MFEM  v4.4.0
Finite element discretization library
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mfem::NewtonSolver Class Reference

Newton's method for solving F(x)=b for a given operator F. More...

#include <solvers.hpp>

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

 NewtonSolver ()
 
 NewtonSolver (MPI_Comm comm_)
 
virtual void SetOperator (const Operator &op)
 Also calls SetOperator for the preconditioner if there is one. More...
 
virtual void SetSolver (Solver &solver)
 Set the linear solver for inverting the Jacobian. More...
 
virtual void Mult (const Vector &b, Vector &x) const
 Solve the nonlinear system with right-hand side b. More...
 
virtual double ComputeScalingFactor (const Vector &x, const Vector &b) const
 This method can be overloaded in derived classes to implement line search algorithms. More...
 
virtual void ProcessNewState (const Vector &x) const
 This method can be overloaded in derived classes to perform computations that need knowledge of the newest Newton state. More...
 
void SetAdaptiveLinRtol (const int type=2, const double rtol0=0.5, const double rtol_max=0.9, const double alpha=0.5 *(1.0+sqrt(5.0)), const double gamma=1.0)
 Enable adaptive linear solver relative tolerance algorithm. More...
 
- Public Member Functions inherited from mfem::IterativeSolver
 IterativeSolver ()
 
 IterativeSolver (MPI_Comm comm_)
 
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...
 
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
 
bool GetConverged () const
 
double GetFinalNorm () const
 
- 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, 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 AdaptiveLinRtolPreSolve (const Vector &x, const int it, const double fnorm) const
 Method for the adaptive linear solver rtol invoked before the linear solve. More...
 
void AdaptiveLinRtolPostSolve (const Vector &x, const Vector &b, const int it, const double fnorm) const
 Method for the adaptive linear solver rtol invoked after the linear solve. 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...
 
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

Vector r
 
Vector c
 
Operatorgrad
 
int lin_rtol_type = 0
 
double lin_rtol0
 
double lin_rtol_max
 
double fnorm_last = 0.0
 
double lnorm_last = 0.0
 
double eta_last = 0.0
 
double gamma
 
double alpha
 
- 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. More...
 
double rel_tol
 Relative tolerance. More...
 
double abs_tol
 Absolute tolerance. More...
 
int final_iter
 
bool converged
 
double final_norm
 
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
}
 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...
 

Detailed Description

Newton's method for solving F(x)=b for a given operator F.

The method GetGradient() must be implemented for the operator F. The preconditioner is used (in non-iterative mode) to evaluate the action of the inverse gradient of the operator.

Definition at line 613 of file solvers.hpp.

Constructor & Destructor Documentation

mfem::NewtonSolver::NewtonSolver ( )
inline

Definition at line 652 of file solvers.hpp.

mfem::NewtonSolver::NewtonSolver ( MPI_Comm  comm_)
inline

Definition at line 655 of file solvers.hpp.

Member Function Documentation

void mfem::NewtonSolver::AdaptiveLinRtolPostSolve ( const Vector x,
const Vector b,
const int  it,
const double  fnorm 
) const
protected

Method for the adaptive linear solver rtol invoked after the linear solve.

Definition at line 1972 of file solvers.cpp.

void mfem::NewtonSolver::AdaptiveLinRtolPreSolve ( const Vector x,
const int  it,
const double  fnorm 
) const
protected

Method for the adaptive linear solver rtol invoked before the linear solve.

Definition at line 1925 of file solvers.cpp.

virtual double mfem::NewtonSolver::ComputeScalingFactor ( const Vector x,
const Vector b 
) const
inlinevirtual

This method can be overloaded in derived classes to implement line search algorithms.

The base class implementation (NewtonSolver) simply returns 1. A return value of 0 indicates a failure, interrupting the Newton iteration.

Reimplemented in mfem::TMOPNewtonSolver.

Definition at line 671 of file solvers.hpp.

void mfem::NewtonSolver::Mult ( const Vector b,
Vector x 
) const
virtual

Solve the nonlinear system with right-hand side b.

If b.Size() != Height(), then b is assumed to be zero.

Implements mfem::Operator.

Reimplemented in mfem::KINSolver, mfem::LBFGSSolver, and mfem::TMOPNewtonSolver.

Definition at line 1804 of file solvers.cpp.

virtual void mfem::NewtonSolver::ProcessNewState ( const Vector x) const
inlinevirtual

This method can be overloaded in derived classes to perform computations that need knowledge of the newest Newton state.

Reimplemented in mfem::TMOPNewtonSolver.

Definition at line 676 of file solvers.hpp.

void mfem::NewtonSolver::SetAdaptiveLinRtol ( const int  type = 2,
const double  rtol0 = 0.5,
const double  rtol_max = 0.9,
const double  alpha = 0.5 * (1.0 + sqrt(5.0)),
const double  gamma = 1.0 
)

Enable adaptive linear solver relative tolerance algorithm.

Compute a relative tolerance for the Krylov method after each nonlinear iteration, based on the algorithm presented in [1].

The maximum linear solver relative tolerance rtol_max should be < 1. For type 1 the parameters alpha and gamma are ignored. For type 2 alpha has to be between 0 and 1 and gamma between 1 and 2.

[1] Eisenstat, Stanley C., and Homer F. Walker. "Choosing the forcing terms in an inexact Newton method."

Definition at line 1912 of file solvers.cpp.

void mfem::NewtonSolver::SetOperator ( const Operator op)
virtual

Also calls SetOperator for the preconditioner if there is one.

Reimplemented from mfem::IterativeSolver.

Reimplemented in mfem::KINSolver, and mfem::LBFGSSolver.

Definition at line 1793 of file solvers.cpp.

virtual void mfem::NewtonSolver::SetSolver ( Solver solver)
inlinevirtual

Set the linear solver for inverting the Jacobian.

This method is equivalent to calling SetPreconditioner().

Reimplemented in mfem::KINSolver, mfem::LBFGSSolver, and mfem::TMOPNewtonSolver.

Definition at line 661 of file solvers.hpp.

Member Data Documentation

double mfem::NewtonSolver::alpha
protected

Definition at line 636 of file solvers.hpp.

Vector mfem::NewtonSolver::c
mutableprotected

Definition at line 616 of file solvers.hpp.

double mfem::NewtonSolver::eta_last = 0.0
mutableprotected

Definition at line 632 of file solvers.hpp.

double mfem::NewtonSolver::fnorm_last = 0.0
mutableprotected

Definition at line 628 of file solvers.hpp.

double mfem::NewtonSolver::gamma
protected

Definition at line 634 of file solvers.hpp.

Operator* mfem::NewtonSolver::grad
mutableprotected

Definition at line 617 of file solvers.hpp.

double mfem::NewtonSolver::lin_rtol0
protected

Definition at line 624 of file solvers.hpp.

double mfem::NewtonSolver::lin_rtol_max
protected

Definition at line 626 of file solvers.hpp.

int mfem::NewtonSolver::lin_rtol_type = 0
protected

Definition at line 622 of file solvers.hpp.

double mfem::NewtonSolver::lnorm_last = 0.0
mutableprotected

Definition at line 630 of file solvers.hpp.

Vector mfem::NewtonSolver::r
mutableprotected

Definition at line 616 of file solvers.hpp.


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