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Development of an Explicit Symplectic Scheme that Optimizes the Dispersion-Relation Equation of the Maxwell's Equations

Development of an Explicit Symplectic Scheme that Optimizes the Dispersion-Relation Equation of the Maxwell's Equations
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Year:    2013

Communications in Computational Physics, Vol. 13 (2013), Iss. 4 : pp. 1107–1133

Abstract

In this paper an explicit finite-difference time-domain scheme for solving the Maxwell's equations in non-staggered grids is presented. The proposed scheme for solving the Faraday's and Ampère's equations in a theoretical manner is aimed to preserve discrete zero-divergence for the electric and magnetic fields. The inherent local conservation laws in Maxwell's equations are also preserved discretely all the time using the explicit second-order accurate symplectic partitioned Runge-Kutta scheme. The remaining spatial derivative terms in the semi-discretized Faraday's and Ampère's equations are then discretized to provide an accurate mathematical dispersion relation equation that governs the numerical angular frequency and the wavenumbers in two space dimensions. To achieve the goal of getting the best dispersive characteristics, we propose a fourth-order accurate space centered scheme which minimizes the difference between the exact and numerical dispersion relation equations. Through the computational exercises, the proposed dual-preserving solver is computationally demonstrated to be efficient for use to predict the long-term accurate Maxwell's solutions.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.280711.230312a

Communications in Computational Physics, Vol. 13 (2013), Iss. 4 : pp. 1107–1133

Published online:    2013-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    27

Keywords:   

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