GPU-Acceleration of Parallel Unconditionally Stable Group Explicit Finite Difference Method

TL;DR

This paper demonstrates that using GPU acceleration significantly improves the efficiency of solving transient diffusion equations with a stable finite difference method, outperforming multi-core CPU implementations even on older GPU hardware.

Contribution

It introduces an optimized GPU implementation of the group explicit finite difference method and compares its performance with CPU-based solutions, encouraging wider adoption of GPU computing in this field.

Findings

GPU implementation is faster than multi-core CPU for the same problem.

Older GPU hardware (GT 335M) still provides significant speedup.

Proposed synchronization and initialization strategies improve performance.

Abstract

Graphics Processing Units (GPUs) are high performance co-processors originally intended to improve the use and quality of computer graphics applications. Once, researchers and practitioners noticed the potential of using GPU for general purposes, GPUs applications have been extended from graphics applications to other fields. The main objective of this paper is to evaluate the impact of using GPU in solution of the transient diffusion type equation by parallel and stable group explicit finite difference method and encourage the researchers in this field to immigrate from implementing their algorithms in CPU to the GPU emerging world. For comparing them, we implemented the method in both GPU and CPU (multi-core) programming context. Moreover, we proposed an optimal synchronization arrangement for the implementation pseudo-code. Also, the interrelation of GPU parallel programming and initializing the algorithm variables were discussed, taking advantage of numerical experiences. The GPU-approach results are faster than those obtained from a much expensive parallel 8-thread CPU-based programming. The GPU used in this paper, is an ordinary old laptop GPU (GT 335M, launched at 2010) and is accessible for everyone and the newer generations of GPU (as discussed in paper) have even more performance priority over the similar-price GPUs. Then, the results are expected to encourage the entire research society to take advantage of GPUs and improve the time efficiency of their studies.