Topology optimization with Node Density Adaptation and Geometric Multigrid solving

This study proposes an adaptive nodal density Solid Isotropic Material with Penalization (SIMP) method for topology optimization to improve computational efficiency by addressing the high computational cost of fixed meshes. By decoupling the density mesh from the analysis mesh, our method eliminates the need for generating complex unstructured analysis meshes and effectively mitigates discontinuities in the density field. Providing a practical framework for large-scale structural optimization, the proposed approach achieves a reduction of over 50% in computational complexity and more than a 36% reduction in computational scale of that required by a uniformly refined mesh. Optimization results for truss and cantilever beam structures demonstrate that this method enhances computational accuracy with fewer fine-scale features, yielding clearer structures with less computational effort. These results highlight the method's robustness and practical manufacturability.