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

#include <solvers.hpp>

Inheritance diagram for mfem::NewtonSolver:

Collaboration diagram for mfem::NewtonSolver:

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 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 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 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...

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...

Type	GetType () const
	Return the type ID of the Operator class. More...

Protected Attributes
Vector	r

Vector	c

Protected Attributes inherited from mfem::IterativeSolver
const Operator *	oper

Solver *	prec

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	Type { ANY_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 259 of file solvers.hpp.

Constructor & Destructor Documentation

mfem::NewtonSolver::NewtonSolver ( )

inline

Definition at line 265 of file solvers.hpp.

mfem::NewtonSolver::NewtonSolver ( MPI_Comm _comm )

inline

Definition at line 268 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 284 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 1250 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 1239 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 274 of file solvers.hpp.

Member Data Documentation

Vector mfem::NewtonSolver::c

mutableprotected

Definition at line 262 of file solvers.hpp.

Vector mfem::NewtonSolver::r

mutableprotected

Definition at line 262 of file solvers.hpp.

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

linalg/solvers.hpp
linalg/solvers.cpp

Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation