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.

Armijo line search strategy is used to search along the direction of the full Newton step for a decreasing residual norm.

#include <NewtonWithLineSearch.h>

Inheritance diagram for NewtonWithLineSearch:

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Public Member Functions
	NewtonWithLineSearch (const OptionSet &options)

Public Member Functions inherited from Newton
	Newton (const OptionSet &options)

Result	solve (NonlinearSystem &system, const NonlinearSystem::Sol< false > &x0) override
	Solve the given nonlinear system.

Public Member Functions inherited from NonlinearSolver
	NonlinearSolver (const OptionSet &options)
	Construct a new NonlinearSolver object.

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.

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.

Static Public Member Functions
static OptionSet	expected_options ()

Static Public Member Functions inherited from Newton
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
void	update (NonlinearSystem &system, NonlinearSystem::Sol< true > &x, const NonlinearSystem::Res< true > &r, const NonlinearSystem::Jac< true > &J) override
	Update trial solution.

virtual Scalar	linesearch (NonlinearSystem &system, const NonlinearSystem::Sol< true > &x, const NonlinearSystem::Sol< true > &dx, const NonlinearSystem::Res< true > &R0) const
	Perform Armijo linesearch.

Protected Member Functions inherited from Newton
virtual void	prepare (const NonlinearSystem &, const NonlinearSystem::Sol< true > &)
	Prepare solver internal data before the iterative update.

virtual bool	converged (size_t itr, const ATensor &nR, const ATensor &nR0) 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	final_update (NonlinearSystem &system, NonlinearSystem::Sol< true > &x, const NonlinearSystem::Res< true > &r, const NonlinearSystem::Jac< true > &J)
	Do a final update to track AD function graph.

virtual NonlinearSystem::Sol< true >	solve_direction (const NonlinearSystem::Res< true > &r, const NonlinearSystem::Jac< true > &J)
	Find the current update direction.

Protected Attributes
unsigned int	_linesearch_miter
	Linesearch maximum iterations.

Real	_linesearch_sigma
	Decrease factor for linesearch.

Real	_linesearch_c
	Stopping criteria for linesearch.

EnumSelection	_type
	Seclect the type of line search.

bool	_check_crit

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
Real	atol
	Absolute tolerance.

Real	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

◆ NewtonWithLineSearch()

NewtonWithLineSearch ( const OptionSet & options )

Member Function Documentation

◆ expected_options()

OptionSet expected_options ( )

static

◆ linesearch()

Scalar linesearch	(	NonlinearSystem &	system,
		const NonlinearSystem::Sol< true > &	x,
		const NonlinearSystem::Sol< true > &	dx,
		const NonlinearSystem::Res< true > &	R0 ) const

protectedvirtual

Perform Armijo linesearch.

◆ update()

void update	(	NonlinearSystem &	system,
		NonlinearSystem::Sol< true > &	x,
		const NonlinearSystem::Res< true > &	r,
		const NonlinearSystem::Jac< true > &	J )

overrideprotectedvirtual

Update trial solution.

Reimplemented from Newton.

Member Data Documentation

◆ _check_crit

bool _check_crit

protected

◆ _linesearch_c

Real _linesearch_c

protected

Stopping criteria for linesearch.

◆ _linesearch_miter

unsigned int _linesearch_miter

protected

Linesearch maximum iterations.

◆ _linesearch_sigma

Real _linesearch_sigma

protected

Decrease factor for linesearch.

◆ _type

EnumSelection _type

protected

Seclect the type of line search.

Detailed Description

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Constructor & Destructor Documentation

◆ NewtonWithLineSearch()

Member Function Documentation

◆ expected_options()

◆ linesearch()

◆ update()

Member Data Documentation

◆ _check_crit

◆ _linesearch_c

◆ _linesearch_miter

◆ _linesearch_sigma

◆ _type