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

Solve constrained system by solving original mixed system; see ConstrainedSolver. More...

#include <constraints.hpp>

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

 SchurConstrainedSolver (MPI_Comm comm, Operator &A_, Operator &B_, Solver &primal_pc_)
 
 SchurConstrainedSolver (Operator &A_, Operator &B_, Solver &primal_pc_)
 
virtual ~SchurConstrainedSolver ()
 
virtual void LagrangeSystemMult (const Vector &x, Vector &y) const override
 Solve for (x, lambda) given (f, r) More...
 
- Public Member Functions inherited from mfem::ConstrainedSolver
 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...
 
- 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 Member Functions

 SchurConstrainedSolver (MPI_Comm comm, Operator &A_, Operator &B_)
 
 SchurConstrainedSolver (Operator &A_, Operator &B_)
 
- 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...
 

Protected Attributes

Array< int > offsets
 
BlockOperatorblock_op
 
TransposeOperatortr_B
 
Solverprimal_pc
 
BlockDiagonalPreconditionerblock_pc
 
Solverdual_pc
 
- Protected Attributes inherited from mfem::ConstrainedSolver
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...
 

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
}
 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...
 

Detailed Description

Solve constrained system by solving original mixed system; see ConstrainedSolver.

Solves the saddle-point problem with a block-diagonal preconditioner, with user-provided preconditioner in the top-left block and (by default) an identity matrix in the bottom-right.

This is the most general ConstrainedSolver, needing only Operator objects to function. But in general it is not very efficient or scalable.

Definition at line 365 of file constraints.hpp.

Constructor & Destructor Documentation

mfem::SchurConstrainedSolver::SchurConstrainedSolver ( MPI_Comm  comm,
Operator A_,
Operator B_,
Solver primal_pc_ 
)

Setup constrained system, with primal_pc a user-provided preconditioner for the top-left block.

Definition at line 492 of file constraints.cpp.

mfem::SchurConstrainedSolver::SchurConstrainedSolver ( Operator A_,
Operator B_,
Solver primal_pc_ 
)

Definition at line 510 of file constraints.cpp.

mfem::SchurConstrainedSolver::~SchurConstrainedSolver ( )
virtual

Definition at line 551 of file constraints.cpp.

mfem::SchurConstrainedSolver::SchurConstrainedSolver ( MPI_Comm  comm,
Operator A_,
Operator B_ 
)
protected

Definition at line 528 of file constraints.cpp.

mfem::SchurConstrainedSolver::SchurConstrainedSolver ( Operator A_,
Operator B_ 
)
protected

Definition at line 541 of file constraints.cpp.

Member Function Documentation

void mfem::SchurConstrainedSolver::LagrangeSystemMult ( const Vector f_and_r,
Vector x_and_lambda 
) const
overridevirtual

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

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

Reimplemented from mfem::ConstrainedSolver.

Definition at line 559 of file constraints.cpp.

Member Data Documentation

BlockOperator* mfem::SchurConstrainedSolver::block_op
protected

Definition at line 386 of file constraints.hpp.

BlockDiagonalPreconditioner* mfem::SchurConstrainedSolver::block_pc
protected

Definition at line 389 of file constraints.hpp.

Solver* mfem::SchurConstrainedSolver::dual_pc
protected

Definition at line 390 of file constraints.hpp.

Array<int> mfem::SchurConstrainedSolver::offsets
protected

Definition at line 385 of file constraints.hpp.

Solver* mfem::SchurConstrainedSolver::primal_pc
protected

Definition at line 388 of file constraints.hpp.

TransposeOperator* mfem::SchurConstrainedSolver::tr_B
protected

Definition at line 387 of file constraints.hpp.


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