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arXiv · 2511.15269

jaxFMM: An Adaptive, GPU-Parallel Implementation of the Fast Multipole Method in JAX

Robert Kraft·Florian Bruckner·Dieter Suess·Claas Abert
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Abstract

We introduce jaxFMM, an open-source, adaptive, highly parallel point-charge Fast Multipole Method implementation for the Laplace kernel written in JAX. It is based on a non-uniform refinement strategy with on-the-fly rotation-based transforms tailored around JAX's just-in-time compiler, which results in extremely concise and simple code. Benchmarks show that the algorithm performs well at moderate accuracies, even for highly non-uniform charge distributions. JaxFMM already massively speeds up stray-field computations in micromagnetics and with JAX features like autodiff, novel applications such as inverse-design problems and machine-learning tasks can be tackled with ease in the future.

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Robert Kraft, Florian Bruckner, Dieter Suess, Claas Abert. 2025-11-19. jaxFMM: An Adaptive, GPU-Parallel Implementation of the Fast Multipole Method in JAX. https://doi.org/10.1016/j.jcp.2026.115130

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