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 &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 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 &, 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	update (NonlinearSystem &system, NonlinearSystem::Sol< true > &x, const NonlinearSystem::Res< true > &r, const NonlinearSystem::Jac< true > &J)
	Update trial solution.
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.

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

Newton()

Newton

(

const OptionSet &

options

)

Member Function Documentation

converged()

bool converged ( size_t itr, const ATensor & nR, const ATensor & nR0 ) 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
nR	The current residual norm
nR0	The initial residual norm

Returns

true Converged

false Not converged

expected_options()

OptionSet expected_options ( )

static

final_update()

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

protectedvirtual

Do a final update to track AD function graph.

prepare()

virtual void prepare ( const NonlinearSystem & , const NonlinearSystem::Sol< true > &  )

inlineprotectedvirtual

Prepare solver internal data before the iterative update.

Reimplemented in NewtonWithTrustRegion.

solve()

Newton::Result solve ( NonlinearSystem & system, const NonlinearSystem::Sol< false > & x0 )

overridevirtual

Solve the given nonlinear system.

Parameters

system	The nonlinear system of equations.
x0	The initial guess

Returns

See also

neml2::NonlinearSolver::Result

Implements NonlinearSolver.

solve_direction()

NonlinearSystem::Sol< true > solve_direction ( const NonlinearSystem::Res< true > & r, const NonlinearSystem::Jac< true > & J )

protectedvirtual

Find the current update direction.

Reimplemented in NewtonWithTrustRegion.

update()

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

protectedvirtual

Update trial solution.

Reimplemented in NewtonWithLineSearch, and NewtonWithTrustRegion.