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Volume 12, Issue 2
Spectral Approximation of Time-Harmonic Maxwell Equations in Three-Dimensional Exterior Domains

Lina Ma, Jie Shen & Li-Lian Wang

Int. J. Numer. Anal. Mod., 12 (2015), pp. 366-383.

Published online: 2015-12

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  • Abstract

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.

  • Keywords

Maxwell equations, exterior problems, transparent boundary conditions, vector spherical harmonics, Legendre spectral method.

  • AMS Subject Headings

65N35, 65N22, 65F05, 35J05

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{IJNAM-12-366, author = {Lina Ma, Jie Shen and Li-Lian Wang}, title = {Spectral Approximation of Time-Harmonic Maxwell Equations in Three-Dimensional Exterior Domains}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2015}, volume = {12}, number = {2}, pages = {366--383}, abstract = {

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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/494.html} }
TY - JOUR T1 - Spectral Approximation of Time-Harmonic Maxwell Equations in Three-Dimensional Exterior Domains AU - Lina Ma, Jie Shen & Li-Lian Wang JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 366 EP - 383 PY - 2015 DA - 2015/12 SN - 12 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/494.html KW - Maxwell equations, exterior problems, transparent boundary conditions, vector spherical harmonics, Legendre spectral method. AB -

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.

Lina Ma, Jie Shen and Li-Lian Wang. (2015). Spectral Approximation of Time-Harmonic Maxwell Equations in Three-Dimensional Exterior Domains. International Journal of Numerical Analysis and Modeling. 12 (2). 366-383. doi:
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