Unstructured to structured: geometric multigrid on complex geometries via domain remapping

For domains that are easily represented by structured meshes, robust geometric multigrid solvers can quickly provide the numerical solution to many discretized elliptic PDEs. However, for complicated domains with unstructured meshes, constructing suitable hierarchies of meshes becomes challenging. We propose a framework for mapping computations from such complex domains to regular computational domains via diffeomorphisms, enabling the use of robust geometric-style multigrid. This mapping facilitates regular memory accesses during solves, improving efficiency and scalability, especially on massively parallel processors such as GPUs. Moreover, we show that the diffeomorphic mapping itself may be approximately learned using an invertible neural network, facilitating automated application to geometries where no analytic mapping is readily available.

• Publication year

  2025

• Venue

  arXiv.org

• Publication date

  2025-09-09

• Fields of study

  Mathematics, Computer Science, Engineering

• Identifiers
  DOI 10.48550/arXiv.2509.08109arXiv 2509.08109
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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