Test Harness on a Preconditioned Conjugate Gradient Solver on GPUs: An Efficiency Analysis

Abstract

International audienceThe parallelization of numerical simulation algorithms, i.e., their adaptation to parallel processing architectures, is an aim to reach in order to hinder exorbitant execution times. The parallelism has been imposed at the level of processor architectures and graphics cards are now used for general-purpose calculation, also known as " General-Purpose computation on Graphics Processing Unit (GPGPU) ". The clear benefit is the excellent performance over price ratio. Besides hiding the low level programming, software engineering leads to a faster and more secure application development. This paper presents the real interest of using GPU processors to increase performance of larger problems which concern electrical machines simulation. Indeed, we show that our auto-generated code applied to several models allows achieving speedups of the order of 10

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

“…RELATED WORKS There are several works, which attempts to optimize the CG method among others for the solution of linear systems [6]- [12]. The first authors analyze the performance of the two GPUs for 2-D electrostatic coaxial cable problem and single precision.…”

“…Okimura et al [11] presented the VP methods with hybrid precision in a 2-D nonlinear FEA on GPU, with speedups ranging from 14 to 39. In [12], static and quasi-static 3-D problems with dual formulations are solved by a PCG method in GPU using OpenCL. It is not said which preconditioners were used.…”

“…It is not said which preconditioners were used. All of the aforementioned works, except [12], have only dealt with the solution of real-arithmetic systems of equations. Unfortunately, the only preconditioners that were able to factorize our complex-arithmetic systems issued from the time-harmonic ungaged A-V edge-FE formulation were both the SIC and the SILU, and neither of them is suitable for parallelization.…”

Computação paralela em GPU para resolução de sistemas de equações algébricas resultantes da aplicação do método de elementos finitos em eletromagnetismo.

“…Eles utilizaram GPU para aumentar o desempenho computacional daqueles problemas maiores de simulação de máquinas elétricas. Eles obtiveram um speedup na ordem de 10 comparado à CPU (RODRIGUES et al, 2013 …”