Meshless Local Petrov-Galerkin Method for Scattering from 2-D Rectangular Cavities in a Ground Plane

Meiling Zhao; Li Li

doi:doi:10.11648/j.acm.20150403.17

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Meshless Local Petrov-Galerkin Method for Scattering from 2-D Rectangular Cavities in a Ground Plane

Meiling Zhao, Li Li

Published in Applied and Computational Mathematics (Volume 4, Issue 3)

Received: 2 April 2015 Accepted: 29 April 2015 Published: 23 May 2015

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Abstract

In this paper, we develop the meshless local Petrov-Galerkin formulation of the scattering from rectangular cavities embedded in a ground plane. The electromagnetic scattering by the cavity is governed by the Helmholtz equation along with Sommerfeld's radiation conditions imposed at infinity. The MLPG method is a truly meshless method wherein no elements or background cells are needed, in either the interpolation or integration. Based on local weak form and the moving least square (MLS) approximation, this truly meshless method is applied to solve the scattering problem. The results of numerical experiments have shown the efficiency and accuracy of the proposed method.

Published in	Applied and Computational Mathematics (Volume 4, Issue 3)
DOI	10.11648/j.acm.20150403.17
Page(s)	145-151
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Meshless Local Petrov-Galerkin Method, Electromagnetic Scattering, 2-D Rectangular Cavities, Moving Least Square Approximation

References

[1]	H. T. Anastassiu, “A review of electromagnetic scattering analysis for intes, cavities, and open ducts,” IEEE Antennas Propag. Mag., Vol. 45, pp. 27-40, 2003
[2]	H. Ammari, G. Bao and A. W. Wood, “Analysis of the electromagnetic scattering from a cavity,” Japan J. Indust. Appl. Math., Vol. 19, pp. 301-310, 2002
[3]	J. Liu and J. M. Jin, “A special high-order finite element method for scattering by deep cavity,” IEEE Tran. Antennas Propag., Vol. 48, pp. 694-703, 2000
[4]	Z. Xiang and T. Chia, “A hybrid BEM-WTM approach for analysis of the EM scattering from large open-ended cavities,” IEEE Trans. Antennas Propag. , Vol. 49, pp. 165-173, 2001
[5]	S. N. Atluri and T. Zhu, “A new meshless local Perov-Galerkin approach in computational mechanics,” Comput. Mech., Vol. 22, pp. 117-127, 1998
[6]	S. N. Atluri and S. Shen, “The meshless local Petrov-Galerkin (MLPG) method: A simple & less-costly alternative to the finite element and boundary element methods,” CMES: Computer Modelling in Engineering, Vol. 3, pp. 11-52, 2002
[7]	S. Fernandez-Mendez and A. Huerta, “Imposing essential boundary conditions in mesh-free methods,” Computer Methods in Applied Mechanics and Engineering, Vol. 193, pp. 1257-1275, 2004
[8]	M. Zhao and Y. Nie, “A study of boundary conditions in the meshless local Petrov-Galerkin (MLPG) method for electromagnetic field computations,” CMES: Computer Modelling in Engineering & Sciences, Vol. 37, pp. 97-112, 2008
[9]	J. Wu, Y. Wang, W. Li and W. Sun, “Toeplitz-type aooroximations to the Hadamard integral operators and their applications in electromagnetic cavity problems,” Appl. Numer. Math., Vol.58, pp. 101-121, 2008
[10]	J. Jin, “The Finite Element Method in Electromagnetics,” John Willey Sons, New York, 1993

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APA Style

Meiling Zhao, Li Li. (2015). Meshless Local Petrov-Galerkin Method for Scattering from 2-D Rectangular Cavities in a Ground Plane. Applied and Computational Mathematics, 4(3), 145-151. https://doi.org/10.11648/j.acm.20150403.17

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ACS Style

Meiling Zhao; Li Li. Meshless Local Petrov-Galerkin Method for Scattering from 2-D Rectangular Cavities in a Ground Plane. Appl. Comput. Math. 2015, 4(3), 145-151. doi: 10.11648/j.acm.20150403.17

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AMA Style

Meiling Zhao, Li Li. Meshless Local Petrov-Galerkin Method for Scattering from 2-D Rectangular Cavities in a Ground Plane. Appl Comput Math. 2015;4(3):145-151. doi: 10.11648/j.acm.20150403.17

