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<p>Multigrid 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.</p>

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On the application of the multigrid method to topology optimization with orthotropic material with varying orientation

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年8月21日

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  • Jan Christoph Krüger,
  • Benedikt Kriegesmann

摘要

Multigrid 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.