In this paper, we apply the parallel method of moments (MOM) to solve the Electric and Magnetic Current Combined Field Integral Equation (JMCFIE) for scattering by large, three-dimensional (3-D), arbitrarily shaped, homogeneous dielectric objects. We first derive the JMCFIE formulation which produces well-conditioned matrix equation when the MOM with Galerkin's type testing and Rao- Wilton-Glisson (RWG) functions is applied. We then develop a parallel conjugate gradient (CG) method on personal computer (PC) clusters using message passing interface (MPI) for solving the matrix equation obtained with JMCFIE. The matrix is decomposed by the row and stored in distributed memory of the node. Several numerical results are presented to demonstrate the accuracy and capability of the proposed method.
1. Umashankar, K. R., A. Taflove, and S. M. Rao, "Electromagnetic scattering by arbitrary shaped three-dimensional homogeneous lossy dielectric objects ," IEEE Trans. Antennas Propag., Vol. 34, 758-766, 1986. doi:10.1109/TAP.1986.1143894
2. Sheng, X. Q., J. M. Jin, J. M. Song, and W. C. Chew, "Solution of combined-field integral equation using multilevel fast multipole algorithm for scattering by homogeneous bodies," IEEE Trans. Antennas Propag., Vol. 46, No. 11, 1718-1726, 1998. doi:10.1109/8.736628
3. Yla-Oijala, P., "Application of a novel CFIE for electromagnetic scattering by dielectric objects," Microwave and Optical Technology Letters, Vol. 35, No. 1, 3-5, 2002. doi:10.1002/mop.10500
4. Yla-Oijala, P. and M. Taskinen, "Application of combined field integral equation for electromagnetic scattering by dielectric and composite objects ," IEEE Trans. Antennas Propag., Vol. 53, No. 3, 1168-1173, 2005. doi:10.1109/TAP.2004.842640
5. Yla-Oijala, P., M. Taskinen, and J. Sarvas, "Surface integral equation method for general composite metallic and dielectric structures with junctions ," Progress In Electromagnetics Research, Vol. 52, 81-108, 2005. doi:10.2528/PIER04071301
6. Yla-Oijala, P. and M. Taskinen, A novel combined field integral equation formulation for solving electromagnetic scattering by dielectric and composite objects, IEEE APS Symposium, Vol. 4B, 297-300, Washington, USA, 2005.
7. Ergul, O. and L. Gurel, Preconditioned MLFMA solution of multiple dielectric-metallic composite objects with the electric and magnetic current combined-field integral equation (JMCFIE), IEEE APS Symposium, 1-4, North Charleston USA, 2009.
8. Hestenes, M. R. and E. Stiefel, "Method of conjugate gradients for solving linear systems," J. Res. Natl. Bur. Stand., Vol. 49, 409-436, 1952.
9. Coifman, R., V. Rokhlin, and S. Wandzura, "The fast multipole method for the wave equation: A pedestrian prescription," IEEE Antennas Propagat. Mag., Vol. 35, No. 3, 7-12, 1993. doi:10.1109/74.250128
10. Song, J. M., C. C. Lu, and W. C. Chew, "Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects," IEEE Trans. Antennas Propag., Vol. 45, No. 10, 1488-1493, 1997. doi:10.1109/8.633855
11. 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. doi:10.2528/PIER09060305
12. Ma, J., L. X. Guo, and A. Q. Wang, "Study of MPI based on parallel MOM on PC clusters for EM-beam scattering by 2-D PEC rough surfaces," Chinese Physics B, Vol. 18, No. 8, 3431-3437, 2009. doi:10.1088/1674-1056/18/8/050
13. Guo, L. X., A. Q.Wang, and J. Ma, "Study on EM scattering from 2-D target above 1-D large scale rough surface with low grazing incidence by parallel MOM based on PC clusters ," Progress In Electromagnetics Research, Vol. 89, 149-166, 2009. doi:10.2528/PIER08121002
14. Dimitra, I. K., K. S. Nikita, and A. Marsh, "Extension of method of moments for electrically large structures based on parallel computations," IEEE Trans. Antennas Propag., Vol. 45, No. 3, 566-568, 1997. doi:10.1109/8.558675
15. Cwik, T., J. Partee, and J. Patterson, "Method of moment solutions to scattering problems in a parallel processing environment," IEEE Trans. Magnetics, Vol. 27, No. 5, 3837-3840, 1991. doi:10.1109/20.104938
16. Que, X. F., Z. P. Nie, and J. Hu, "Analysis of EM scattering by composite conducting and dielectric object using combined field integral equation with MLFMA," Acta Electronica Sinica, Vol. 35, No. 11, 2062-2066, 2007.
17. Rao, S. M., D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas Propag., Vol. 30, No. 3, 409-418, 1982. doi:10.1109/TAP.1982.1142818
18. Li, L. W., Y. J. Wang, and E. P. Li, "MPI-based parallelized pre-corrected FFT algorithm for analyzing scattering by arbitrarily shaped three-dimensional objects," Progress In Electromagnetics Research, Vol. 42, 247-259, 2003. doi:10.2528/PIER03030701