Accelerating Large-scale Topology Optimization: State-of-the-Art and Challenges

• Published in: Archives of computational methods in engineering 2021-12, Vol.28 (7), p.4549-4571
• Main Authors: Mukherjee, Sougata, Lu, Dongcheng, Raghavan, Balaji, Breitkopf, Piotr, Dutta, Subhrajit, Xiao, Manyu, Zhang, Weihong
• Format: Article
• Language: English
• Subjects: Design engineering; Engineering; Engineering Sciences; Industrial design; Iterative methods; Machine learning; Mathematical and Computational Engineering; Model reduction; Optimization; Original Paper; Software; Three dimensional models; Topology optimization
• ISSN: 1134-3060; 1886-1784
• DOI: 10.1007/s11831-021-09544-3

Large-scale structural topology optimization has always suffered from prohibitively high computational costs that have till date hindered its widespread use in industrial design. The first and major contributor to this problem is the cost of solving the Finite Element equations during each iteration of the optimization loop. This is compounded by the frequently very fine 3D models needed to accurately simulate mechanical or multi-physical performance. The second issue stems from the requirement to embed the high-fidelity simulation within the iterative design procedure in order to obtain the optimal design. The prohibitive number of calculations needed as a result of both these issues, is often beyond the capacities of existing industrial computers and software. To alleviate these issues, the last decade has opened promising pathways into accelerating the topology optimization procedure for large-scale industrial sized problems, using a variety of techniques, including re-analysis, multi-grid solvers, model reduction, machine learning and high-performance computing, and their combinations. This paper attempts to give a comprehensive review of the research activities in all of these areas, so as to give the engineer both an understanding as well as a critical appreciation for each of these developments.