A GPU-Accelerated Cartesian Grid Method for PDEs on Irregular Domain (Communications in Computational Physics, 2025)
The kernel-free boundary integral (KFBI) method has successfully solvedpartial differential equations (PDEs) on irregular domains. Diverging from traditionalboundary integral methods, the computation of boundary integrals in KFBI is executedthrough 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 computationalbottlenecks. This paper delineates the algorithms adapted for both single-GPU andmultiple-GPU applications. On a single GPU, assigning individual threads can control correction, interpolation, and jump calculations. The algorithm is expanded tomultiple GPUs to enhance the processing of larger-scale problems. The arrowheaddecomposition method is employed in multiple-GPU settings, ensuring optimal computational efficiency and load balancing. Numerical examples show that the proposedalgorithm is second-order accurate and efficient. Single-GPU solver runs 50-200 timesfaster than traditional CPU, and the parallel efficiency of a multiple-GPU distributedsolver within the same NUMA node reaches up to 80%.
Keywords: GPU-accelerated kernel-free boundary integral method; GPU parallel computing; arrowhead decomposition method; irregular domains.