Parallel 3D topology optimization with multiple constraints and objectives

This paper introduces a parallel Topology Optimization (TO) platform capable of optimizing designs for multiple objectives, whilst subject to multiple constraints, in the open source Fierro Finite Element code. The TO methodology uses a continuous material interpolation scheme, which avoids checkerboard designs without additional filters and constraints as seen with piece-wise constant material interpolation schemes. Additionally, analytic Hessian-vector products are used, with the relevant adjoint calculation shown. The code utilizes OpenMPI to make parallel the major computational segments of TO: global equation assembly, global equation solution, and the non-linear optimization of the design. The algorithm leverages several software packages: ELEMENTS (grants FE basis functions), MATAR (grants efficient multidimensional dense and sparse matrix storage), Zoltan2 (Mesh Decomposition Algorithm), MueLu (parallel multi-grid solver for the global equilibrium equations), and ROL (non-linear optimization). It is found that the Fierro TO platform optimizes problems with mechanical and thermal objectives subject to multiple constraints: mass, several moment of inertia targets, and constraints related to load bearing regions. Additionally, the performance of several ROL algorithms using analytic Hessian-vector products is compared with the Method of Moving Asymptotes, approximate Hessian, for topology optimization.