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Solution of Maxwell's Equations Using the MQ Method

D.L. Young1,3, C.S. Chen2, T.K. Wong3
Corresponding author, Fax and Tel: +886-2-23626114, E-mail:dlyoung@ntu.edu.tw
Department of Mathematics, University of Southern Mississippi,Hattiesburg, MS 39406, USA
Department of Civil Engineering & Hydrotech Research Institute,National Taiwan University, Taipei, Taiwan

Computers, Materials & Continua 2005, 2(4), 267-276. https://doi.org/10.3970/cmc.2005.002.267

Abstract

A meshless time domain numerical method based on the radial basis functions using multiquadrics (MQ) is employed to simulate electromagnetic field problems by directly solving the time-varying Maxwell's equations without transforming to simplified versions of the wave or Helmholtz equations. In contrast to the conventional numerical schemes used in the computational electromagnetism such as FDTD, FETD or BEM, the MQ method is a truly meshless method such that no mesh generation is required. It is also easy to deal with the appropriate partial derivatives, divergences, curls, gradients, or integrals like semi-analytic solutions. For illustration purposes, the MQ method is employed to calculate the propagations of the electric and magnetic waves in the homogeneous, isotropic, and non-lossy 2D rectangular waveguide as well as 3D cavity resonator. Good agreements are obtained as compared to analytical solutions. By directly solving the Maxwell's equations, the MQ scheme provides a very simple and effective numerical scheme for the computational electromagnetism.

Keywords

Multiquadrics (MQ) method, Maxwell's equations, Meshless time-domain method, 2D waveguide, 3D cavity resonator.

Cite This Article

D. . Young, C. . Chen and T. . Wong, "Solution of maxwell's equations using the mq method," Computers, Materials & Continua, vol. 2, no.4, pp. 267–276, 2005.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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