Adaptive Multidimensional Quadrature on Multi-GPU Systems
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.
Cite
@article{arxiv.2511.01573,
title = {Adaptive Multidimensional Quadrature on Multi-GPU Systems},
author = {Melanie Tonarelli and Simone Riva and Pietro Benedusi and Fabrizio Ferrandi and Rolf Krause},
journal= {arXiv preprint arXiv:2511.01573},
year = {2025}
}
Comments
9 pages, 8 figures. Submitted to the proceedings of the 29th International Conference on Domain Decomposition Methods (DD29)