NonLinearSolver package

Module NonLinearSolver

This module contains all the nonlinear solvers type that are provided by pyHarm. The module is organized around an abstract class ABCNLSolver and a FactoryNonLinearSolver that is in charge of creating the objects. All analysis object must comply with the ABCNLSolver abstract class. The section below presents the different classes that are available in this module.

ABNLSolver

The ABCNLSolver class is an abstract class defining the essential components of any nonlinear solver. One abstract method is defined :

Methods	Use
Solve	Abstract method : From a provided SystemSolution, returns the solution obtained with the nonlinear solver by completing the provided SystemSolution

Examples of creating an ABNLSolver and adding it into an input dictionary:

To be created, an ABNLSolver subclass needs its abstract method to be defined :

class FakeSolver(ABNLSolver): # inherits from abstract class
    factory_keyword="fakesolver" # madatory to define
    def Solve(self,sol:SystemSolution,SolList:list[SystemSolution]) -> SystemSolution:
        Solution = ... # routine to be completed such that the system is solved and a completed SystemSolution is returned
        return Solution

dict_solver_options = {...}

INP = {
    "analysis":{
        "FRF":{
            "study":"frf",
            ...,
            "solver":"fakesolver", # call the criterion using factory_keyword.
            "solver_options":dict_solver_options,
            ...,
        },
        ...,
    },
    "plugin":[FakeSolver], # add to the factory using plugin
    ...,
}

FactoryNonLinearSolver

This file contains the dictionary of all the nonlinear solvers that are available as well as the function generateNonLinearSolver that creates the nonlinear solver object based on the type of solver desired.

Solver_ScipyRoot scipyroot

This solver is a wrapping of the scipy.optimize.root function. The parameters are the following :

Parameter	Use	Default
end_status_accepted	List of status that are considered to be accepted after exiting the root function [list[int]]	✓ : [1]
residual_tolerance	tolerance on the residual if status is not 1 and in the accepted list [float]	✓ : 1e-4
root	Dictionary of options given to root (see scipy.optimize.root options) [dict]	✓ : {“method”:”hybr”,”options”:{“diag”:None}}

Solver_NewtonRaphson NewtonRaphson

This solver is an implementation of a basic Newton Raphson procedure for solving the nonlinear system iteratively using linear solving techniques. The parameters are the following :

Parameter	Use	Default
tol_residual	Tolerance on the norm of the residual value for considering the point to be solved [float]	✓ : 1e-8
tol_delta_x	Tolerance over the change in displacement solution for considering the point to be solved [float]	✓ : 1e-8
max_iter	Max number of iteration before exiting [int]	✓ : 50

Solver_MoorePenrose MoorePenrose

This solver is an implementation of the MoorePenrose iterative solver. It is an iterative solver that seeks for a solution perpendicularly to the direction of the previous iteration. It is equivalent to the Newton Raphson solver with pseudo arc length corrector at the first iteration, but the direction of search is updated at each iteration. See for more details [1]. The parameters are the following :

Parameter	Use	Default
tol_residual	Tolerance on the norm of the residual value for considering the point to be solved [float]	✓ : 1e-8
tol_delta_x	Tolerance over the change in displacement solution for considering the point to be solved [float]	✓ : 1e-8
max_iter	Max number of iteration before exiting [int]	✓ : 50

References

[1] E. Allgower and K. Georg, *Numerical Continuation Methods – An Introduction. Soc. Ind Appl Math. 2003.

API links

pyHarm.NonLinearSolver