Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-17T16:21:31.014Z Has data issue: false hasContentIssue false
  • English
  • Français

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:  17 January 2017

Shanghui Jia ,
Changhui Yao  and
Hehu Xie
Shanghui Jia*
Affiliation:
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
Hehu Xie*
Affiliation:
LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
*
*Corresponding author. Email:shjia@lsec.cc.ac.cn (S. H. Jia), chyao@lsec.cc.ac.cn (C. H. Yao), hhxie@lsec.cc.ac.cn (H. H. Xie)
*Corresponding author. Email:shjia@lsec.cc.ac.cn (S. H. Jia), chyao@lsec.cc.ac.cn (C. H. Yao), hhxie@lsec.cc.ac.cn (H. H. Xie)
*Corresponding author. Email:shjia@lsec.cc.ac.cn (S. H. Jia), chyao@lsec.cc.ac.cn (C. H. Yao), hhxie@lsec.cc.ac.cn (H. H. Xie)
Get access

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 65N22: Solution of discretized equations
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 3 , June 2017 , pp. 543 - 553
Copyright
Copyright © Global-Science Press 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] 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. Amer. A, 26 (2009), pp. 1915–1925.Google Scholar
[2] 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
[3] 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
[4] 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
[5] 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
[6] Li, J. and Huang, Y., Time-Domain Finite Element Methods for Maxwell's Equations in Metamaterials, Springer Series in Computational Mathematics, Vol.43, Springer, January 2013.Google Scholar
[7] Huang, Y. and Li, J., Numerical analysis of a PML model for time-dependent Maxwell's equations, J. Comput. Appl. Math., 235 (2011), pp. 3932–3942.Google Scholar
[8] Bao, G., Finite element approximation of time harmonic waves in periodic structures, SIAM J. Numer. Anal., 32(4) (1995), pp. 1155–1169.Google Scholar
[9] 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
[10] 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
[11] 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
[12] 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
[13] 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
[14] 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.CrossRefGoogle Scholar
[15] Feng, X., Absorbing boundary conditions for electromagnetic wave propagation, Math. Comput., 68(225) (1999), pp. 145–168.Google Scholar
[16] Zhang, D., Study of Some Electromagnetic Scattering and Inverse Scattering Problem for Chiral Media, Phd. Thesis, University of Jilin, 2004.Google Scholar
[17] Arnold, D., An interior penalty finite element method with discontinuous elements, SIAM J. Numer. Anal., 19 (1982), pp. 742–760.Google Scholar
[18] Babuska, I. and Suri, M., The h-p version of the finite element method with quasiuniform meshes, Math. Model Numer. Anal., 21 (1987), pp. 199–238.Google Scholar
[19] 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
[20] 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
[21] 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
[22] 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
[23] 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
[24] Lin, Q. and Lin, J., Finite Element Methods: Accuracy and Inprovement, China Sci. Tech. Press, 2005.Google Scholar
[25] Lin, Q. and Yan, N., The Construction and Analysis of High Efficiency Finite Element Methods, HeBei University Publishers, China, 1995.Google Scholar
[26] Lin, Q. and Xie, H., Superconvergence measurement for general meshes by linear finite element method, Math. Practice Theory, 41(1) (2011), pp. 138–152.Google Scholar