MFEM
v4.5.2
Finite element discretization library
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Solve constrained system with penalty method; see ConstrainedSolver. More...
#include <constraints.hpp>
Public Member Functions | |
PenaltyConstrainedSolver (HypreParMatrix &A, SparseMatrix &B, double penalty_) | |
PenaltyConstrainedSolver (HypreParMatrix &A, HypreParMatrix &B, double penalty_) | |
PenaltyConstrainedSolver (HypreParMatrix &A, HypreParMatrix &B, Vector &penalty_) | |
~PenaltyConstrainedSolver () | |
void | Mult (const Vector &x, Vector &y) const override |
Solve for \( x \) given \( f \). More... | |
void | SetOperator (const Operator &op) override |
Also calls SetOperator for the preconditioner if there is one. More... | |
void | SetPreconditioner (Solver &precond) override |
This should be called before SetOperator. 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 | 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 | 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 | 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... | |
void | SetRelTol (double rtol) |
void | SetAbsTol (double atol) |
void | SetMaxIter (int max_it) |
virtual void | SetPrintLevel (int print_lvl) |
Legacy method to set the level of verbosity of the solver output. More... | |
virtual void | SetPrintLevel (PrintLevel) |
Set the level of verbosity of the solver output. More... | |
int | GetNumIterations () const |
Returns the number of iterations taken during the last call to Mult() More... | |
bool | GetConverged () const |
Returns true if the last call to Mult() converged successfully. More... | |
double | GetInitialNorm () const |
Returns the initial residual norm from the last call to Mult(). More... | |
double | GetFinalNorm () const |
Returns the final residual norm after termination of the solver during the last call to Mult(). More... | |
double | 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. 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 void | AddMult (const Vector &x, Vector &y, const double a=1.0) const |
Operator application: y+=A(x) (default) or y+=a*A(x) . More... | |
virtual void | AddMultTranspose (const Vector &x, Vector &y, const double a=1.0) const |
Operator transpose application: y+=A^t(x) (default) or y+=a*A^t(x) . More... | |
virtual void | ArrayMult (const Array< const Vector *> &X, Array< Vector *> &Y) const |
Operator application on a matrix: Y=A(X) . More... | |
virtual void | ArrayMultTranspose (const Array< const Vector *> &X, Array< Vector *> &Y) const |
Action of the transpose operator on a matrix: Y=A^t(X) . More... | |
virtual void | ArrayAddMult (const Array< const Vector *> &X, Array< Vector *> &Y, const double a=1.0) const |
Operator application on a matrix: Y+=A(X) (default) or Y+=a*A(X) . More... | |
virtual void | ArrayAddMultTranspose (const Array< const Vector *> &X, Array< Vector *> &Y, const double a=1.0) const |
Operator transpose application on a matrix: Y+=A^t(X) (default) or Y+=a*A^t(X) . More... | |
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. 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 Operator * | GetProlongation () const |
Prolongation operator from linear algebra (linear system) vectors, to input vectors for the operator. NULL means identity. More... | |
virtual const Operator * | GetRestriction () const |
Restriction operator from input vectors for the operator to linear algebra (linear system) vectors. NULL means identity. More... | |
virtual const Operator * | GetOutputProlongation () const |
Prolongation operator from linear algebra (linear system) vectors, to output vectors for the operator. NULL means identity. More... | |
virtual const Operator * | GetOutputRestrictionTranspose () const |
Transpose of GetOutputRestriction, directly available in this form to facilitate matrix-free RAP-type operators. More... | |
virtual const Operator * | GetOutputRestriction () 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, int m=0) const |
Prints operator with input size n and output size m in Matlab format. More... | |
virtual void | PrintMatlab (std::ostream &out) const |
Prints operator in Matlab format. More... | |
virtual | ~Operator () |
Virtual destructor. More... | |
Type | GetType () const |
Return the type ID of the Operator class. More... | |
Protected Member Functions | |
void | Initialize (HypreParMatrix &A, HypreParMatrix &B, HypreParMatrix &D) |
virtual Solver * | BuildPreconditioner () const =0 |
Build preconditioner for penalized system. More... | |
virtual IterativeSolver * | BuildKrylov () const =0 |
Select krylov solver for penalized system. 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 |
PrintLevel | FromLegacyPrintLevel (int) |
Convert a legacy print level integer to a PrintLevel object. More... | |
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... | |
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". More... | |
Protected Attributes | |
Vector | penalty |
Operator & | constraintB |
HypreParMatrix * | penalized_mat |
IterativeSolver * | krylov |
Solver * | prec |
Protected Attributes inherited from mfem::ConstrainedSolver | |
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. More... | |
double | rel_tol |
Relative tolerance. More... | |
double | abs_tol |
Absolute tolerance. More... | |
int | final_iter = -1 |
bool | converged = false |
double | initial_norm = -1.0 |
double | final_norm = -1.0 |
int | print_level = -1 |
(DEPRECATED) Legacy print level definition, which is left for compatibility with custom iterative solvers. More... | |
PrintLevel | print_options |
Output behavior for the iterative solver. More... | |
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, 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. More... | |
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. More... | |
Solve constrained system with penalty method; see ConstrainedSolver.
Only approximates the solution, better approximation with higher penalty, but with higher penalty the preconditioner is less effective.
Definition at line 319 of file constraints.hpp.
mfem::PenaltyConstrainedSolver::PenaltyConstrainedSolver | ( | HypreParMatrix & | A, |
SparseMatrix & | B, | ||
double | penalty_ | ||
) |
Definition at line 374 of file constraints.cpp.
mfem::PenaltyConstrainedSolver::PenaltyConstrainedSolver | ( | HypreParMatrix & | A, |
HypreParMatrix & | B, | ||
double | penalty_ | ||
) |
Definition at line 413 of file constraints.cpp.
mfem::PenaltyConstrainedSolver::PenaltyConstrainedSolver | ( | HypreParMatrix & | A, |
HypreParMatrix & | B, | ||
Vector & | penalty_ | ||
) |
Definition at line 430 of file constraints.cpp.
mfem::PenaltyConstrainedSolver::~PenaltyConstrainedSolver | ( | ) |
Definition at line 446 of file constraints.cpp.
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protectedpure virtual |
Select krylov solver for penalized system.
Implemented in mfem::PenaltyGMRESSolver, and mfem::PenaltyPCGSolver.
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protectedpure virtual |
Build preconditioner for penalized system.
Implemented in mfem::PenaltyGMRESSolver, and mfem::PenaltyPCGSolver.
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protected |
Initialize the matrix A + B*D*B^T for the constrained linear system A - original matrix (N x N square matrix) B - constraint matrix (M x N rectangular matrix) D - diagonal matrix of penalty values (M x M square matrix)
Definition at line 364 of file constraints.cpp.
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 453 of file constraints.cpp.
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inlineoverridevirtual |
Also calls SetOperator for the preconditioner if there is one.
Reimplemented from mfem::ConstrainedSolver.
Definition at line 335 of file constraints.hpp.
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inlineoverridevirtual |
This should be called before SetOperator.
Reimplemented from mfem::IterativeSolver.
Definition at line 338 of file constraints.hpp.
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protected |
Definition at line 354 of file constraints.hpp.
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mutableprotected |
Definition at line 356 of file constraints.hpp.
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protected |
Definition at line 355 of file constraints.hpp.
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protected |
Definition at line 353 of file constraints.hpp.
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mutableprotected |
Definition at line 357 of file constraints.hpp.