Simulation of Maxwell's Equations on GPU Using a High-Order Error-Minimized Scheme (Communications in Computational Physics, 2018)
In this study an explicit Finite Difference Method (FDM) based scheme is developedto solve the Maxwell's equations in time domain for a lossless medium. Thismanuscript focuses on two unique aspects – the three dimensional time-accurate discretizationof the hyperbolic system of Maxwell equations in three-point non-staggeredgrid stencil and it's application to parallel computing through the use of Graphics ProcessingUnits (GPU). The proposed temporal scheme is symplectic, thus permittingconservation of all Hamiltonians in the Maxwell equation. Moreover, to enable accuratepredictions over large time frames, a phase velocity preserving scheme is developedfor treatment of the spatial derivative terms. As a result, the chosen timeincrement and grid spacing can be optimally coupled. An additional theoretical investigationinto this pairing is also shown. Finally, the application of the proposed schemeto parallel computing using one Nvidia K20 Tesla GPU card is demonstrated. For thebenchmarks performed, the parallel speedup when compared to a single core of anIntel i7-4820K CPU is approximately 190x.