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arXiv · 2511.01573

Adaptive Multidimensional Quadrature on Multi-GPU Systems

Melanie Tonarelli·Simone Riva·Pietro Benedusi·Fabrizio Ferrandi·Rolf Krause
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Abstract

We introduce a distributed adaptive quadrature method that formulates multidimensional integration as a hierarchical domain decomposition problem on multi-GPU architectures. The integration domain is recursively partitioned into subdomains whose refinement is guided by local error estimators. Each subdomain evolves independently on a GPU, which exposes a significant load imbalance as the adaptive process progresses. To address this challenge, we introduce a decentralised load redistribution schemes based on a cyclic round-robin policy. This strategy dynamically rebalance subdomains across devices through non-blocking, CUDA-aware MPI communication that overlaps with computation. The proposed strategy has two main advantages compared to a state-of-the-art GPU-tailored package: higher efficiency in high dimensions; and improved robustness w.r.t the integrand regularity and the target accuracy.

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Melanie Tonarelli, Simone Riva, Pietro Benedusi, Fabrizio Ferrandi, Rolf Krause. 2025-11-03. Adaptive Multidimensional Quadrature on Multi-GPU Systems. https://arxiv.org/abs/2511.01573

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