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.

virtual void	SetSolver (Solver &solver)
	Set the linear solver for inverting the Jacobian.

virtual void	Mult (const Vector &b, Vector &x) const
	Solve the nonlinear system with right-hand side b.

virtual real_t	ComputeScalingFactor (const Vector &x, const Vector &b) const
	This method can be overloaded in derived classes to implement line search algorithms.

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.

void	SetAdaptiveLinRtol (const int type=2, const real_t rtol0=0.5, const real_t rtol_max=0.9, const real_t alpha=0.5 *(1.0+sqrt(5.0)), const real_t gamma=1.0)
	Enable adaptive linear solver relative tolerance algorithm.

Public Member Functions inherited from mfem::IterativeSolver
	IterativeSolver ()

	IterativeSolver (MPI_Comm comm_)

virtual void	SetPreconditioner (Solver &pr)
	This should be called before SetOperator.

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 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.

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 Operator *	GetProlongation () const
	Prolongation operator from linear algebra (linear system) vectors, to input vectors for the operator. `NULL` means identity.

virtual const Operator *	GetRestriction () const
	Restriction operator from input vectors for the operator to linear algebra (linear system) vectors. `NULL` means identity.

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

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

virtual const Operator *	GetOutputRestriction () 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	AdaptiveLinRtolPreSolve (const Vector &x, const int it, const real_t fnorm) const
	Method for the adaptive linear solver rtol invoked before the linear solve.

void	AdaptiveLinRtolPostSolve (const Vector &x, const Vector &b, const int it, const real_t fnorm) const
	Method for the adaptive linear solver rtol invoked after the linear solve.

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()

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".

Protected Attributes
Vector	r

Vector	c

Operator *	grad

int	lin_rtol_type = 0

real_t	lin_rtol0

real_t	lin_rtol_max

real_t	fnorm_last = 0.0

real_t	lnorm_last = 0.0

real_t	eta_last = 0.0

real_t	gamma

real_t	alpha

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.

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.

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.

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

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 666 of file solvers.hpp.

Constructor & Destructor Documentation

◆ NewtonSolver() [1/2]

mfem::NewtonSolver::NewtonSolver ( )

inline

Definition at line 705 of file solvers.hpp.

◆ NewtonSolver() [2/2]

mfem::NewtonSolver::NewtonSolver ( MPI_Comm comm_ )

inline

Definition at line 708 of file solvers.hpp.

Member Function Documentation

◆ AdaptiveLinRtolPostSolve()

void mfem::NewtonSolver::AdaptiveLinRtolPostSolve	(	const Vector &	x,
		const Vector &	b,
		const int	it,
		const real_t	fnorm ) const

protected

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

Definition at line 1989 of file solvers.cpp.

◆ AdaptiveLinRtolPreSolve()

void mfem::NewtonSolver::AdaptiveLinRtolPreSolve	(	const Vector &	x,
		const int	it,
		const real_t	fnorm ) const

protected

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

Definition at line 1942 of file solvers.cpp.

◆ ComputeScalingFactor()

virtual real_t 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 724 of file solvers.hpp.

◆ Mult()

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 1821 of file solvers.cpp.

◆ ProcessNewState()

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 729 of file solvers.hpp.

◆ SetAdaptiveLinRtol()

void mfem::NewtonSolver::SetAdaptiveLinRtol	(	const int	type = 2,
		const real_t	rtol0 = 0.5,
		const real_t	rtol_max = 0.9,
		const real_t	alpha = 0.5 * (1.0 + sqrt(5.0)),
		const real_t	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 1929 of file solvers.cpp.

◆ SetOperator()

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 1810 of file solvers.cpp.

◆ SetSolver()

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 714 of file solvers.hpp.

Member Data Documentation

◆ alpha

real_t mfem::NewtonSolver::alpha

protected

Definition at line 689 of file solvers.hpp.

◆ c

Vector mfem::NewtonSolver::c

protected

Definition at line 669 of file solvers.hpp.

◆ eta_last

real_t mfem::NewtonSolver::eta_last = 0.0

mutableprotected

Definition at line 685 of file solvers.hpp.

◆ fnorm_last

real_t mfem::NewtonSolver::fnorm_last = 0.0

mutableprotected

Definition at line 681 of file solvers.hpp.

◆ gamma

real_t mfem::NewtonSolver::gamma

protected

Definition at line 687 of file solvers.hpp.

◆ grad

Operator* mfem::NewtonSolver::grad

mutableprotected

Definition at line 670 of file solvers.hpp.

◆ lin_rtol0

real_t mfem::NewtonSolver::lin_rtol0

protected

Definition at line 677 of file solvers.hpp.

◆ lin_rtol_max

real_t mfem::NewtonSolver::lin_rtol_max

protected

Definition at line 679 of file solvers.hpp.

◆ lin_rtol_type

int mfem::NewtonSolver::lin_rtol_type = 0

protected

Definition at line 675 of file solvers.hpp.

◆ lnorm_last

real_t mfem::NewtonSolver::lnorm_last = 0.0

mutableprotected

Definition at line 683 of file solvers.hpp.

◆ r

Vector mfem::NewtonSolver::r

mutableprotected

Definition at line 669 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 Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ NewtonSolver() [1/2]

◆ NewtonSolver() [2/2]

Member Function Documentation

◆ AdaptiveLinRtolPostSolve()

◆ AdaptiveLinRtolPreSolve()

◆ ComputeScalingFactor()

◆ Mult()

◆ ProcessNewState()

◆ SetAdaptiveLinRtol()

◆ SetOperator()

◆ SetSolver()

Member Data Documentation

◆ alpha

◆ c

◆ eta_last

◆ fnorm_last

◆ gamma

◆ grad

◆ lin_rtol0

◆ lin_rtol_max

◆ lin_rtol_type

◆ lnorm_last

◆ r