NewtonSolver Class Reference

This class defines a Newton solver for nonlinear systems of equations of the form \(F(x) = 0\). More...

#include <NewtonSolver.h>

Public Member Functions
	NewtonSolver (MPI_Comm comm)
	Create nonlinear solver.
	NewtonSolver (NewtonSolver &&solver)=delete
	NewtonSolver (const NewtonSolver &solver)=delete
NewtonSolver &	operator= (const NewtonSolver &solver)=delete
NewtonSolver &	operator= (const NewtonSolver &&solver)=delete
	~NewtonSolver ()
	Destructor.
void	setF (const std::function< void(const Vec, Vec)> &F, Vec b)
	Set the function for computing the residual and the vector to the assemble the residual into.
void	setJ (const std::function< void(const Vec, Mat)> &J, Mat Jmat)
	Set the function for computing the Jacobian (dF/dx) and the matrix to assemble the residual into.
void	setP (const std::function< void(const Vec, Mat)> &P, Mat Pmat)
	Set the function for computing the preconditioner matrix (optional)
const la::petsc::KrylovSolver &	get_krylov_solver () const
	Get the internal Krylov solver used to solve for the Newton updates const version The Krylov solver prefix is nls_solve_.
la::petsc::KrylovSolver &	get_krylov_solver ()
	Get the internal Krylov solver used to solve for the Newton updates non-const version The Krylov solver prefix is nls_solve_.
void	set_form (const std::function< void(Vec)> &form)
	Set the function that is called before the residual or Jacobian are computed. It is commonly used to update ghost values.
void	set_convergence_check (const std::function< std::pair< double, bool >(const NewtonSolver &, const Vec)> &c)
	Set function that is called at the end of each Newton iteration to test for convergence.
void	set_update (const std::function< void(const NewtonSolver &solver, const Vec, Vec)> &update)
	Set function that is called after each Newton iteration to update the solution.
std::pair< int, bool >	solve (Vec x)
	Solve the nonlinear problem \(`F(x) = 0\) for given \(F\) and Jacobian \(\dfrac{\partial F}{\partial x}\).
int	iteration () const
	The number of Newton iterations. It can can called by functions that check for convergence during a solve.
int	krylov_iterations () const
	Return number of Krylov iterations elapsed since solve started.
double	residual () const
	Return current residual.
double	residual0 () const
	Return initial residual.
MPI_Comm	comm () const
	Return MPI communicator.

Public Attributes
int	max_it = 50
	Maximum number of iterations.
double	rtol = 1e-9
	Relative tolerance.
double	atol = 1e-10
	Absolute tolerance.
std::string	convergence_criterion = "residual"
	Convergence criterion.
bool	report = true
	Monitor convergence.
bool	error_on_nonconvergence = true
	Throw error if solver fails to converge.
double	relaxation_parameter = 1.0
	Relaxation parameter.

Detailed Description

This class defines a Newton solver for nonlinear systems of equations of the form \(F(x) = 0\).

Constructor & Destructor Documentation

NewtonSolver()

NewtonSolver ( MPI_Comm  comm )

explicit

Create nonlinear solver.

Parameters

[in]

comm

The MPI communicator for the solver

Member Function Documentation

get_krylov_solver() [1/2]

la::petsc::KrylovSolver & get_krylov_solver

(

)

Get the internal Krylov solver used to solve for the Newton updates non-const version The Krylov solver prefix is nls_solve_.

Returns

The Krylov solver

get_krylov_solver() [2/2]

const la::petsc::KrylovSolver & get_krylov_solver

(

)

const

Get the internal Krylov solver used to solve for the Newton updates const version The Krylov solver prefix is nls_solve_.

Returns

The Krylov solver

iteration()

int iteration

(

)

const

The number of Newton iterations. It can can called by functions that check for convergence during a solve.

Returns

The number of Newton iterations performed

krylov_iterations()

int krylov_iterations

(

)

const

Return number of Krylov iterations elapsed since solve started.

Returns

Number of iterations.

residual()

double residual

(

)

const

Return current residual.

Returns

Current residual

residual0()

double residual0

(

)

const

Return initial residual.

Returns

Initial residual

set_convergence_check()

void set_convergence_check

(

const std::function< std::pair< double, bool >(const NewtonSolver &, const Vec)> &

c

)

Set function that is called at the end of each Newton iteration to test for convergence.

Parameters

[in]

c

The function that tests for convergence

set_form()

void set_form

(

const std::function< void(Vec)> &

form

)

Set the function that is called before the residual or Jacobian are computed. It is commonly used to update ghost values.

Parameters

[in]

form

The function to call. It takes the latest solution vector x as an argument

set_update()

void set_update

(

const std::function< void(const NewtonSolver &solver, const Vec, Vec)> &

update

)

Set function that is called after each Newton iteration to update the solution.

Parameters

[in]

update

The function that updates the solution

setF()

void setF	(	const std::function< void(const Vec, Vec)> &	F,
		Vec	b
	)

Set the function for computing the residual and the vector to the assemble the residual into.

Parameters

[in]	F	Function to compute the residual vector b (x, b)
[in]	b	The vector to assemble to residual into

setJ()

void setJ	(	const std::function< void(const Vec, Mat)> &	J,
		Mat	Jmat
	)

Set the function for computing the Jacobian (dF/dx) and the matrix to assemble the residual into.

Parameters

[in]	J	Function to compute the Jacobian matrix b (x, A)
[in]	Jmat	The matrix to assemble the Jacobian into

setP()

void setP	(	const std::function< void(const Vec, Mat)> &	P,
		Mat	Pmat
	)

Set the function for computing the preconditioner matrix (optional)

Parameters

[in]	P	Function to compute the preconditioner matrix b (x, P)
[in]	Pmat	The matrix to assemble the preconditioner into

solve()

std::pair< int, bool > solve

(

Vec

x

)

Solve the nonlinear problem \(`F(x) = 0\) for given \(F\) and Jacobian \(\dfrac{\partial F}{\partial x}\).

Parameters

[in,out]

x

The vector

Returns

(number of Newton iterations, whether iteration converged)

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

• /__w/dolfinx/dolfinx/cpp/dolfinx/nls/NewtonSolver.h
• /__w/dolfinx/dolfinx/cpp/dolfinx/nls/NewtonSolver.cpp