolver() [2/2]

mfem::HdivSaddlePointSolver::HdivSaddlePointSolver	(	ParMesh &	mesh_,
		ParFiniteElementSpace &	fes_rt_,
		ParFiniteElementSpace &	fes_l2_,
		Coefficient &	R_coeff_,
		const Array< int > &	ess_rt_dofs_ )

Creates a linear solver for the case when the L2 diagonal block is zero (for Darcy problems).

Equivalent to passing ConstantCoefficient(0.0) as L_coeff_ and Mode::DARCY as mode_ to the primary constructor (see above).

Definition at line 155 of file hdiv_linear_solver.cpp.

Member Function Documentation

◆ EliminateBC()

void mfem::HdivSaddlePointSolver::EliminateBC ( Vector & b ) const

Eliminates the BCs (called internally, not public interface).

Definition at line 277 of file hdiv_linear_solver.cpp.

◆ GetMINRES()

MINRESSolver & mfem::HdivSaddlePointSolver::GetMINRES ( )

inline

Returns the internal MINRES solver.

Definition at line 170 of file hdiv_linear_solver.hpp.

◆ GetNumIterations()

int mfem::HdivSaddlePointSolver::GetNumIterations ( ) const

inline

Get the number of MINRES iterations.

Definition at line 164 of file hdiv_linear_solver.hpp.

◆ GetOffsets()

const Array< int > & mfem::HdivSaddlePointSolver::GetOffsets ( ) const

inline

Return the offsets of the block system.

Definition at line 168 of file hdiv_linear_solver.hpp.

◆ Mult()

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

overridevirtual

Solve the linear system for L2 (scalar) and RT (flux) unknowns.

If the problem has essential boundary conditions (i.e. if ess_rt_dofs is not empty), then SetBC() must be called before Mult().

Implements mfem::Operator.

Definition at line 330 of file hdiv_linear_solver.cpp.

◆ SetBC()

void mfem::HdivSaddlePointSolver::SetBC ( const Vector & x_rt )

inline

Sets the Dirichlet boundary conditions at the RT essential DOFs.

Definition at line 155 of file hdiv_linear_solver.hpp.

◆ SetOperator()

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

inlineoverridevirtual

No-op.

Implements mfem::Solver.

Definition at line 162 of file hdiv_linear_solver.hpp.

◆ Setup()

void mfem::HdivSaddlePointSolver::Setup ( )

Build the linear operator and solver. Must be called when the coefficients change.

Definition at line 162 of file hdiv_linear_solver.cpp.

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

miniapps/hdiv-linear-solver/hdiv_linear_solver.hpp
miniapps/hdiv-linear-solver/hdiv_linear_solver.cpp

Public Types

Public Member Functions

Additional Inherited Members

Detailed Description

Member Enumeration Documentation

◆ Mode

Constructor & Destructor Documentation

◆ HdivSaddlePointSolver() [1/2]

◆ HdivSaddlePointSolver() [2/2]

Member Function Documentation

◆ EliminateBC()

◆ GetMINRES()

◆ GetNumIterations()

◆ GetOffsets()

◆ Mult()

◆ SetBC()

◆ SetOperator()

◆ Setup()