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2019-09-09
Discontinuous Galerkin VSIE Method for Electromagnetic Scattering from Composite Metallic and Dielectric Structures
By
Progress In Electromagnetics Research M, Vol. 84, 197-209, 2019
Abstract
In this paper, an efficient volume surface integral equation (VSIE) method with nonconformal discretization is developed for the analysis of electromagnetic scattering from composite metallic and dielectric (CMD) structures. This VSIE scheme utilizes curved tetrahedral (triangular) elements for volume (surface) modeling and the associated CRWG (CSWG) basis functions for volume current (surface) current modeling. Further, a discontinuous Galerkin (DG) volume integral equation (VIE) method and a DG surface integral equation (SIE) approach are adopted for dielectric and metallic parts, respectively, which allow both conformal and nonconformal volume/surface discretization improving meshing flexibility considerably. Numerical results are provided to demonstrate the accuracy, efficiency, and flexibility of our scheme.
Citation
Yu-Yu Zhu, Qiang-Ming Cai, Runren Zhang, Xin Cao, Yan-Wen Zhao, Bin Gao, and Jun Fan, "Discontinuous Galerkin VSIE Method for Electromagnetic Scattering from Composite Metallic and Dielectric Structures," Progress In Electromagnetics Research M, Vol. 84, 197-209, 2019.
doi:10.2528/PIERM19060701
References

1. Ouyang, J., F. Yang, S. W. Yang, and Z. P. Nie, "Exact simulation method VSWIE-MLFMA for analysis radiation pattern of probe-feed conformal microstrip antennas and the application of synthesis radiation pattern," Journal of Electromagnetic Waves and Application, Vol. 21, No. 14, 1995-2008, 2007.
doi:10.1163/156939307783152803        Google Scholar

2. Yuan, N., T. S. Yeo, X. C. Nie, Y. B. Gan, and L. W. Li, "Analysis of probe-fed conformal microstrip antennas on finite grounded substrate," IEEE Trans. Antennas Propag., Vol. 54, No. 2, 554-563, Feb. 2006.
doi:10.1109/TAP.2005.863115        Google Scholar

3. Rao, S. M., D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas Propag., Vol. 30, 409-418, May 1982.
doi:10.1109/TAP.1982.1142818        Google Scholar

4. Schaubert, D. H., D. R. Wilton, and A. W. Glisson, "A tetrahedral modeling method for electromagnetic scattering by arbitrarily shaped inhomogeneous dielectric bodies," IEEE Trans. Antennas Propag., Vol. 32, 77-85, Jan. 1984.
doi:10.1109/TAP.1984.1143193        Google Scholar

5. Cai, Q.-M., Y.-W. Zhao, W.-F. Huang, Y.-T. Zheng, Z.-P. Zhang, Z.-P. Nie, and Q. H. Liu, "Volume surface integral equation method based on higher order hierarchical vector basis functions for EM scattering and radiation from composite metallic and dielectric structures," IEEE Trans. Antennas Propag., Vol. 64, No. 12, 5359-5372, Dec. 2016.
doi:10.1109/TAP.2016.2621018        Google Scholar

6. Peng, Z., K.-H. Lim, and J.-F. Lee, "A discontinuous Galerkin surface integral equation method for electromagnetic wave scattering from nonpenetrable targets," IEEE Trans. Antennas Propag., Vol. 61, No. 7, 3617-3628, Jul. 2013.
doi:10.1109/TAP.2013.2258394        Google Scholar

7. Wang, X. C., Z. Peng, and J. F. Lee, "A new integral equation based domain decomposition method for electromagnetic analysis of large multi-scale problems," Proc. IEEE Antennas Propag. Soc. Int. Symp. (APSURSI'12), 1-2, Jul. 2012.        Google Scholar

8. Cai, Q.-M., Y.-W. Zhao, L. Gu, Z. -P. Nie, and Q. H. Liu, "Analysis of multi-scale problems from PEC objects by a discontinuous Galerkin SIE based on higher order hierarchical vector basis functions," Proc. Int. IEEE AP-S Symp., 1611-1612, 2016.        Google Scholar

9. Han, K., Y. Chen, X. Que, et al. "A domain decomposition scheme with curvilinear discretizations for solving Large and complex PEC scattering problems," IEEE Antennas Wireless Propag. Lett., Vol. 17, 242-246, 2018.
doi:10.1109/LAWP.2017.2782734        Google Scholar

10. Zhang, L. M. and X. Q. Sheng, "Discontinuous Galerkin volume integral equation solution of scattering from inhomogeneous dielectric objects by using the SWG basis function," IEEE Trans. Antennas Propag., Vol. 65, 1500-1504, Mar. 2017.
doi:10.1109/TAP.2016.2647686        Google Scholar

11. Ozdemir, N. A. and J.-F. Lee, "A nonconformal volume integral equation for electromagnetic scattering from penetrable objects," IEEE Trans. Magn., Vol. 43, No. 4, 1369-1372, Apr. 2007.
doi:10.1109/TMAG.2007.891031        Google Scholar

