Open AccessComparison of FETI-based domain decomposition methods for topology optimization problems
Author(s) -
Tomás Medrický,
Martin Doškář,
Ivana Pultarová,
Jan Zeman
Publication year - 2022
Publication title -
acta polytechnica ctu proceedings
Language(s) - English
Resource type - Journals
ISSN - 2336-5382
DOI - 10.14311/app.2022.34.0043
Subject(s) - feti , orthogonalization , domain decomposition methods , mathematical optimization , mathematics , topology (electrical circuits) , scaling , convergence (economics) , domain (mathematical analysis) , topology optimization , qr decomposition , computer science , algorithm , finite element method , eigenvalues and eigenvectors , mathematical analysis , combinatorics , geometry , physics , quantum mechanics , economics , thermodynamics , economic growth
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.