Density gradient‐based adaptive refinement of analysis mesh for efficient multiresolution topology optimization

Abstract

AbstractIn topology optimization, the finite‐element analysis of the problem is generally the most computationally demanding task of the solution process. In order to improve the efficiency of this phase, in this article we propose to represent regions with zero density gradient by a coarser analysis mesh. The design is instead represented in a uniform mesh. We motivate the density gradient‐based adaptive refinement by discussing the topological meaning of the density gradient and how it can help avoid loss of information during projections or interpolations between design and analysis meshes. We also study the adaptiveness of the mesh and its ability to detect the topology change of the design. An a posteriori error analysis is performed as well. Furthermore, we provide theoretical and numerical considerations on the reduction of the number of degrees of freedoms of the adaptive analysis mesh with respect to the uniform case. This translates into a faster solution of the analysis, as we show numerically. Finally, we solve several test problems, including large 3D problems that we solve in parallel on computer cluster, demonstrating the applicability of our procedure in large scale computing and with iterative solvers.