Non-overlapping domain decomposition methods in structural mechanics

TL;DR

This paper reviews non-overlapping domain decomposition methods for efficiently solving large, ill-conditioned linear systems in complex structural mechanics simulations, highlighting their theoretical foundations, practical implementation issues, and numerical performance.

Contribution

It provides a comprehensive review of existing approaches, their mechanical interpretations, and introduces a hybrid method for multifield problems, enhancing solution strategies.

Findings

Various approaches are connected and compared.

Numerical assessments demonstrate effectiveness in academic and industrial problems.

A hybrid approach offers a versatile framework for multifield problems.

Abstract

The modern design of industrial structures leads to very complex simulations characterized by nonlinearities, high heterogeneities, tortuous geometries... Whatever the modelization may be, such an analysis leads to the solution to a family of large ill-conditioned linear systems. In this paper we study strategies to efficiently solve to linear system based on non-overlapping domain decomposition methods. We present a review of most employed approaches and their strong connections. We outline their mechanical interpretations as well as the practical issues when willing to implement and use them. Numerical properties are illustrated by various assessments from academic to industrial problems. An hybrid approach, mainly designed for multifield problems, is also introduced as it provides a general framework of such approaches.