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Superconvergence Analysis of Gradient Recovery Method for TM Model of Electromagnetic Scattering in the Cavity

Part of: Partial differential equations, boundary value problems

Published online by Cambridge University Press:  11 July 2017

Shanghui Jia  and
Changhui Yao
Shanghui Jia*
Affiliation:
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan 450001, China School of Statistic and Mathematics, Central University of Finance and Economics, Beijing 100081, China
Changhui Yao*
Affiliation:
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan 450001, China
*
*Corresponding author. Email:shjia@lsec.cc.ac.cn (S. H. Jia), chyao@lsec.cc.ac.cn (C. H. Yao)
*Corresponding author. Email:shjia@lsec.cc.ac.cn (S. H. Jia), chyao@lsec.cc.ac.cn (C. H. Yao)
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Abstract

In this paper, we consider the transform magnetic (TM) model of electromagnetic scattering in the cavity. By the Polynomial Preserving Recovery technique, we present superconvergence analysis for the vertex-edge-face type finite element. From the numerical example, we can see that the provided method is efficient and stable.

Keywords

ScatteringcavityTM modelgradient recovery methodsuperconvergence

MSC classification

Secondary: 65N06: Finite difference methods
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 5 , October 2017 , pp. 1133 - 1144
Copyright
Copyright © Global-Science Press 2017 

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References

[1] Naga, A. and Zhang, Z., A posteriori error estimates based on the polynomial preserving recovery, SIAM J. Numer. Anal., 42(4) (2004), pp. 1780–1800.Google Scholar
[2] Wood, A. W., Analysis of electromagnetic scattering from an overfilled cavity in the ground plane, J. Comput. Phys., 215 (2006), pp. 630–641.Google Scholar
[3] Alavikia, B. and Ramahi, O. M., Finite-element solution of the problem of scattering from cavities in metallic screens using the surface integral equation as a boundary constraint, J. Opt. Soc. Am. A, 26 (2009), pp. 1915–1925.Google Scholar
[4] Arnold, D., An interior penalty finite element method with discontinuous elements, SIAM J. Numer. Anal., 19 (1982), pp. 742–760.Google Scholar
[5] Zhang, D., Study of Some Electromagnetic Scattering and Inverse Scattering Problem for Chiral Media, Phd. thesis, University of Jilin, 2004.Google Scholar
[6] Bao, G., Finite element approximation of time harmonic waves in periodic structures, SIAM J. Numer. Anal., 32(4) (1995), pp. 1155–1169.CrossRefGoogle Scholar
[7] Zhu, L. and Wu, H., Pre-asymptotic error analysis of CIP-FEM and FEM for Helmholtz equation with high wave number part II: hp version, SIAM J. Numer. Anal., 51 (2013), pp. 1828–1852.Google Scholar
[8] Babuska, I. and Suri, M., The hp version of the finite element method with quasiuniform meshes, Math. Model. Numer. Anal., 21 (1987), pp. 199–238.Google Scholar
[9] Li, J. and Huang, Y., Time-Domain Finite Element Methods for Maxwell's Equations in Metamaterials, Springer Series in Computational Mathematics, Vol. 43, Springer, 2013.Google Scholar
[10] Huang, J., Wood, A. W. and Havrilla, Michael J., A hybrid finite element-Laplace transform method for the analysis of transient electromagnetic scattering by an over-filled cavity in the ground plane, Commun. Comput. Phys., 5(1) (2009), pp. 126–141.Google Scholar
[11] Du, K., Two transparent boundary conditions for the electromagnetic scattering from two-dimensional overfilled cavities, J. Comput. Phys., 230 (2011), pp. 5822–5835.Google Scholar
[12] Du, K., Sun, W. and Zhang, X., Arbitrary high-order C0 tensor product Galerkin finite element methods for the electromagnetic scattering from a large cavity, J. Comput. Phys., 242 (2013), pp. 181–195.Google Scholar
[13] Ammari, H., Bao, G. and Wood, A. W., An integral equation method for the electromagnetic scattering from cavities, Math. Methods Appl. Sci., 23 (2000), pp. 1057–1072.Google Scholar
[14] Ammari, H., Bao, G. and Wood, A. W., Analysis of the electromagnetic scattering from a cavity, Japan J. Ind. Appl. Math., 19 (2002), pp. 301–310.Google Scholar
[15] Chen, H., Lu, P. and Xu, X., A hybridizable discontinuous Galerkin method for the Helmholtz equation with high wave number, SIAM J. Numer. Anal., 51(4) (2013), pp. 2166–2188.Google Scholar
[16] Zienkiewicz, O. C. and Zhu, J. Z., The superconvergence patch recovery and a posteriori error estimates, part 1: The recovery technique, Int. J. Numer. Methods Eng., 33 (1992), pp. 1331–1364.Google Scholar
[17] Lin, Q. and Lin, J., Finite Element Methods: Accuracy and Inprovement, China Sci. Tech. Press, 2005.Google Scholar
[18] Lin, Q. and Yan, N., The Construction and Analysis ofHigh Efficiency Finite Element Methods, HeBei University Publishers, China, 1995.Google Scholar
[19] Lin, Q. and Xie, H., Superconvergence measurement for general meshes by linear finite element method, Math. Practice Theory, 41(1) (2011), pp. 138–152 (in Chinese).Google Scholar
[20] Van, Tri and Wood, A. W., Finite element analysis of electromagnetic scattering from a cavity, IEEE. Trans. Antennas Propagation, 51(1) (2003), pp. 130–137.Google Scholar
[21] Feng, X. and Wu, H., Discontinuous Galerkin methods for the Helmholtz equation with large wave numbers, SIAM J. Numer. Anal., 47 (2009), pp. 2872–2896.Google Scholar
[22] Feng, X. and Wu, H., hp-discontinuous Galerkin methods for the Helmholtz equation with large wave number, Math. Comput., 80 (2011), pp. 1997–2024.Google Scholar
[23] Feng, X., Absorbing boundary conditions for electromagnetic wave propagation, Math. Comput., 68(225) (1999), pp. 145–168.Google Scholar
[24] Feng, X. and Xing, Y., Absolutely stable local discontinuous Galerkin methods for the Helmholtz equation with large wave number, Math. Comput., 82 (2013), pp. 1269–1296.Google Scholar
[25] Huang, Y. and Li, J., Numerical analysis of a PML model for time-dependentMaxwell's equations, J. Comput. Appl. Math., 235 (2011), pp. 3932–3942.CrossRefGoogle Scholar
[26] Zhang, Z. and Naga, A., A new finite element gradient recovery method: Superconvergence property, SIAM J. Sci. Comput., 26(4) (2005), pp. 1192–1213.Google Scholar
[27] Chen, Z. and Wu, H., An adaptive finite element method with perfectly matched absorbing layers for the wave scattering by periodic structures, SIAM J. Numer. Anal., 41 (2003), pp. 799–826.Google Scholar