Newton Class Reference

The nonlinear solver solves a nonlinear system of equations. More...

Detailed Description

The nonlinear solver solves a nonlinear system of equations.

The Newton-Raphson method is used to iteratively update the initial guess until the residual becomes zero within specified tolerances.

#include <Newton.h>

Inheritance diagram for Newton:

Public Member Functions
	Newton (const OptionSet &options)
Result	solve (NonlinearSystem &) override
	Solve the given nonlinear system.
Public Member Functions inherited from NonlinearSolver
	NonlinearSolver (const OptionSet &options)
void	to (const TensorOptions &) override
	Change the device and dtype of the solver's internal data.
Public Member Functions inherited from Solver
	Solver (const OptionSet &options)
	Construct a new Solver object.
Public Member Functions inherited from NEML2Object
	NEML2Object ()=delete
	NEML2Object (NEML2Object &&)=delete
	NEML2Object (const NEML2Object &)=delete
NEML2Object &	operator= (NEML2Object &&)=delete
NEML2Object &	operator= (const NEML2Object &)=delete
virtual	~NEML2Object ()=default
	NEML2Object (const OptionSet &options)
	Construct a new NEML2Object object.
const OptionSet &	input_options () const
virtual void	setup ()
	Setup this object.
const std::string &	name () const
	A readonly reference to the object's name.
const std::string &	type () const
	A readonly reference to the object's type.
const std::string &	path () const
	A readonly reference to the object's path.
const std::string &	doc () const
	A readonly reference to the object's docstring.
Factory *	factory () const
	Get the factory that created this object.
const Settings &	settings () const
	Settings.
template<typename T = NEML2Object>
const T *	host () const
	Get a readonly pointer to the host.
template<typename T = NEML2Object>
T *	host ()
	Get a writable pointer to the host.
template<typename T>
const T &	resolve_tensor (const std::string &name)
	Resolve a TensorName to a Tensor.
template<class T>
std::shared_ptr< T >	get_object (const std::string &section, const std::string &name)
template<class T = EquationSystem>
std::shared_ptr< T >	get_es (const std::string &name)
	Get an equation system from the factory.
template<class T = Solver>
std::shared_ptr< T >	get_solver (const std::string &name)
	Get a solver from the factory.
template<class T = Data>
std::shared_ptr< T >	get_data (const std::string &name)
	Get a data from the factory.
template<class T = Model>
std::shared_ptr< T >	get_model (const std::string &name)
	Get a model from the factory.
template<class T = Driver>
std::shared_ptr< T >	get_driver (const std::string &name)
	Get a driver from the factory.
template<class T = WorkScheduler>
std::shared_ptr< T >	get_scheduler (const std::string &name)
	Get a scheduler from the factory.

Static Public Member Functions
static OptionSet	expected_options ()
Static Public Member Functions inherited from NonlinearSolver
static OptionSet	expected_options ()
Static Public Member Functions inherited from Solver
static OptionSet	expected_options ()
Static Public Member Functions inherited from NEML2Object
static OptionSet	expected_options ()

Protected Member Functions
virtual void	prepare (const NonlinearSystem &)
	Prepare solver internal data before the iterative update.
virtual bool	converged (size_t itr, const Scalar &nb, const Scalar &nb0) const
	Check for convergence. The current iteration is said to be converged if the residual norm is below the absolute tolerance or or the ratio between the residual norm and the initial residual norm is below the relative tolerance.
virtual void	update (NonlinearSystem &sys)
	Update trial solution with fresh function graph.
virtual void	final_update (NonlinearSystem &sys)
	Update solution with function graph.

Additional Inherited Members
Public Types inherited from NonlinearSolver
enum class	RetCode : std::uint8_t { SUCCESS = 0 , MAXITER = 1 , FAILURE = 2 }
Public Attributes inherited from NonlinearSolver
std::shared_ptr< LinearSolver >	linear_solver
	Linear solver used by the nonlinear solver.
double	atol
	Absolute tolerance.
double	rtol
	Relative tolerance.
unsigned int	miters
	Maximum number of iterations.
Public Attributes inherited from Solver
const bool	verbose
	Whether to print additional (debugging) information during the solve.

Constructor & Destructor Documentation

Newton()

Newton

(

const OptionSet &

options

)

Member Function Documentation

converged()

virtual bool converged ( size_t itr, const Scalar & nb, const Scalar & nb0 ) const

protectedvirtual

Check for convergence. The current iteration is said to be converged if the residual norm is below the absolute tolerance or or the ratio between the residual norm and the initial residual norm is below the relative tolerance.

Parameters

itr	The current iteration number
nb	The current residual norm
nb0	The initial residual norm

expected_options()

OptionSet expected_options ( )

static

final_update()

virtual void final_update ( NonlinearSystem & sys )

protectedvirtual

Update solution with function graph.

prepare()

virtual void prepare ( const NonlinearSystem & )

inlineprotectedvirtual

Prepare solver internal data before the iterative update.

solve()

Result solve ( NonlinearSystem & system )

overridevirtual

Solve the given nonlinear system.

Parameters

system

The nonlinear system to solve

Returns

See also

neml2::NonlinearSolver::Result

Implements NonlinearSolver.

update()

virtual void update ( NonlinearSystem & sys )

protectedvirtual

Update trial solution with fresh function graph.

Reimplemented in NewtonWithLineSearch.