Krüger, Jan ChristophJan ChristophKrügerKriegesmann, BenediktBenediktKriegesmann2025-09-082025-09-082025-08-01Structural and multidisciplinary optimization 68 (8): 158 (2025)https://hdl.handle.net/11420/57298Multigrid methods are known to show good performance for most topology optimization problems, but suffer from anisotropies. The main problems are caused by poor performance of the smoothing algorithms. This paper analyzes different standard and advanced smoothing algorithms using the local Fourier analysis with regard to orthotropic materials in the linear elasticity problem. The results are generalized to real problems and contrast-rich topology designs using numeric experiments. Based on the analyses, recommendations are given and a new spatial Jacobi smoothing algorithm is presented. The results are finally approved by a topology optimization example and a material orientation and topology optimization example.en1615-148820258Springerhttps://creativecommons.org/licenses/by/4.0/Large scaleMaterial orientation and topology optimizationMultigrid methodOrthotropic materialTopology optimizationTechnology::620: Engineering::620.1: Engineering Mechanics and Materials ScienceJournal Articlehttps://doi.org/10.15480/882.1583910.1007/s00158-025-04102-y10.15480/882.15839Journal Article