Parallelization of improved variable-reduction method using GPU

• Published in: Journal of Advanced Simulation in Science and Engineering Vol. 12; no. 1; pp. 100 - 112
• Main Authors: Ikuno, Soichiro, Sato, Yuya, Kamitani, Atsushi
• Format: Journal Article
• Language: English
• Published: Japan Society for Simulation Technology 2025
• Subjects: Element-free Galerkin method; GPU parallelization; Improved variable-reduction method; Krylov subspace method; Saddle-point problem
• ISSN: 2188-5303; 2188-5303
• DOI: 10.15748/jasse.12.100

In this study, we compare the parallel performance of the Improved Variable-Reduction Method (iVRM) and a variable preconditioned Krylov subspace method (VP Krylov) on a single GPU.We treat Poisson equations discretized by the element-free Galerkin method as target problems. iVRM avoids QR decomposition and eliminates Lagrange multipliers, enabling efficient solving of saddle-point systems dominated by sparse matrix operations. Numerical experiments show that both methods converge quickly, with iVRM exhibiting higher CPU efficiency. However, GPU results suggest that larger-scale problems are needed to fully utilize GPU resources. These findings guide the parallel design of iVRM for large-scale saddle-point problems.