Parallel Solution of the Linear Elasticity problem with Applications in Topology Optimization

TL;DR

This paper presents a parallel domain decomposition method for solving linear elasticity problems efficiently, with a focus on applications in topology optimization where repeated solutions are needed.

Contribution

It introduces a non-overlapping domain decomposition approach for parallel solving of linear elasticity, specifically tailored for iterative topology optimization processes.

Findings

Efficient parallel solution of elasticity equations achieved.

Application to topology optimization demonstrated.

Potential for reducing computational time in iterative design processes.

Abstract

In this paper, we aim to solve the system of equations governing linear elasticity in parallel using domain decomposition. Through a non-overlapping decomposition of the domain, our approach aims to target the resulting interface problem, allowing for the parallel computation of solutions in an efficient manner. As a major application of our work, we apply our results to the field of topology optimization, where typical solvers require repeated solutions of linear elasticity problems resulting from the use of a Picard approach.