De Zutter, Daniël

Dupré, Luc

Van de Wiele, Ben

Vansteenkiste, Arne

English

Ghent University Academic Bibliography

Fast Fourier transforms for the evaluation of convolution productsin electromagnetism: CPU versus GPU implementationBen Van de Wiele1, Arne Vansteenkiste2, Luc Dupre´1, and Danie¨l DeZutter31 Department of Electrical Energy, Systems and Automation, GhentUniversity, B-9000 Ghent, BelgiumE-mail: ben.vandewiele@ugent.be2 Department of Solid State Physics, Ghent University, B-9000 Ghent,Belgium3 Department of Information Technology, Ghent University, B-9000Ghent, BelgiumTo evaluate electromagnetic fields in space and time one often has to rely on nu-merical techniques to solve Maxwell’s equations. In various cases, the observationpoints in which the fields are to be evaluated are densely distributed and coincidewith the sources that generate the field. E.g. distributed charges that generate elec-trical fields, distributed currents and/or magnetic moments that generate magneticfields, etc. In such cases, a common approach is to write Maxwell’s equations ina volume integral formulation where the fields in all points r are expressed as aconvolution product of a Green’s function g over all sources sf(r) =∫Vg(r− r′)s(r′) dr′. (1)To solve this class of electromagnetic problems, the geometry is usually discretizedusing a uniform grid of finite difference cells. The evaluation of the convolutionintegral (1) in N finite difference cells requires then O(N2) evaluations. Theapplication of fast Fourier transforms (FFTs) reduces this computational burdento O(N log(N)) evaluations. In many computational schemes, convolution prod-uct(s) are to be evaluated a huge number of times pushing the need to further re-duce the computation time. Recently, Graphics Processing Units (GPUs) becamevery popular to speed up numerical computations. While originally designed forpurely graphical purposes, their huge parallel computation power can be exploitedto speed-up simulations up to two orders of magnitude.This paper describes how the application of FFT algorithms for the evaluation ofconvolution products can be yet optimized for finite 2D and 3D electromagneticproblems in which zero padding of the source matrices is required. Here, usinggeneral off-the-shelf 2D and 3D FFT algorithms results in many Fourier transformson arrays containing only zeros. A non-execution of these Fourier transforms givesrise to non-negligible reductions in computation times. This paper describes theimplementation of such an approach on GPU and compares the time gains on GPUwith those on CPU. It is found that on CPU the speed-up corresponds with thetheoretical limit, while in the GPU implementation the memory bandwidth limitsthe speed-up ratio.

Fast fourier transforms for the evaluation of convolution products in electromagnetism: CPU versus GPU implementation

https://biblio.ugent.be/publication/4250869/file/4250896

Fast fourier transforms for the evaluation of convolution products in electromagnetism: CPU versus GPU implementation

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Ghent University Academic Bibliography