12. Ng, T.-H., J.-F. Lee, Z. Peng, and K. H. Lim, "A non-conformal volume surface integral equation for electromagnetic scatterings from composite PEC and inhomogenous anisotropic scatterers," Proc. IEEE APS Int. Symp. Dig., 728-729, Oct. 2013.        Google Scholar

13. Li, X. J., L. Lei, et al. "VSIE-based domain decomposition method with simplified prism vector basis functions for planar thin dielectric-conductor composite objects," IEEE Antennas Wireless Propag. Lett., Vol. 17, 1608-1612, Sep. 2018.
doi:10.1109/LAWP.2018.2857476        Google Scholar

14. Tong, M. S., Z. G. Qian, and W. C. Chew, "Nyström method solution of volume integral equations for electromagnetic scattering by 3D penetrable objects," IEEE Trans. Antennas Propag., Vol. 58, No. 5, 1645-1652, May 2010.
doi:10.1109/TAP.2010.2044350        Google Scholar

15. Markkanen, J., P. Ylä-oijala, and A. Sihvola, "Discretization of volume integral equation formulations for extremely anisotropic materials," IEEE Trans. Antennas Propag., Vol. 60, No. 11, 5195-5202, Nov. 2012.
doi:10.1109/TAP.2012.2207675        Google Scholar

16. Ylä-Oijala, P., J. Markkanen, and S. Järvenpää, "Current-based volume integral equation formulation for bianisotropic materials," IEEE Trans. Antennas Propag., Vol. 64, No. 8, 3470-3477, Aug. 2016.
doi:10.1109/TAP.2016.2570258        Google Scholar

17. Schols, Y. and G. A. E. Vandenbosch, "Separation of horizontal and vertical dependencies in a surface/volume integral equation approach to model quasi 3-D structures in multilayered media," IEEE Trans. Antennas Propag., Vol. 55, No. 4, 1086-1094, Apr. 2007.
doi:10.1109/TAP.2007.893400        Google Scholar

18. Cai, Q.-M., Z.-P. Zhang, Y.-W. Zhao, W.-F. Huang, Y.-T. Zheng, Z.-P. Nie, and Q. H. Liu, "Nonconformal discretization of electric current volume integral equation with higher order hierarchical vector basis functions," IEEE Trans. Antennas Propag., Vol. 65, No. 8, 4155-4169, Aug. 2017.
doi:10.1109/TAP.2017.2710211        Google Scholar

19. Markkanen, J. and P. Ylä-Oijala, "Discretization of electric current volume integral equation with piecewise linear basis functions," IEEE Trans. Antennas Propag., Vol. 62, No. 9, 4877-4880, Sep. 2013.
doi:10.1109/TAP.2014.2334705        Google Scholar

20. van Beurden, M. C. and S. J. L. van Eijndhoven, "Well-posedness of domain integral equations for a dielectric object in homogeneous background," J. Eng. Math, Vol. 62, 289-302, 2008.
doi:10.1007/s10665-008-9218-2        Google Scholar

21. Houston, P., I. Perugia, and D. Schötzau, "An a posteriori error indicator for discontinuous Galerkin discretizations of (curl)-elliptic partial differential equations," IMA J. Numer. Anal., Vol. 27, No. 1, 122-150, 2007.
doi:10.1093/imanum/drl012        Google Scholar

22. Arnold, D., "An interior penalty finite element method with discontinuous elements," SIAMJ. Numer. Anal., Vol. 19, No. 4, 742-760, 1982.
doi:10.1137/0719052        Google Scholar

23. Lu, C. C. and W. C. Chew, "A coupled surface-volume integral equation approach for the calculation of electromagnetic scattering from composite metallic and material targets," IEEE Trans. Antennas Propag., Vol. 48, No. 12, 1866-1868, Dec. 2000.
doi:10.1109/8.901277        Google Scholar

24. Duffy, M. G., "Quadrature over a pyramid or cube of integrands with a singularity," SIAM J. Numer. Anal., Vol. 19, No. 6, 1260-1262, Dec. 1982.
doi:10.1137/0719090        Google Scholar

25. Gang, K., J. M. Song, W. C. Weng, K. C. Donepudi, and J. M. Jin, "A novel grid-robust higher order vector basis function for the method of moments," IEEE Trans. Antennas Propag., Vol. 49, No. 6, 908-915, Jun. 2001.
doi:10.1109/8.931148        Google Scholar

26. Altair Feko, Altair Engineering, Inc., www.altairhyperworks.com/feko.        Google Scholar

27. Järvenpää, S., M. Taskinen, and P. Ylä-Oijala, "Singularity subtraction technique for high-order polynomial vector basis functions on planar triangles," IEEE Trans. Antennas Propag., Vol. 54, No. 1, 42-49, Jan. 2006.
doi:10.1109/TAP.2005.861556        Google Scholar