Substructured formulations of nonlinear structure problems - influence of the interface condition

TL;DR

This paper explores innovative substructured formulations for nonlinear structural problems using domain decomposition, aiming to reduce communication and enhance parallelism by solving independent nonlinear subproblems.

Contribution

It introduces a novel framework swapping Newton and domain decomposition steps, with various interface conditions, for nonlinear problems, which differs from traditional linear approaches.

Findings

Different interface conditions lead to non-equivalent formulations.

Primal, dual, and mixed variants are developed and tested.

Framework shows potential for improved parallelism in nonlinear problems.

Abstract

We investigate the use of non-overlapping domain decomposition (DD) methods for nonlinear structure problems. The classic techniques would combine a global Newton solver with a linear DD solver for the tangent systems. We propose a framework where we can swap Newton and DD, so that we solve independent nonlinear problems for each substructure and linear condensed interface problems. The objective is to decrease the number of communications between subdomains and to improve parallelism. Depending on the interface condition, we derive several formulations which are not equivalent, contrarily to the linear case. Primal, dual and mixed variants are described and assessed on a simple plasticity problem.