A finite element-boundary integral-domain decomposition method is presented for analyzing electromagnetic scattering problems involving multiple three-dimensional cavities. Specifically, the edge-based finite element method is applied inside each cavity to derive a linear system of equations associated with unknown fields. The boundary integral equation is then applied on the apertures of all the cavities to truncate the computational domain and to connect the matrix subsystem generated from each cavity. With the help of an iterative domain decomposition method, the coupling system of equations is reduced to a small one which only includes the unknowns on the apertures. To further reduce computational burdens, the multilevel fast multipole algorithm is adopted to solve the reduced system. The numerical results for the near and far fields of several selected multi-cavity problems are presented to demonstrate the validity and capability of the proposed method.
2. Depine, R. A. and D. C. Skigin, "Scattering from metallic surfaces having a finite number of rectangular grooves," J. Opt. Soc. Am. A, Vol. 11, No. 11, 2844-2850, 1994.
3. Reed, J. A. and D. M. Byrne, "Frequency-selective surfaces with multiple apertures within a periodic cell," J. Opt. Soc. Am. A, Vol. 15, No. 3, 660-668, 1998.
4. Schiavone, G. A., K. O'Neill, and K. D. Paulsen, "Scattering from groove patterns in a perfectly conducting surface," J. Opt. Soc. Am. A, Vol. 14, No. 9, 660-668, 1997.
5. Alavikia, B. and O. M. Ramahi, "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, Vol. 26, No. 9, 1915-1925, 2009.
6. Altintas, A., P. H. Pathak, and M. C. Liang, "A selective modal scheme for the analysis of EM coupling into or radiation from large open-ended waveguide," IEEE Trans. Antennas Propagat., Vol. 36, No. 1, 84-96, 1988.
7. Anastassiu, H. T., J. L. Volakis, and D. C. Ross, "The mode matching technique for electromagnetic scattering by cylindrical waveguides with canonical terminations ," Journal of Electromagnetic Waves and Applications, Vol. 9, No. 11-12, 1363-1391, 1995.
8. Wang, T., R. F. Harrington, and J. R. Mautz, "Electromagnetic scattering and transmission through arbitrary apertures in conducting bodies," IEEE Trans. Antennas Propagat., Vol. 38, No. 1, 1805-1814, 1990.
9. Barkeshli, K. and J. L. Volakis, "Electromagnetic scattering from an aperture formed by a rectangular cavity recessed in a ground plane," Journal of Electromagnetic Waves and Applications, Vol. 5, No. 7, 715-734, 1991.
10. Wang, T. M. and H. Ling, "Electromagnetic scattering from three- dimensional cavities via a connection scheme," IEEE Trans. Antennas Propagat., Vol. 39, No. 10, 1505-1513, Oct. 1991.
11. Jin, J. M. and J. L. Volakis, "A finite element-boundary integral formulation for scattering by three-dimensional cavity-backed apertures," IEEE Trans. Antennas Propagat., Vol. 39, No. 1, 97-104, Jan. 1991.
12. Hua, Y. and J. Li, "Analysis of longitudinal shunt waveguide slots using FE-BI," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 14-15, 2041-2046, 2009.
13. Yang, M. L. and X. Q. Sheng, "Parallel high-order FE-BI-MLFMA for scattering by large and deep coated cavities loaded with obstacles," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 13, 1813-1823, 2009.
14. Peng, Z., X.-Q. Sheng, and F. Yin, "An efficient twofold iterative algorithm of FE-BI-MLFMA using multilevel inverse-based ILU preconditioning," Progress In Electromagnetics Research, Vol. 93, 369-384, 2009.
15. Toselli, A. and O. Widlund, Domain Decomposition Methods --- Algorithms and Theory, Springer, Berlin, 2005.
16. Cui, Z. W. and Y. P. Han, "The substructure method for scattering by large open-ended cavities," Chinese Journal of Radio Science, Vol. 24, No. 5, 914-919, Oct. 2009.
17. Martini, E., G. Carli, and S. Maci, "A domain decomposition method based on a generalized scattering matrix formalism and a complex source expansion," Progress In Electromagnetics Research B, Vol. 19, 445-473, 2010.
18. Song, J. M., C. C. Lu, and W. C. Chew, "Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects," IEEE Trans. Antennas Propagat., Vol. 45, No. 10, 1488-1493, 1997.
19. Gürel, L., O. Ergül, A. Ünal, and T. Malas, "Fast and accurate analysis of large metamaterial structures using the multilevel fast multipole algorithm," Progress In Electromagnetics Research, Vol. 95, 179-198, 2009.
20. Taboada, J. M., M. G. Araújo, J. M. Bértolo, L. Landesa, F. Obelleiro, and J. L. Rodriguez, .
21. Ergül, O., T. Malas, and L. Gürel, "Solutions of largescale electromagnetics problems using an iterative inner-outer scheme with ordinary and approximate multilevel fast multipole algorithms," Progress In Electromagnetics Research, Vol. 106, 203-223, 2010.
22. Ergül, O. and L. Gürel, "Efficient solutions of metamaterial problems using a low-frequency multilevel fast multipole algorithm," Progress In Electromagnetics Research, Vol. 108, 81-99, 2010.
23. Shao, H., J. Hu, Z.-P. Nie, G. Han, and S. He, "Hybrid tangential equivalence principle algorithm with MLFMA for analysis of array structures," Progress In Electromagnetics Research, Vol. 113, 127-141, 2011.
24. Jin, J. M., "The Finite Element Method in Electromagnetics," Wiley, New York, 2002.
25. Rao, S. M., D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas Propagat., Vol. 30, No. 3, 409-418, 1982.
26. Liu, J. W. H., "The multifrontal method for sparse matrix solution: Theory and practice," SIAM Rev., Vol. 34, 82-109, 1992.
27. Tian, J., Z.-Q. Lv, X.-W. Shi, L. Xu, and F. Wei, "An efficient approach for multifrontal algorithm to solve non-positive-definite ¯nite element equations in electromagnetics problems," Progress In Electromagnetics Research, Vol. 95, 121-133, 2009.
28. Irons, B. M., "A frontal solution program for finite element analysis," SIAM Rev., Vol. 2, 5-32, 1970.
29. Ping, X. W., T. J. Cui, and W. B. Lu, "The combination of bcgstab with multifrontal algorithm to solve FE-BI-MLFMA linear systems arising from inhomogeneous electromagnetic scattering problems," Progress In Electromagnetics Research, Vol. 93, 91-105, 2009.
30. Ergül, O. and L. Gürel, "Improving iterative solutions of the electric¯eld integral equation via transformations into normal equations ," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 16, 2129-2138, 2010.