MFEM  v4.3.0 Finite element discretization library
mfem::ConstrainedSolver Class Reference

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

#include <constraints.hpp>

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## 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. More...

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

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

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

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

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

IterativeSolver (MPI_Comm comm_)

void SetRelTol (double rtol)

void SetAbsTol (double atol)

void SetMaxIter (int max_it)

void SetPrintLevel (int print_lvl)

int GetNumIterations () const

int GetConverged () const

double GetFinalNorm () const

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

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

MPI_Comm GetComm () const
Return the associated MPI communicator, or MPI_COMM_NULL if no communicator is set. 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=0, int m=0) const
Prints operator with input size n and output size m in Matlab format. More...

virtual ~Operator ()
Virtual destructor. More...

Type GetType () const
Return the type ID of the Operator class. More...

## Protected Attributes

OperatorA

OperatorB

Vector constraint_rhs

Vector multiplier_sol

Vector workb

Vector workx

Protected Attributes inherited from mfem::IterativeSolver
const Operatoroper

Solverprec

IterativeSolverMonitormonitor = nullptr

int max_iter

int print_level

double rel_tol

double abs_tol

int final_iter

int converged

double final_norm

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...

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
}
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::IterativeSolver
double Dot (const Vector &x, const Vector &y) const

double Norm (const Vector &x) const

void Monitor (int it, double norm, const Vector &r, const Vector &x, bool final=false) const

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...

## 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

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

Definition at line 643 of file constraints.cpp.

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

Definition at line 651 of file constraints.cpp.

 virtual mfem::ConstrainedSolver::~ConstrainedSolver ( )
inlinevirtual

Definition at line 61 of file constraints.hpp.

## Member Function Documentation

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

Return the Lagrange multiplier solution in 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.

 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 692 of file constraints.cpp.

 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::PenaltyConstrainedSolver, and mfem::EliminationSolver.

Definition at line 664 of file constraints.cpp.

 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 658 of file constraints.cpp.

 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::PenaltyConstrainedSolver, and mfem::EliminationSolver.

Definition at line 63 of file constraints.hpp.

## Member Data Documentation

 Operator& mfem::ConstrainedSolver::A
protected

Definition at line 97 of file constraints.hpp.

 Operator& mfem::ConstrainedSolver::B
protected

Definition at line 98 of file constraints.hpp.

 Vector mfem::ConstrainedSolver::constraint_rhs
mutableprotected

Definition at line 100 of file constraints.hpp.

 Vector mfem::ConstrainedSolver::multiplier_sol
mutableprotected

Definition at line 101 of file constraints.hpp.

 Vector mfem::ConstrainedSolver::workb
mutableprotected

Definition at line 102 of file constraints.hpp.

 Vector mfem::ConstrainedSolver::workx
mutableprotected

Definition at line 103 of file constraints.hpp.

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