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We present a comprehensive comparison of the multigrid method and the UNet architecture for solving Poisson’s equation. Those two methods show a lot of similarity and also have the very interesting characteristic that their solving time should scale linearly with the number of mesh nodes. Nevertheless, for Poisson’s equation, an analysis of the number of floating-point operations demonstrates that the multigrid V-Cycle should be faster than the UNet. We have realized a practical comparison of the two methods solving time for different number of mesh nodes on the same computation nodes using GPU.

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Comparison of Multigrid and Machine Learning-Based Poisson Solvers

  • 会议论文

  • 发表日期：

    2025年

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  • Hadrien Godé,
  • Carola Kruse,
  • Richard Angersbach,
  • Harald Köstler,
  • Michaël Bauerheim,
  • Ulrich Rüde

摘要

We present a comprehensive comparison of the multigrid method and the UNet architecture for solving Poisson’s equation. Those two methods show a lot of similarity and also have the very interesting characteristic that their solving time should scale linearly with the number of mesh nodes. Nevertheless, for Poisson’s equation, an analysis of the number of floating-point operations demonstrates that the multigrid V-Cycle should be faster than the UNet. We have realized a practical comparison of the two methods solving time for different number of mesh nodes on the same computation nodes using GPU.