ptems::NonlinearSolver< T > Class Template Reference

Nonlinear solver using (damped) Newton. More...

#include <ptems/solvers/nonlinearsolver.hpp>

Public Types
typedef T	value_type
	The type of the nonlinear system. More...
typedef remove_complex_t< value_type >	real_type
	The underlying real-valued type (either value_type or the underlying type of std::complex) More...

Public Member Functions
	NonlinearSolver (const DampingParameters< real_type > &dampingParams)
	Creates a damped Newton nonlinear solver. More...
	NonlinearSolver ()
	Creates an un-damped Newton solver. More...
template<typename Solver , typename Residual , std::size_t DIM, std::size_t N>
DiscreteFunction< DIM, value_type, N, N >	SolveWithStatus (Solver solve, Residual residual, DiscreteFunction< DIM, value_type, N, N > initialGuess, double &tolerance, std::size_t &iterations)
	Solve the nonlinear system \(F(u) = 0\), where \(F(u)\) is the residual, and returns, via reference arguments, the actual number of iterations and achieved residual tolerance. More...
template<typename Solver , typename Residual , std::size_t DIM, std::size_t N>
DiscreteFunction< DIM, value_type, N, N >	SolveWithStatus (Solver solve, Residual residual, const DiscreteFunction< DIM, value_type, N, N > &initialGuess, std::size_t &iterations)
	Solve the nonlinear system \(F(u) = 0\), where \(F(u)\) is the residual, and returns, via reference arguments, the actual number of iterations. More...
template<typename Solver , typename Residual , std::size_t DIM, std::size_t N>
DiscreteFunction< DIM, value_type, N, N >	Solve (Solver solve, Residual residual, DiscreteFunction< DIM, value_type, N, N > initialGuess, double tolerance=1e-8, std::size_t maxItns=100)
	Solve the nonlinear system \(F(u) = 0\), where \(F(u)\) is the residual. More...
template<typename Solver , typename Residual , std::size_t DIM, std::size_t N>
DiscreteFunction< DIM, value_type, N, N >	Solve (Solver solve, Residual residual, const DiscreteFunction< DIM, value_type, N, N > &initialGuess, std::size_t maxItns)
	Solve the nonlinear system \(F(u) = 0\), where \(F(u)\) is the residual. More...

Detailed Description

template<typename T>
class ptems::NonlinearSolver< T >

Nonlinear solver using (damped) Newton.

Todo:

This is for damped Newton only, should try to generalise!

Template Parameters

T	The type of the nonlinear system

Member Typedef Documentation

real_type

template<typename T >

typedef remove_complex_t<value_type> ptems::NonlinearSolver< T >::real_type

The underlying real-valued type (either value_type or the underlying type of std::complex)

value_type

template<typename T >

typedef T ptems::NonlinearSolver< T >::value_type

The type of the nonlinear system.

Constructor & Destructor Documentation

NonlinearSolver() [1/2]

template<typename T >

ptems::NonlinearSolver< T >::NonlinearSolver ( const DampingParameters< real_type > &  dampingParams )

inline

Creates a damped Newton nonlinear solver.

Parameters

dampingParams

The damping parameters for the damped Newton solver

NonlinearSolver() [2/2]

template<typename T >

ptems::NonlinearSolver< T >::NonlinearSolver ( )

inline

Creates an un-damped Newton solver.

Member Function Documentation

Solve() [1/2]

template<typename T >

template<typename Solver , typename Residual , std::size_t DIM, std::size_t N>

DiscreteFunction<DIM, value_type, N, N> ptems::NonlinearSolver< T >::Solve ( Solver  solve, Residual  residual, const DiscreteFunction< DIM, value_type, N, N > &  initialGuess, std::size_t  maxItns  )

inline

Solve the nonlinear system \(F(u) = 0\), where \(F(u)\) is the residual.

Uses default tolerance of 1e-8.

Exceptions

std::invalid_argument

If tolerance is non-positive

Template Parameters

Solver	Type of the function to solve \(F'(u)v = F(u)\), where \(F'(u)v\) is the Frechet derivative of F in the direction \(v\) at \(u\).
Residual	Type of the residual ( \(F\)) function
DIM	The dimension of the underlying domain
N	The number of variables in the underlying finite element space

Parameters

solve	Function to solve \(F'(u)v = F(u)\), where \(F'(u)v\) is the Frechet derivative of F in the direction \(v\) at \(u\). Should take form DiscreteFunction<DIM, value_type, N>(const DiscreteFunction<DIM, value_type, N>&, const std::vector<value_type>&) where the first argument is the function \(u\) and the second is the right hand side (residual \(F(u)\) evaluated at \(u\)), and should return the update \(v\).
residual	Function to compute the residual \(u\). Should have the form void(const DiscreteFunction<DIM, value_type, N>&, std::vector<value_type>&) where the first argument is the function \(u\) and the second is the residual vector \(F(u)\) to update - note this vector must be returned the same size as passed.
initialGuess	The initial guess for the Newton solver
maxItns	Maximum number of Newton iterations to compute the solution.

Returns

The solution to the nonlinear solve

Solve() [2/2]

template<typename T >

template<typename Solver , typename Residual , std::size_t DIM, std::size_t N>

DiscreteFunction<DIM, value_type, N, N> ptems::NonlinearSolver< T >::Solve ( Solver  solve, Residual  residual, DiscreteFunction< DIM, value_type, N, N >  initialGuess, double  tolerance = 1e-8, std::size_t  maxItns = 100  )

inline

Solve the nonlinear system \(F(u) = 0\), where \(F(u)\) is the residual.

