2010-05-06
Higher Order Finite Element Method for Inhomogeneous Axisymmetric Resonators
By
Progress In Electromagnetics Research B, Vol. 21, 189-201, 2010
Abstract
To analyze resonances in an axisymmetric inhomogeneous cavity, a higher-order finite element method (FEM) is developed. Mixed higher-order node-based and edge-based elements are applied to eigenvalue analysis for the azimuthal component and meridian components of the field, respectively. Compared with the lower-order FEM, the higher-order FEM can improve accuracy with the same number of unknowns and can reduce the CPU time and memory requirement for specified accuracy. Numerical results are given to demonstrate the validity and efficiency of the proposed method.
Citation
Xi Rui, Jun Hu, and Qing Huo Liu, "Higher Order Finite Element Method for Inhomogeneous Axisymmetric Resonators," Progress In Electromagnetics Research B, Vol. 21, 189-201, 2010.
doi:10.2528/PIERB10031605
References

1. Andreasen, M. G., "Scattering from bodies of revolution," IEEE Trans. Antennas Propag., Vol. 13, 303-310, Mar. 1965.
doi:10.1109/TAP.1965.1138406        Google Scholar

2. Mautz, J. R. and R. F. Harrington, "Radiation and scattering from bodies of revolution," Appl. Sci. Res., Vol. 20, 405-435, Jun. 1969.
doi:10.1007/BF00382412        Google Scholar

3. Wu, T. K. and L. L. Tsai, "Scattering from arbitrarily-shaped lossy dielectric bodies of revolution," Radio Sci., Vol. 12, 709-718, Sep.-Oct. 1977.
doi:10.1029/RS012i005p00709        Google Scholar

4. Medgyesi-Mitschg, L. N. and J. M. Putnam, "Electromagnetic scattering from axially inhomogeneous bodies of revolution," IEEE Trans. Antennas Propag., Vol. 32, 797-806, Aug. 1984.
doi:10.1109/TAP.1984.1143430        Google Scholar

5. Huddleston, P. L., L. N. Medgyesi-Mitschg, and J. M. Putnam, "Combined field integral equation formulation for scattering by dielectrically coated conducting bodies," IEEE Trans. Antennas Propag., Vol. 34, 510-520, Apr. 1986.
doi:10.1109/TAP.1986.1143846        Google Scholar

6. Liu, Q. H. and W. C. Chew, "Diffraction of nonaxisymmetric waves in cylindrically layered media by horizontal discontinuities," Radio Sci., Vol. 27, No. 5, 569-581, 1992.
doi:10.1029/92RS00910        Google Scholar

7. Liu, Q. H., "Electromagnetic field generated by an off-axis source in a cylindrically layered medium with an arbitrary number of horizontal discontinuities," Geophysics, Vol. 58, No. 5, 616-625, 1993.
doi:10.1190/1.1443445        Google Scholar

8. Cao, X.-Y. and J. Gao, "The singularity problem at the wire/surface junction region for antenna and arrays with bodies of revolution," Progress In Electromagnetics Research B, Vol. 10, 117-130, 2008.
doi:10.2528/PIERB08092304        Google Scholar

9. Rui, X., J. Hu, and Q. H. Liu, "Fast inhomogeneous plane wave algorithm for homogeneous dielectric body of revolution," Commun. Comput. Phys., accepted.        Google Scholar

10. Qiu, Z. and C. M. Butler, "Analysis of a wire in the presence of an open body of revolution," Progress In Electromagnetics Research, Vol. 15, 1-26, 1997.
doi:10.2528/PIER95121500        Google Scholar

11. Abdelmageed, A. K., "Efficient evaluation of modal Green's functions arising in EM scattering by bodies of revolution," Progress In Electromagnetics Research, Vol. 27, 337-356, 2000.
doi:10.2528/PIER99061601        Google Scholar

12. Lee, J. F., G. Wilkins, and R. Mittra, "Finite-element analysis of axisymmetric cavity resonator using a hybrid edge element technique ," IEEE Trans. Microwave Theory Tech., Vol. 41, 1981-1987, 1993.        Google Scholar

13. Wong, M. F., M. Park, and V. Frouad Hanna, "Axisymmetric edge-based finite element formulation for bodies of revolution: Application to dielectric resonators," IEEE Microwave Symp. MTT-S, Orlando, FL, 1995.

14. Richalot, E., M. F. Wong, V. Frouad Hanna, and H. Naudrand, "Analysis of radiating axisymmetric structures using a 2-D finite-element and spherical mode expansion," Microwave Opt. Technol. Lett., Vol. 20, 8-13, 1999.
doi:10.1002/(SICI)1098-2760(19990105)20:1<8::AID-MOP2>3.0.CO;2-9        Google Scholar

15. Hoppe, D. J., L. W. Epp, and J. F. Lee, "A hybrid symmetric FEM/MOM formulation applied to scattering by inhomogeneous bodies of revolution," IEEE Trans. Antennas Propag., Vol. 42, 798-805, Jun. 1994.
doi:10.1109/8.301698        Google Scholar

16. Moneum, M. A. A., Z. Shen, J. L. Volakis, and O. Graham, "Hybrid PO-MoM analysis of large axi-symmetric radomes," IEEE Trans. Antennas Propag., Vol. 49, 1657-1666, Dec. 2001.
doi:10.1109/8.982444        Google Scholar

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

18. Anderson, E., Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK User's Guide, 3rd Ed., SIAM, Philadelphia, 1999.

19. Jin, J. M., The Finite Element Method in Electromagnetics, John Wiley & Sons, New York, 1993.

20. Peterson, A. F., S. L. Ray, and R. Mittra, "Computational Methods for Electromagnetics," IEEE Press, 1998.        Google Scholar

21. Greenwood, A. D. and J. M. Jin, "A novel efficient algorithm for scattering from a complex BOR using mixed finite elements and cylindrical PML," IEEE Trans. Antennas Propag., Vol. 47, 620-629, 1999.
doi:10.1109/8.768800        Google Scholar

22. Greenwood, A. D. and J. M. Jin, "Finite-element analysis of complex axisymmetric radiating structures," IEEE Trans. Antennas Propag., Vol. 47, 1260-1266, 1999.
doi:10.1109/8.791941        Google Scholar

23. Savage, J. S. and A. F. Peterson, "Higher order vector finite elements for tetrahedral cells," IEEE Trans. Microwave Theory Tech., Vol. 44, 874-879, 1996.
doi:10.1109/22.506446        Google Scholar

24. Lebaric, J. E. and D. Kajfez, "Analysis of dielectric resonator cavities using the finite integration technique," IEEE Trans. Microwave Theory Tech., Vol. 37, 1740-1748, 1989.
doi:10.1109/22.41039        Google Scholar