Topology Optimization Using GPGPU

Abstract

In this paper we present a matrix-free geometric multigrid method for solving a linear system of equations needed at every iteration of the topology optimization process. The multigrid solver is parallelized on an Nvidia graphics card using CUDA, therefore reducing simulation time drastically. This enables users to derive optimal topologies represented with a high number of elements while having low execution time. Computational domain is discretized with a regular structured hexahedral mesh. To improve the accuracy of the non-conformal discretizazion, the Dirichlet boundary conditions are imposed in a weak form using Nitsche method.