Exceptions

std::invalid_argument

If tolerance is non-positive

Template Parameters

Solver	Type of the function to solve \(F'(u)v = F(u)\), where \(F'(u)v\) is the Frechet derivative of F in the direction \(v\) at \(u\).
Residual	Type of the residual ( \(F\)) function
DIM	The dimension of the underlying domain
N	The number of variables in the underlying finite element space

Parameters

solve	Function to solve \(F'(u)v = F(u)\), where \(F'(u)v\) is the Frechet derivative of F in the direction \(v\) at \(u\). Should take form DiscreteFunction<DIM, value_type, N>(const DiscreteFunction<DIM, value_type, N>&, const std::vector<value_type>&) where the first argument is the function \(u\) and the second is the right hand side (residual \(F(u)\) evaluated at \(u\)), and should return the update \(v\).
residual	Function to compute the residual \(u\). Should have the form void(const DiscreteFunction<DIM, value_type, N>&, std::vector<value_type>&) where the first argument is the function \(u\) and the second is the residual vector \(F(u)\) to update - note this vector must be returned the same size as passed.
initialGuess	The initial guess for the Newton solver
tolerance	Tolerance to acheive in the Newton solver. (default=1e-8)
maxItns	Maximum number of Newton iterations to compute the solution. (default = 100)

Returns

The solution to the nonlinear solve

SolveWithStatus() [1/2]

template<typename T >

template<typename Solver , typename Residual , std::size_t DIM, std::size_t N>

DiscreteFunction<DIM, value_type, N, N> ptems::NonlinearSolver< T >::SolveWithStatus ( Solver  solve, Residual  residual, const DiscreteFunction< DIM, value_type, N, N > &  initialGuess, std::size_t &  iterations  )

inline

Solve the nonlinear system \(F(u) = 0\), where \(F(u)\) is the residual, and returns, via reference arguments, the actual number of iterations.

Uses default tolerance of 1e-8.

Template Parameters

Solver	Type of the function to solve \(F'(u)v = F(u)\), where \(F'(u)v\) is the Frechet derivative of F in the direction \(v\) at \(u\).
Residual	Type of the residual ( \(F\)) function
DIM	The dimension of the underlying domain
N	The number of variables in the underlying finite element space

Parameters

solve	Function to solve \(F'(u)v = F(u)\), where \(F'(u)v\) is the Frechet derivative of F in the direction \(v\) at \(u\). Should take form DiscreteFunction<DIM, value_type, N>(const DiscreteFunction<DIM, value_type, N>&, const std::vector<value_type>&) where the first argument is the function \(u\) and the second is the right hand side (residual \(F(u)\) evaluated at \(u\)), and should return the update \(v\).
residual	Function to compute the residual \(u\). Should have the form void(const DiscreteFunction<DIM, value_type, N>&, std::vector<value_type>&) where the first argument is the function \(u\) and the second is the residual vector \(F(u)\) to update - note this vector must be returned the same size as passed.
initialGuess	The initial guess for the Newton solver
iterations	Maximum number of Newton iterations to compute the solution. Updated at exit with the number of actual iterations performed

Returns

The solution to the nonlinear solve

SolveWithStatus() [2/2]

template<typename T >

template<typename Solver , typename Residual , std::size_t DIM, std::size_t N>

DiscreteFunction<DIM, value_type, N, N> ptems::NonlinearSolver< T >::SolveWithStatus ( Solver  solve, Residual  residual, DiscreteFunction< DIM, value_type, N, N >  initialGuess, double &  tolerance, std::size_t &  iterations  )

inline

Solve the nonlinear system \(F(u) = 0\), where \(F(u)\) is the residual, and returns, via reference arguments, the actual number of iterations and achieved residual tolerance.

Exceptions

std::invalid_argument

If tolerance is non-positive

Template Parameters

Solver	Type of the function to solve \(F'(u)v = F(u)\), where \(F'(u)v\) is the Frechet derivative of F in the direction \(v\) at \(u\).
Residual	Type of the residual ( \(F\)) function
DIM	The dimension of the underlying domain
N	The number of variables in the underlying finite element space

Parameters

solve	Function to solve \(F'(u)v = F(u)\), where \(F'(u)v\) is the Frechet derivative of F in the direction \(v\) at \(u\). Should take form DiscreteFunction<DIM, value_type, N>(const DiscreteFunction<DIM, value_type, N>&, const std::vector<value_type>&) where the first argument is the function \(u\) and the second is the right hand side (residual \(F(u)\) evaluated at \(u\)), and should return the update \(v\).
residual	Function to compute the residual \(u\). Should have the form void(const DiscreteFunction<DIM, value_type, N>&, std::vector<value_type>&) where the first argument is the function \(u\) and the second is the residual vector \(F(u)\) to update - note this vector must be returned the same size as passed.
initialGuess	The initial guess for the Newton solver
tolerance	Tolerance to acheive in the Newton solver. Updated at exit with the achieved tolerance
iterations	Maximum number of Newton iterations to compute the solution. Updated at exit with the number of actual iterations performed

Returns

The solution to the nonlinear solve

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

• ptems/solvers/nonlinearsolver.hpp