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@article{10.11648/j.acm.20150403.17,
  author = {Meiling Zhao and Li Li},
  title = {Meshless Local Petrov-Galerkin Method for Scattering from 2-D Rectangular Cavities in a Ground Plane},
  journal = {Applied and Computational Mathematics},
  volume = {4},
  number = {3},
  pages = {145-151},
  doi = {10.11648/j.acm.20150403.17},
  url = {https://doi.org/10.11648/j.acm.20150403.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20150403.17},
  abstract = {In this paper, we develop the meshless local Petrov-Galerkin formulation of the scattering from rectangular cavities embedded in a ground plane. The electromagnetic scattering by the cavity is governed by the Helmholtz equation along with Sommerfeld's radiation conditions imposed at infinity. The MLPG method is a truly meshless method wherein no elements or background cells are needed, in either the interpolation or integration. Based on local weak form and the moving least square (MLS) approximation, this truly meshless method is applied to solve the scattering problem. The results of numerical experiments have shown the efficiency and accuracy of the proposed method.},
 year = {2015}
}

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TY  - JOUR
T1  - Meshless Local Petrov-Galerkin Method for Scattering from 2-D Rectangular Cavities in a Ground Plane
AU  - Meiling Zhao
AU  - Li Li
Y1  - 2015/05/23
PY  - 2015
N1  - https://doi.org/10.11648/j.acm.20150403.17
DO  - 10.11648/j.acm.20150403.17
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 145
EP  - 151
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20150403.17
AB  - In this paper, we develop the meshless local Petrov-Galerkin formulation of the scattering from rectangular cavities embedded in a ground plane. The electromagnetic scattering by the cavity is governed by the Helmholtz equation along with Sommerfeld's radiation conditions imposed at infinity. The MLPG method is a truly meshless method wherein no elements or background cells are needed, in either the interpolation or integration. Based on local weak form and the moving least square (MLS) approximation, this truly meshless method is applied to solve the scattering problem. The results of numerical experiments have shown the efficiency and accuracy of the proposed method.
VL  - 4
IS  - 3
ER  -

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Author Information

Meiling Zhao

School of Mathematics and Physics, North China Electric Power University, Baoding, China
Li Li

School of Control and Computer Engineering, North China Electric Power University, Baoding, China

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APA Style

Meiling Zhao, Li Li. (2015). Meshless Local Petrov-Galerkin Method for Scattering from 2-D Rectangular Cavities in a Ground Plane. Applied and Computational Mathematics, 4(3), 145-151. https://doi.org/10.11648/j.acm.20150403.17

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ACS Style

Meiling Zhao; Li Li. Meshless Local Petrov-Galerkin Method for Scattering from 2-D Rectangular Cavities in a Ground Plane. Appl. Comput. Math. 2015, 4(3), 145-151. doi: 10.11648/j.acm.20150403.17

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AMA Style

Meiling Zhao, Li Li. Meshless Local Petrov-Galerkin Method for Scattering from 2-D Rectangular Cavities in a Ground Plane. Appl Comput Math. 2015;4(3):145-151. doi: 10.11648/j.acm.20150403.17

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@article{10.11648/j.acm.20150403.17,
  author = {Meiling Zhao and Li Li},
  title = {Meshless Local Petrov-Galerkin Method for Scattering from 2-D Rectangular Cavities in a Ground Plane},
  journal = {Applied and Computational Mathematics},
  volume = {4},
  number = {3},
  pages = {145-151},
  doi = {10.11648/j.acm.20150403.17},
  url = {https://doi.org/10.11648/j.acm.20150403.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20150403.17},
  abstract = {In this paper, we develop the meshless local Petrov-Galerkin formulation of the scattering from rectangular cavities embedded in a ground plane. The electromagnetic scattering by the cavity is governed by the Helmholtz equation along with Sommerfeld's radiation conditions imposed at infinity. The MLPG method is a truly meshless method wherein no elements or background cells are needed, in either the interpolation or integration. Based on local weak form and the moving least square (MLS) approximation, this truly meshless method is applied to solve the scattering problem. The results of numerical experiments have shown the efficiency and accuracy of the proposed method.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Meshless Local Petrov-Galerkin Method for Scattering from 2-D Rectangular Cavities in a Ground Plane
AU  - Meiling Zhao
AU  - Li Li
Y1  - 2015/05/23
PY  - 2015
N1  - https://doi.org/10.11648/j.acm.20150403.17
DO  - 10.11648/j.acm.20150403.17
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 145
EP  - 151
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20150403.17
AB  - In this paper, we develop the meshless local Petrov-Galerkin formulation of the scattering from rectangular cavities embedded in a ground plane. The electromagnetic scattering by the cavity is governed by the Helmholtz equation along with Sommerfeld's radiation conditions imposed at infinity. The MLPG method is a truly meshless method wherein no elements or background cells are needed, in either the interpolation or integration. Based on local weak form and the moving least square (MLS) approximation, this truly meshless method is applied to solve the scattering problem. The results of numerical experiments have shown the efficiency and accuracy of the proposed method.
VL  - 4
IS  - 3
ER  -

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