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Simulation of Maxwell's Equations on GPU Using a High-Order Error-Minimized Scheme

Part of: Computer aspects of numerical algorithms Equations of mathematical physics and other areas of application Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  08 March 2017

Tony W. H. Sheu ,
S. Z. Wang ,
J. H. Li  and
Matthew R. Smith
Tony W. H. Sheu*
Affiliation:
Department of Engineering Science and Ocean Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei, Taiwan Center for Advanced Study in Theoretical Sciences, National Taiwan University, Taipei, Taiwan Institute of Applied Mathematical Sciences, National Taiwan University, Taipei, Taiwan
S. Z. Wang*
Affiliation:
Department of Engineering Science and Ocean Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei, Taiwan
J. H. Li*
Affiliation:
Department of Engineering Science and Ocean Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei, Taiwan
Matthew R. Smith*
Affiliation:
Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan
*
*Corresponding author. Email addresses:twhsheu@ntu.edu.tw (T.W. H. Sheu), r01221024@ntu.edu.tw (S. Z. Wang), jiahan@ntu.edu.tw (J. H. Li), msmith@mail.ncku.edu.tw (M. R. Smith)
*Corresponding author. Email addresses:twhsheu@ntu.edu.tw (T.W. H. Sheu), r01221024@ntu.edu.tw (S. Z. Wang), jiahan@ntu.edu.tw (J. H. Li), msmith@mail.ncku.edu.tw (M. R. Smith)
*Corresponding author. Email addresses:twhsheu@ntu.edu.tw (T.W. H. Sheu), r01221024@ntu.edu.tw (S. Z. Wang), jiahan@ntu.edu.tw (J. H. Li), msmith@mail.ncku.edu.tw (M. R. Smith)
*Corresponding author. Email addresses:twhsheu@ntu.edu.tw (T.W. H. Sheu), r01221024@ntu.edu.tw (S. Z. Wang), jiahan@ntu.edu.tw (J. H. Li), msmith@mail.ncku.edu.tw (M. R. Smith)
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Abstract

In this study an explicit Finite Difference Method (FDM) based scheme is developed to solve the Maxwell's equations in time domain for a lossless medium. This manuscript focuses on two unique aspects – the three dimensional time-accurate discretization of the hyperbolic system of Maxwell equations in three-point non-staggered grid stencil and it's application to parallel computing through the use of Graphics Processing Units (GPU). The proposed temporal scheme is symplectic, thus permitting conservation of all Hamiltonians in the Maxwell equation. Moreover, to enable accurate predictions over large time frames, a phase velocity preserving scheme is developed for treatment of the spatial derivative terms. As a result, the chosen time increment and grid spacing can be optimally coupled. An additional theoretical investigation into this pairing is also shown. Finally, the application of the proposed scheme to parallel computing using one Nvidia K20 Tesla GPU card is demonstrated. For the benchmarks performed, the parallel speedup when compared to a single core of an Intel i7-4820K CPU is approximately 190x.

Keywords

Hamiltonian systemssymplecticityGPU3-D Maxwell's equationsdispersion relation equation

MSC classification

Secondary: 35Q61: Maxwell equations 65M06: Finite difference methods 65Y05: Parallel computation
Type
Research Article
Information
Communications in Computational Physics , Volume 21 , Issue 4 , April 2017 , pp. 1039 - 1064
Copyright
Copyright © Global-Science Press 2017 

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Footnotes

Communicated by Weng Cho Chew

References

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