Adaptive Multidimensional Quadrature on Multi-GPU Systems

TL;DR

This paper presents a distributed adaptive quadrature method for multidimensional integration on multi-GPU systems, using hierarchical domain decomposition and dynamic load balancing to improve efficiency and robustness.

Contribution

It introduces a novel decentralized load redistribution scheme with CUDA-aware MPI for adaptive multidimensional integration on multi-GPU architectures.

Findings

Higher efficiency in high-dimensional integration

Enhanced robustness to integrand regularity and accuracy requirements

Effective load balancing through non-blocking communication

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.