A Parallel Multi-Constraint Topology Optimization Solver

Abstract This paper presents an open source parallel Topology Optimization (TO) code capable of optimizing mechanical designs subject to multiple inertial constraints. The code utilizes Open-MPI and Kokkos to enable fine-grained parallelism in every major computational segment of a TO code: global equation assembly, global equation solution, and the non-linear optimization of the design. Most of the the Finite Element (FE) infrastructure for the TO code is implemented on the Fierro open source code base; which also leverages the ELEMENTS (grants FE basis functions) and MATAR (grants efficient multidimensional sparse matrix storage) libraries. Essential Numerical Algorithms such as a parallel multi-grid solver for the global equilibrium equations and non-linear optimization come from the MueLu and ROL packages (both found in the Trilinos library) respectively. It is found that the Fierro TO algorithm is capable of providing minimum compliance solutions in multi-constraint problems involving mass, several moment of inertia targets, and constraints related to load bearing regions; where the relative error in the satisfaction of all constraints seen in this work does not exceed 3%. Additionally, this work demonstrates the use of a piece-wise continuous interpolation of material density; which avoids the implementation of filters to avoid well-known mesh dependent issues such as checker-boarding.