Efficient distributed approach for density-based topology optimization using coarsening and h-refinement

Abstract

This work presents an efficient parallel implementation of density-based topology optimization using Adaptive Mesh Refinement (AMR) schemes to reduce the computational burden of the bottleneck of the process, the evaluation of the objective function using Finite Element Analysis (FEA). The objective is to obtain an equivalent design to the one generated on a uniformly fine mesh using distributed memory computing but at a much cheaper computational cost. We propose using a fine mesh for the optimization and a coarse mesh for the analysis using coarsening and refinement criteria based on the thresholding of design variables. We evaluate the functional on the coarse mesh using a distributed conjugate gradient solver preconditioned by an algebraic multigrid (AMG) method showing its computational advantages in some cases by comparing with geometric multigrid (GMG) and AMG methods in two- and three-dimensional problems. We use different computational resources with small regularization distances for such comparisons. We also evaluate the performance and scalability of the proposal using a different number of computing cores and distributed computing hosts. The numerical results show a significant increment of the computing performance for the overall computing time of the proposal combining dynamic coarsening, adaptive mesh refinement, and distributed memory computing architectures.