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Volume 23, Issue 3
An Efficient Monte Carlo-Transformed Field Expansion Method for Electromagnetic Wave Scattering by Random Rough Surfaces

Xiaobing Feng, Junshan Lin & David P. Nicholls

DOI: 10.4208/cicp.OA-2017-0041

Commun. Comput. Phys., 23 (2018), pp. 685-705.

Published online: 2018-03

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  • Abstract

This paper develops an efficient and accurate numerical method for the computation of electromagnetic waves scattered by random rough surfaces. The method is based upon a combination of the Transformed Field Expansion method, which represents the solution as a provably convergent power series, and the Monte Carlo technique for sampling the probability space. The compelling aspect of the proposed method is that, at each perturbation order and every sample, the governing Transformed Field Expansion equations share the same deterministic Helmholtz operator on a deterministic domain. Thus, an LU factorization of the matrix discretization of this single operator can be employed repeatedly for all orders and every sample. Consequently, the computational complexity of the whole algorithm is significantly reduced as a result. Numerical examples are described which demonstrate the accuracy of the algorithm.

  • Keywords

Computational electromagnetic methods, random rough surface, Monte Carol method, spectral method.

  • AMS Subject Headings

35J05, 35Q60, 65C05, 65C30, 78M22

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-23-685, author = {Xiaobing Feng, Junshan Lin and David P. Nicholls}, title = {An Efficient Monte Carlo-Transformed Field Expansion Method for Electromagnetic Wave Scattering by Random Rough Surfaces}, journal = {Communications in Computational Physics}, year = {2018}, volume = {23}, number = {3}, pages = {685--705}, abstract = {

This paper develops an efficient and accurate numerical method for the computation of electromagnetic waves scattered by random rough surfaces. The method is based upon a combination of the Transformed Field Expansion method, which represents the solution as a provably convergent power series, and the Monte Carlo technique for sampling the probability space. The compelling aspect of the proposed method is that, at each perturbation order and every sample, the governing Transformed Field Expansion equations share the same deterministic Helmholtz operator on a deterministic domain. Thus, an LU factorization of the matrix discretization of this single operator can be employed repeatedly for all orders and every sample. Consequently, the computational complexity of the whole algorithm is significantly reduced as a result. Numerical examples are described which demonstrate the accuracy of the algorithm.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2017-0041}, url = {http://global-sci.org/intro/article_detail/cicp/10544.html} }
TY - JOUR T1 - An Efficient Monte Carlo-Transformed Field Expansion Method for Electromagnetic Wave Scattering by Random Rough Surfaces AU - Xiaobing Feng, Junshan Lin & David P. Nicholls JO - Communications in Computational Physics VL - 3 SP - 685 EP - 705 PY - 2018 DA - 2018/03 SN - 23 DO - http://doi.org/10.4208/cicp.OA-2017-0041 UR - https://global-sci.org/intro/article_detail/cicp/10544.html KW - Computational electromagnetic methods, random rough surface, Monte Carol method, spectral method. AB -

This paper develops an efficient and accurate numerical method for the computation of electromagnetic waves scattered by random rough surfaces. The method is based upon a combination of the Transformed Field Expansion method, which represents the solution as a provably convergent power series, and the Monte Carlo technique for sampling the probability space. The compelling aspect of the proposed method is that, at each perturbation order and every sample, the governing Transformed Field Expansion equations share the same deterministic Helmholtz operator on a deterministic domain. Thus, an LU factorization of the matrix discretization of this single operator can be employed repeatedly for all orders and every sample. Consequently, the computational complexity of the whole algorithm is significantly reduced as a result. Numerical examples are described which demonstrate the accuracy of the algorithm.

Xiaobing Feng, Junshan Lin and David P. Nicholls. (2018). An Efficient Monte Carlo-Transformed Field Expansion Method for Electromagnetic Wave Scattering by Random Rough Surfaces. Communications in Computational Physics. 23 (3). 685-705. doi:10.4208/cicp.OA-2017-0041
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