Improved convergence of forward and inverse finite element models

TL;DR

This paper presents enhanced mathematical techniques that improve the convergence of forward and inverse finite element models, especially in highly non-linear systems, by increasing convergence basins and reducing steps needed.

Contribution

It introduces novel improvements to root-finding and minimisation methods, enhancing the convergence behavior of FEM-based models in complex non-linear scenarios.

Findings

Larger convergence basins achieved with new techniques

Fewer steps required for convergence in tested models

Demonstrated practical application in FEM simulations

Abstract

Forward and inverse models are used throughout different engineering fields to predict and understand the behaviour of systems and to find parameters from a set of observations. These models use root-finding and minimisation techniques respectively to achieve their goals. This paper introduces improvements to these mathematical methods to then improve the convergence behaviour of the overarching models when used in highly non-linear systems. The performance of the new techniques is examined in detail and compared to that of the standard methods. The improved techniques are also tested with FEM models to show their practical application. Depending on the specific configuration of the problem, the improved models yielded larger convergence basins and/or took fewer steps to converge.