GPU Accelerated Krylov Subspace Methods for Computational Electromagnetics

Abstract

Programmable graphics processor units (GPU), such as the NVIDIA <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sup> Geforce 8800 series, offer a raw computing power that is often an order of magnitude larger than even the most modern multicore CPUs, making them a relatively inexpensive platform for high performance computing. In this paper, we report the development of two Krylov subspace solvers, the generalized minimal residual (GMRES) and the quasi-minimal residual (QMR) algorithms, on the GPU using the NVIDIA CUDA <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sup> programming model. The algorithms have been implemented as a stand-alone library. We report a speed-up of up to 13 times, on a single GPU, in our preliminary experiments with the classic problem of computing the capacitance of conductors using an integral equation method.