Vol. 84
Latest Volume
All Volumes
PIERM 114 [2022] PIERM 113 [2022] PIERM 112 [2022] PIERM 111 [2022] PIERM 110 [2022] PIERM 109 [2022] PIERM 108 [2022] PIERM 107 [2022] PIERM 106 [2021] PIERM 105 [2021] PIERM 104 [2021] PIERM 103 [2021] PIERM 102 [2021] PIERM 101 [2021] PIERM 100 [2021] PIERM 99 [2021] PIERM 98 [2020] PIERM 97 [2020] PIERM 96 [2020] PIERM 95 [2020] PIERM 94 [2020] PIERM 93 [2020] PIERM 92 [2020] PIERM 91 [2020] PIERM 90 [2020] PIERM 89 [2020] PIERM 88 [2020] PIERM 87 [2019] PIERM 86 [2019] PIERM 85 [2019] PIERM 84 [2019] PIERM 83 [2019] PIERM 82 [2019] PIERM 81 [2019] PIERM 80 [2019] PIERM 79 [2019] PIERM 78 [2019] PIERM 77 [2019] PIERM 76 [2018] PIERM 75 [2018] PIERM 74 [2018] PIERM 73 [2018] PIERM 72 [2018] PIERM 71 [2018] PIERM 70 [2018] PIERM 69 [2018] PIERM 68 [2018] PIERM 67 [2018] PIERM 66 [2018] PIERM 65 [2018] PIERM 64 [2018] PIERM 63 [2018] PIERM 62 [2017] PIERM 61 [2017] PIERM 60 [2017] PIERM 59 [2017] PIERM 58 [2017] PIERM 57 [2017] PIERM 56 [2017] PIERM 55 [2017] PIERM 54 [2017] PIERM 53 [2017] PIERM 52 [2016] PIERM 51 [2016] PIERM 50 [2016] PIERM 49 [2016] PIERM 48 [2016] PIERM 47 [2016] PIERM 46 [2016] PIERM 45 [2016] PIERM 44 [2015] PIERM 43 [2015] PIERM 42 [2015] PIERM 41 [2015] PIERM 40 [2014] PIERM 39 [2014] PIERM 38 [2014] PIERM 37 [2014] PIERM 36 [2014] PIERM 35 [2014] PIERM 34 [2014] PIERM 33 [2013] PIERM 32 [2013] PIERM 31 [2013] PIERM 30 [2013] PIERM 29 [2013] PIERM 28 [2013] PIERM 27 [2012] PIERM 26 [2012] PIERM 25 [2012] PIERM 24 [2012] PIERM 23 [2012] PIERM 22 [2012] PIERM 21 [2011] PIERM 20 [2011] PIERM 19 [2011] PIERM 18 [2011] PIERM 17 [2011] PIERM 16 [2011] PIERM 14 [2010] PIERM 13 [2010] PIERM 12 [2010] PIERM 11 [2010] PIERM 10 [2009] PIERM 9 [2009] PIERM 8 [2009] PIERM 7 [2009] PIERM 6 [2009] PIERM 5 [2008] PIERM 4 [2008] PIERM 3 [2008] PIERM 2 [2008] PIERM 1 [2008]
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 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
http://www.jpier.org/PIERM/pier.php?paper=19060701
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

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

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

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

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

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

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.

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.

9. Han, K., 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

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

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

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.

13. Li, X. J., 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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