Analysis of FDTD to UPML for Maxwell equations in polar coordinates |
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| Authors: | Fang Nengsheng Ying Longan |
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| Affiliation: | aSchool of Finance, Southwestern University of Finance and Economics, Chengdu 611130, China;bSchool of Mathematical Sciences, Xiamen University, Xiamen 361005, China;cSchool of Mathematics Sciences, Peking University, Beijing 100871, China |
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| Abstract: | An FDTD system associated with uniaxial perfectly matched layer (UPML) for an electromagnetic scattering problem in two-dimensional space in polar coordinates is considered. Particularly the FDTD system of an initial-boundary value problems of the transverse magnetic (TM) mode to Maxwell's equations is obtained by Yee's algorithm, and the open domain of the scattering problem is truncated by a circle with a UPML. Besides, an artificial boundary condition is imposed on the outer boundary of the UPML. Afterwards, stability of the FDTD system on the truncated domain is established through energy estimates by the Gronwall inequality. Numerical experiments are designed to approve the theoretical analysis. |
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| Keywords: | Maxwell's equations uniaxial perfectly matched layer initial boundary value problem stability finite difference time domain polar coordinates |
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