Spectral approximation of time-harmonic Maxwell equations in three-dimensional exterior domains

Spectral approximation of time-harmonic Maxwell equations in three-dimensional exterior domains

We develop in this paper an efficient and robust spectral-Galerkin method for solving the three-dimensional time-harmonic Maxwell equations in exterior domains. We first reduce the problem to a bounded domain by using the capacity operator which characterizes the transparent boundary condition (TBC)...

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Bibliographic Details
Main Authors: Shen, Jie, Wang, Li-Lian, Ma, Lina
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2019
Subjects:
Maxwell Equations
Exterior Problems
DRNTU::Science::Mathematics
Online Access:https://hdl.handle.net/10356/85427
http://hdl.handle.net/10220/48223
http://www.global-sci.org.ezlibproxy1.ntu.edu.sg/intro/article_detail/ijnam/494.html
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Institution: Nanyang Technological University
Language: English
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Summary:We develop in this paper an efficient and robust spectral-Galerkin method for solving the three-dimensional time-harmonic Maxwell equations in exterior domains. We first reduce the problem to a bounded domain by using the capacity operator which characterizes the transparent boundary condition (TBC). Then, we adopt the transformed field expansion (TFE) approach to reduce the problem to a sequence of Maxwell equations in a spherical shell. Finally, we develop an efficient spectral algorithm by using Legendre approximation in the radial direction and vector spherical harmonic expansion in the tangential directions.

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