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

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COPYRIGHT: © Global Science Press

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@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 KW - exterior problems KW - transparent boundary conditions KW - vector spherical harmonics KW - 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 & Li-Lian Wang. (1970). 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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