Title: Using GPUs to improve multigrid solver performance on a cluster

Authors: Dominik Goddeke, Robert Strzodka, Jamaludin Mohd-Yusof, Patrick McCormick, Hilmar Wobker, Christian Becker, Stefan Turek

Addresses: Institut fur Angewandte Mathematik, TU Dortmund, Germany. ' Max Planck Center, Max Planck Institut Informatik, Saarbrucken, Germany. ' Computer, Computational and Statistical Sciences Division, Los Alamos National Laboratory, USA. ' Computer, Computational and Statistical Sciences Division, Los Alamos National Laboratory, USA. ' Institut fur Angewandte Mathematik, TU Dortmund, Germany. ' Institut fur Angewandte Mathematik, TU Dortmund, Germany. ' Institut fur Angewandte Mathematik, TU Dortmund, Germany

Abstract: This paper explores the coupling of coarse and fine-grained parallelism for Finite Element (FE) simulations based on efficient parallel multigrid solvers. The focus lies on both system performance and a minimally invasive integration of hardware acceleration into an existing software package, requiring no changes to application code. Because of their excellent price performance ratio, we demonstrate the viability of our approach by using commodity Graphics Processing Units (GPUs), addressing the issue of limited precision on GPUs by applying a mixed precision, iterative refinement technique. Our results show that we do not compromise any software functionality and gain speedups of two and more for large problems.

Keywords: parallel scientific computing; finite element method; FEM; GPUs; graphics processing units; floating-point co-processors; mixed precision; parallel multigrid solvers; domain decomposition; simulation.

DOI: 10.1504/IJCSE.2008.021111

International Journal of Computational Science and Engineering, 2008 Vol.4 No.1, pp.36 - 55

Available online: 04 Nov 2008 *

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