MFEM v4.7.0 Finite element discretization library
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mfem::EliminationSolver Class Referenceabstract

Solve constrained system by eliminating the constraint; see ConstrainedSolver. More...

#include <constraints.hpp>

Inheritance diagram for mfem::EliminationSolver:
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Collaboration diagram for mfem::EliminationSolver:
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## Public Member Functions

EliminationSolver (HypreParMatrix &A, SparseMatrix &B, Array< int > &primary_dofs, Array< int > &secondary_dofs)
Constructor, with explicit splitting into primary/secondary dofs.

EliminationSolver (HypreParMatrix &A, SparseMatrix &B, Array< int > &constraint_rowstarts)
Constructor, elimination is by blocks.

~EliminationSolver ()

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

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

void SetPreconditioner (Solver &precond) override
This should be called before SetOperator.

Public Member Functions inherited from mfem::ConstrainedSolver
ConstrainedSolver (MPI_Comm comm, Operator &A_, Operator &B_)

ConstrainedSolver (Operator &A_, Operator &B_)

virtual ~ConstrainedSolver ()

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 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_)

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 OperatorGetGradient (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 OperatorGetProlongation () const
Prolongation operator from linear algebra (linear system) vectors, to input vectors for the operator. NULL means identity.

virtual const OperatorGetRestriction () const
Restriction operator from input vectors for the operator to linear algebra (linear system) vectors. NULL means identity.

virtual const OperatorGetOutputProlongation () const
Prolongation operator from linear algebra (linear system) vectors, to output vectors for the operator. NULL means identity.

virtual const OperatorGetOutputRestrictionTranspose () const
Transpose of GetOutputRestriction, directly available in this form to facilitate matrix-free RAP-type operators.

virtual const OperatorGetOutputRestriction () 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 Member Functions

void BuildExplicitOperator ()
Internal utility routine; assembles eliminated matrix explicitly.

virtual SolverBuildPreconditioner () const =0
Build preconditioner for eliminated system.

virtual IterativeSolverBuildKrylov () const =0
Select krylov solver for eliminated system.

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()

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".

## Protected Attributes

HypreParMatrixhA

Array< Eliminator * > eliminators

EliminationProjectionprojector

HypreParMatrixh_explicit_operator

IterativeSolverkrylov

Solverprec

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
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.

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.

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

Solve constrained system by eliminating the constraint; see ConstrainedSolver.

Solves the system with the operator $$P^T A P + Z_P$$, where P is EliminationProjection and Z_P is the identity on the eliminated dofs.

Definition at line 202 of file constraints.hpp.

## ◆ EliminationSolver() [1/2]

 mfem::EliminationSolver::EliminationSolver ( HypreParMatrix & A, SparseMatrix & B, Array< int > & primary_dofs, Array< int > & secondary_dofs )

Constructor, with explicit splitting into primary/secondary dofs.

This constructor uses a single elimination block (per processor), which provides the most general algorithm but is also not scalable

The secondary_dofs are eliminated from the system in this algorithm, as they can be written in terms of the primary_dofs.

Both primary_dofs and secondary_dofs are in the local truedof numbering; All elimination has to be done locally on processor, though the global system can be parallel.

Definition at line 233 of file constraints.cpp.

## ◆ EliminationSolver() [2/2]

 mfem::EliminationSolver::EliminationSolver ( HypreParMatrix & A, SparseMatrix & B, Array< int > & constraint_rowstarts )

Constructor, elimination is by blocks.

Each block is eliminated independently; if the blocks are reasonably small this can be reasonably efficient.

The nonzeros in B are assumed to be in disjoint rows and columns; the rows are identified with the constraint_rowstarts array, the secondary dofs are assumed to be the first nonzeros in the rows.

Definition at line 255 of file constraints.cpp.

## ◆ ~EliminationSolver()

 mfem::EliminationSolver::~EliminationSolver ( )

Definition at line 202 of file constraints.cpp.

## ◆ BuildExplicitOperator()

 void mfem::EliminationSolver::BuildExplicitOperator ( )
protected

Internal utility routine; assembles eliminated matrix explicitly.

Definition at line 214 of file constraints.cpp.

## ◆ BuildKrylov()

 virtual IterativeSolver * mfem::EliminationSolver::BuildKrylov ( ) const
protectedpure virtual

Select krylov solver for eliminated system.

Implemented in mfem::EliminationCGSolver, and mfem::EliminationGMRESSolver.

## ◆ BuildPreconditioner()

 virtual Solver * mfem::EliminationSolver::BuildPreconditioner ( ) const
protectedpure virtual

Build preconditioner for eliminated system.

Implemented in mfem::EliminationCGSolver, and mfem::EliminationGMRESSolver.

## ◆ Mult()

 void mfem::EliminationSolver::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()

Reimplemented from mfem::ConstrainedSolver.

Definition at line 316 of file constraints.cpp.

## ◆ SetOperator()

 void mfem::EliminationSolver::SetOperator ( const Operator & op )
inlineoverridevirtual

Also calls SetOperator for the preconditioner if there is one.

Reimplemented from mfem::ConstrainedSolver.

Definition at line 235 of file constraints.hpp.

## ◆ SetPreconditioner()

 void mfem::EliminationSolver::SetPreconditioner ( Solver & pr )
inlineoverridevirtual

This should be called before SetOperator.

Reimplemented from mfem::IterativeSolver.

Definition at line 238 of file constraints.hpp.

## ◆ eliminators

 Array mfem::EliminationSolver::eliminators
protected

Definition at line 251 of file constraints.hpp.

## ◆ h_explicit_operator

 HypreParMatrix* mfem::EliminationSolver::h_explicit_operator
protected

Definition at line 253 of file constraints.hpp.

## ◆ hA

 HypreParMatrix& mfem::EliminationSolver::hA
protected

Definition at line 250 of file constraints.hpp.

## ◆ krylov

 IterativeSolver* mfem::EliminationSolver::krylov
mutableprotected

Definition at line 254 of file constraints.hpp.

## ◆ prec

 Solver* mfem::EliminationSolver::prec
mutableprotected

Definition at line 255 of file constraints.hpp.

## ◆ projector

 EliminationProjection* mfem::EliminationSolver::projector
protected

Definition at line 252 of file constraints.hpp.

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