Performance Analysis of Multi-GPU Implementations of Krylov-Subspace Methods Applied to FEA of Electromagnetic Phenomena

We present a comparison of performances of various graphic processing unit (GPU)-CUDA implementations of preconditioned Krylov-subspace methods, showing the impact of using a multi-GPU configuration. We aim to show that this resource allows the massively parallelized solution of large-scale real-world problems in state-of-the-art desktop PCs, since it overcomes the low-memory capacity of a single GPU, while still providing significant speedups when compared with either the usual sequential execution on a single-core CPU or an OpenMP implementation with four cores. The methods were selected based on their suitability to solve large-scale systems of equations arising from the 3-D finite-element analysis of open-bound earth current diffusion problems, both in steady state and under time-harmonic loading. In the latter, an ungauged harmonic edge-element formulation using the magnetic vector potential and the electric scalar potential was used. As the preconditioners suitable to this case, based on incomplete factorizations, are not appropriate for parallelization, we propose a hybrid CPU–GPU scheme to solve such problems, which still exhibits a competitive performance in low-cost PC desktops.