Topology optimization with adaptive mesh refinement

We outline a robust method for topology optimization with adaptive mesh refinement and derefinement (AMR). Since the total volume fraction in topology optimization is usually modest, after a few initial iterations the domain of computation is largely void. It is inefficient to have many small elements in such regions, as these contribute significantly to the overall computational cost but little to the accuracy of computation and design. At the same time, we want high spatial resolution for accurate three-dimensional designs to avoid significant postprocessing or interpretation. AMR offers the possibility to balance these two requirements, but it has received little attention in the context of topology optimization. We will discus approaches by Costas and Alves [2] and Stainko [3]. Unfortunately, both approaches may lead to suboptimal designs that are mesh dependent. We extend these approaches to obtain a method that yields optimal designs, and we show experimentally that our improvements lead to designs that are equivalent to designs computed on uniform meshes at the finest level of refinement. Furthermore, we demonstrate significant reductions of run time by using AMR and efficient methods for the solution of the resulting large, linear systems, following Wang et al. [4].