GPU computing with Kaczmarz's and other iterative algorithms for linear systems

The graphics processing unit (GPU) is used to solve large linear systems derived from partial differential equations. The differential equations studied are strongly convection-dominated, of various sizes, and common to many fields, including computational fluid dynamics, heat transfer, and structural mechanics. The paper presents comparisons between GPU and CPU implementations of several well-known iterative methods, including Kaczmarz’s, Cimmino’s, component averaging, conjugate gradient normal residual (CGNR), symmetric successive overrelaxation-preconditioned conjugate gradient, and conjugate-gradientaccelerated component-averaged row projections (CARP-CG). Computations are preformed with dense as well as general banded systems. The results demonstrate that our GPU implementation outperforms CPU implementations of these algorithms, as well as previously studied parallel implementations on Linux clusters and shared memory systems. While the CGNR method had begun to fall out...

• Type: Journal
• Year: 2010
• Where: PC
• Authors: Joseph M. Elble, Nikolaos V. Sahinidis, Panagiotis D. Vouzis
• Keywords: CPU Implementations, Differential Equations, Iterative Methods, Management, PC 2010