Comparison of FETI-based domain decomposition methods for topology optimization problems

TL;DR

This paper evaluates various FETI-based domain decomposition methods for topology optimization, finding that the FETI Dual-Primal with multiple search directions and k-scaling is the most robust for heterogeneous structures.

Contribution

The study compares multiple variants of FETI methods, identifying the most effective approach for topology optimization with high heterogeneity.

Findings

Original methods are slow with high heterogeneity

Full orthogonalization helps only for mild heterogeneity

FETI Dual-Primal with multiple directions and k-scaling is most robust

Abstract

We critically assess the performance of several variants of dual and dual-primal domain decomposition strategies in problems with fixed subdomain partitioning and high heterogeneity in stiffness coefficients typically arising in topology optimization of modular structures. Our study considers Total FETI and FETI Dual-Primal methods along with three enhancements: k-scaling, full orthogonalization of the search directions, and considering multiple search-direction at once, which gives us twelve variants in total. We test these variants both on academic examples and snapshots of topology optimization iterations. Based on the results, we conclude that (i) the original methods exhibit very slow convergence in the presence of severe heterogeneity in stiffness coefficients, which makes them practically useless, (ii) the full orthogonalization enhancement helps only for mild heterogeneity, and (iii) the only robust method is FETI Dual-Primal with multiple search direction and k-scaling.