An Efficient GPU-Accelerated Algorithm for Solving Dynamic Response of Fluid-Saturated Porous Media

Wancang Lin, Qinglong Zhou (), Xinyi Chen, Wenhao Shi and Jie Ai
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Wancang Lin: School of Resources and Security Engineering, Central South University, Changsha 410083, China
Qinglong Zhou: School of Resources and Security Engineering, Central South University, Changsha 410083, China
Xinyi Chen: School of Resources and Security Engineering, Central South University, Changsha 410083, China
Wenhao Shi: School of Resources and Security Engineering, Central South University, Changsha 410083, China
Jie Ai: School of Resources and Security Engineering, Central South University, Changsha 410083, China

Mathematics, 2025, vol. 13, issue 2, 1-21

Abstract: The traditional finite element program is executed on the CPU; however, it is challenging for the CPU to compute the ultra-large scale finite element model. In this paper, we present a set of efficient algorithms based on GPU acceleration technology for the dynamic response of fluid-saturated porous media, named PNAM, encompassing the assembly of the global matrix and the iterative solution of equations. In the assembly part, the CSR storage format of the global matrix is directly obtained from the element matrix. For data with two million degrees of freedom, it merely takes approximately 1 s to generate all the data of global matrices, which is significantly superior to the CPU version. Regarding the iterative solution of equations, a novel algorithm based on the CUDA kernel function is proposed. For a data set with two million degrees of freedom, it takes only about 0.05 s to compute an iterative step and transfer the data to the CPU. The program is designed to calculate either in single or double precision. The change in precision has little impact on the assembly of the global matrix, but the calculation time of double precision is generally 1.5 to 2 times that of single precision in the iterative solution part for a model with 2 million degrees of freedom. PNAM has high computational efficiency and great compatibility, which can be used to solve not only saturated fluid problems but also a variety of other problems.

Keywords: CUDA; u-p dynamic formulation; finite elements; speedup; GPU-acceleration (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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