Journals
Resources
About Us
Open Access

A GPU-Accelerated Cartesian Grid Method for PDEs on Irregular Domain

A GPU-Accelerated Cartesian Grid Method for PDEs on Irregular Domain

Year:    2025

Author:    Liwei Tan, Minsheng Huang, Shuai Zhu, Pan Wang, Wenjun Ying

Communications in Computational Physics, Vol. 37 (2025), Iss. 5 : pp. 1250–1276

Abstract

The kernel-free boundary integral (KFBI) method has successfully solved partial differential equations (PDEs) on irregular domains. Diverging from traditional boundary integral methods, the computation of boundary integrals in KFBI is executed through the resolution of equivalent simple interface problems on Cartesian grids, utilizing fast algorithms. While existing implementations of KFBI methods predominantly utilize CPU platforms, GPU architecture’s superior computational capabilities and extensive memory bandwidth offer an efficient resolution to computational bottlenecks. This paper delineates the algorithms adapted for both single-GPU and multiple-GPU applications. On a single GPU, assigning individual threads can control correction, interpolation, and jump calculations. The algorithm is expanded to multiple GPUs to enhance the processing of larger-scale problems. The arrowhead decomposition method is employed in multiple-GPU settings, ensuring optimal computational efficiency and load balancing. Numerical examples show that the proposed algorithm is second-order accurate and efficient. Single-GPU solver runs 50-200 times faster than traditional CPU, and the parallel efficiency of a multiple-GPU distributed solver within the same NUMA node reaches up to 80%.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2024-0039

Communications in Computational Physics, Vol. 37 (2025), Iss. 5 : pp. 1250–1276

Published online:    2025-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    27

Keywords:    GPU-accelerated kernel-free boundary integral method GPU parallel computing arrowhead decomposition method irregular domains.

Author Details

Liwei Tan

Minsheng Huang

Shuai Zhu

Pan Wang

Wenjun Ying