Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-23T08:28:46.563Z 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:  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:[email protected] (S. H. Jia), [email protected] (C. H. Yao)
*Corresponding author. Email:[email protected] (S. H. Jia), [email protected] (C. H. Yao)
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
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 

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] 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