MFEM  v3.3.2 Finite element discretization library
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... 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... 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
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 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 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...

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...

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(). 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...

## Protected Attributes

Vector r

Vector c Protected Attributes inherited from mfem::IterativeSolver
const Operatoroper

Solverprec

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  Type {
MFEM_SPARSEMAT, Hypre_ParCSR, PETSC_MATAIJ, PETSC_MATIS,
PETSC_MATSHELL, PETSC_MATNEST, PETSC_MATHYPRE, PETSC_MATGENERIC
}
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

## 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 258 of file solvers.hpp.

## Constructor & Destructor Documentation

 mfem::NewtonSolver::NewtonSolver ( )
inline

Definition at line 264 of file solvers.hpp.

 mfem::NewtonSolver::NewtonSolver ( MPI_Comm _comm )
inline

Definition at line 267 of file solvers.hpp.

## Member Function Documentation

 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.

Definition at line 283 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.

Definition at line 1241 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.

Definition at line 1230 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.

Definition at line 273 of file solvers.hpp.

## Member Data Documentation

 Vector mfem::NewtonSolver::c
mutableprotected

Definition at line 261 of file solvers.hpp.

 Vector mfem::NewtonSolver::r
mutableprotected

Definition at line 261 of file solvers.hpp.

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