PAGANI: A Parallel Adaptive GPU Algorithm for Numerical

TL;DR

This paper introduces PAGANI, a GPU-based adaptive parallel algorithm for multi-dimensional numerical integration that significantly outperforms existing CPU methods by efficiently utilizing GPU resources and improving accuracy for complex integrands.

Contribution

The paper presents a novel GPU algorithm that processes all sub-regions in parallel, overcoming load imbalance and synchronization issues of previous methods.

Findings

Orders of magnitude speedup over CPU methods

Extended accuracy for difficult integrands

Outperforms existing deterministic parallel methods

Abstract

We present a new adaptive parallel algorithm for the challenging problem of multi-dimensional numerical integration on massively parallel architectures. Adaptive algorithms have demonstrated the best performance, but efficient many-core utilization is difficult to achieve because the adaptive work-load can vary greatly across the integration space and is impossible to predict a priori. Existing parallel algorithms utilize sequential computations on independent processors, which results in bottlenecks due to the need for data redistribution and processor synchronization. Our algorithm employs a high-throughput approach in which all existing sub-regions are processed and sub-divided in parallel. Repeated sub-region classification and filtering improves upon a brute-force approach and allows the algorithm to make efficient use of computation and memory resources. A CUDA implementation shows orders of magnitude speedup over the fastest open-source CPU method and extends the achievable accuracy for difficult integrands. Our algorithm typically outperforms other existing deterministic parallel methods.