An abstract class to solve the constrained system \( Ax = f \) subject to the constraint \( B x = r \). More...

#include <constraints.hpp>

Inheritance diagram for mfem::ConstrainedSolver:

Collaboration diagram for mfem::ConstrainedSolver:

Public Member Functions
	ConstrainedSolver (MPI_Comm comm, Operator &A_, Operator &B_)

	ConstrainedSolver (Operator &A_, Operator &B_)

virtual	~ConstrainedSolver ()

virtual void	SetOperator (const Operator &op) override
	Also calls SetOperator for the preconditioner if there is one.

virtual void	SetConstraintRHS (const Vector &r)
	Set the right-hand side r for the constraint B x = r.

void	GetMultiplierSolution (Vector &lambda) const
	Return the Lagrange multiplier solution in lambda.

virtual void	Mult (const Vector &f, Vector &x) const override
	Solve for \( x \) given \( f \).

virtual void	LagrangeSystemMult (const Vector &f_and_r, Vector &x_and_lambda) const
	Solve for (x, lambda) given (f, r)

Public Member Functions inherited from mfem::IterativeSolver
	IterativeSolver ()

	IterativeSolver (MPI_Comm comm_)

virtual void	SetPreconditioner (Solver &pr)
	This should be called before SetOperator.

void	SetMonitor (IterativeSolverMonitor &m)
	Set the iterative solver monitor.

MPI_Comm	GetComm () const
	Return the associated MPI communicator, or MPI_COMM_NULL if no communicator is set.

void	SetRelTol (real_t rtol)

void	SetAbsTol (real_t atol)

void	SetMaxIter (int max_it)

virtual void	SetPrintLevel (int print_lvl)
	Legacy method to set the level of verbosity of the solver output.

virtual void	SetPrintLevel (PrintLevel)
	Set the level of verbosity of the solver output.

int	GetNumIterations () const
	Returns the number of iterations taken during the last call to Mult()

bool	GetConverged () const
	Returns true if the last call to Mult() converged successfully.

real_t	GetInitialNorm () const
	Returns the initial residual norm from the last call to Mult().

real_t	GetFinalNorm () const
	Returns the final residual norm after termination of the solver during the last call to Mult().

real_t	GetFinalRelNorm () const
	Returns the final residual norm after termination of the solver during the last call to Mult(), divided by the initial residual norm. Returns -1 if one of these norms is left undefined by the 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.

Protected Attributes
Operator &	A

Operator &	B

Vector	constraint_rhs

Vector	multiplier_sol

Vector	workb

Vector	workx

Protected Attributes inherited from mfem::IterativeSolver
const Operator *	oper

Solver *	prec

IterativeSolverMonitor *	monitor = nullptr

int	max_iter
	Limit for the number of iterations the solver is allowed to do.

real_t	rel_tol
	Relative tolerance.

real_t	abs_tol
	Absolute tolerance.

int	final_iter = -1

bool	converged = false

real_t	initial_norm = -1.0

real_t	final_norm = -1.0

int	print_level = -1
	(DEPRECATED) Legacy print level definition, which is left for compatibility with custom iterative solvers.

PrintLevel	print_options
	Output behavior for the iterative solver.

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.

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::IterativeSolver
virtual real_t	Dot (const Vector &x, const Vector &y) const
	Return the standard (l2, i.e., Euclidean) inner product of x and y.

real_t	Norm (const Vector &x) const
	Return the inner product norm of x, using the inner product defined by Dot()

void	Monitor (int it, real_t norm, const Vector &r, const Vector &x, bool final=false) const
	Monitor both the residual r and the solution x.

PrintLevel	FromLegacyPrintLevel (int)
	Convert a legacy print level integer to a PrintLevel object.

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".

Static Protected Member Functions inherited from mfem::IterativeSolver
static int	GuessLegacyPrintLevel (PrintLevel)
	Use some heuristics to guess a legacy print level corresponding to the given PrintLevel.

Detailed Description

An abstract class to solve the constrained system \( Ax = f \) subject to the constraint \( B x = r \).

Although implementations may not use the below formulation, for understanding some of its methods and notation you can think of it as solving the saddle-point system

( A B^T ) ( x ) ( f ) ( B ) ( lambda ) = ( r )

Do not confuse with ConstrainedOperator, which handles only simple pointwise constraints and is not a Solver.

The height and width of this object as an IterativeSolver are the same as just the unconstrained operator \( A \), and the Mult() interface just takes \( f \) as an argument. You can set \( r \) with SetConstraintRHS() (it defaults to zero) and get the Lagrange multiplier solution with GetMultiplierSolution().

Alternatively, you can use LagrangeSystemMult() to solve the block system shown above.

This abstract object unifies this interface so that derived classes can solve whatever linear system makes sense and the interface will provide uniform access to solutions, Lagrange multipliers, etc.

Definition at line 53 of file constraints.hpp.

Constructor & Destructor Documentation

◆ ConstrainedSolver() [1/2]

mfem::ConstrainedSolver::ConstrainedSolver	(	MPI_Comm	comm,
		Operator &	A_,
		Operator &	B_ )

Definition at line 691 of file constraints.cpp.

◆ ConstrainedSolver() [2/2]

mfem::ConstrainedSolver::ConstrainedSolver	(	Operator &	A_,
		Operator &	B_ )

Definition at line 699 of file constraints.cpp.

◆ ~ConstrainedSolver()

virtual mfem::ConstrainedSolver::~ConstrainedSolver ( )

inlinevirtual

Definition at line 61 of file constraints.hpp.

Member Function Documentation

◆ GetMultiplierSolution()

void mfem::ConstrainedSolver::GetMultiplierSolution ( Vector & lambda ) const

inline

Return the Lagrange multiplier solution in lambda.

Mult() only gives you x, this provides access to lambda

Does not make sense unless you've already solved the constrained system with Mult() or LagrangeSystemMult()

Definition at line 76 of file constraints.hpp.

◆ LagrangeSystemMult()

void mfem::ConstrainedSolver::LagrangeSystemMult	(	const Vector &	f_and_r,
		Vector &	x_and_lambda ) const

virtual

Solve for (x, lambda) given (f, r)

The base class implementation calls Mult(), so derived classes must implement either this or Mult()

Reimplemented in mfem::SchurConstrainedSolver.

Definition at line 740 of file constraints.cpp.

◆ Mult()

void mfem::ConstrainedSolver::Mult	(	const Vector &	f,
		Vector &	x ) const

overridevirtual

Solve for \( x \) given \( f \).

If you want to set \( r \), call SetConstraintRHS() before this.

If you want to get \( \lambda \), call GetMultiplierSolution() after this.

The base class implementation calls LagrangeSystemMult(), so derived classes must implement either this or LagrangeSystemMult()

Implements mfem::Operator.

Reimplemented in mfem::EliminationSolver, and mfem::PenaltyConstrainedSolver.

Definition at line 712 of file constraints.cpp.

◆ SetConstraintRHS()

void mfem::ConstrainedSolver::SetConstraintRHS ( const Vector & r )

virtual

Set the right-hand side r for the constraint B x = r.

(r defaults to zero if you don't call this)

Definition at line 706 of file constraints.cpp.

◆ SetOperator()

virtual void mfem::ConstrainedSolver::SetOperator ( const Operator & op )

inlineoverridevirtual

Also calls SetOperator for the preconditioner if there is one.

Reimplemented from mfem::IterativeSolver.

Reimplemented in mfem::EliminationSolver, and mfem::PenaltyConstrainedSolver.

Definition at line 63 of file constraints.hpp.

Member Data Documentation

◆ A

Operator& mfem::ConstrainedSolver::A

protected

Definition at line 97 of file constraints.hpp.

◆ B

Operator& mfem::ConstrainedSolver::B

protected

Definition at line 98 of file constraints.hpp.

◆ constraint_rhs

Vector mfem::ConstrainedSolver::constraint_rhs

mutableprotected

Definition at line 100 of file constraints.hpp.

◆ multiplier_sol

Vector mfem::ConstrainedSolver::multiplier_sol

mutableprotected

Definition at line 101 of file constraints.hpp.

◆ workb

Vector mfem::ConstrainedSolver::workb

mutableprotected

Definition at line 102 of file constraints.hpp.

◆ workx

Vector mfem::ConstrainedSolver::workx

mutableprotected

Definition at line 103 of file constraints.hpp.

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

linalg/constraints.hpp
linalg/constraints.cpp

Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ ConstrainedSolver() [1/2]

◆ ConstrainedSolver() [2/2]

◆ ~ConstrainedSolver()

Member Function Documentation

◆ GetMultiplierSolution()

◆ LagrangeSystemMult()

◆ Mult()

◆ SetConstraintRHS()

◆ SetOperator()

Member Data Documentation

◆ A

◆ B

◆ constraint_rhs

◆ multiplier_sol

◆ workb

◆ workx