Calculating the RCS (Radar Cross Section) of two 3D scatterers needs to numerically solve a set of integral equations involving numerous unknowns. Such a 3D problem can not be solved easily with a conventional Method of Moments (MoM) by using a direct LU inversion. Thus, a hybridization between the Extended Propagation-Inside-Layer Expansion (E-PILE) and the Physical Optics approximation (PO) reduces signicantly the memory requirements and CPU time. The resulting method called E-PILE+PO. In this work, we take advantage of the rank-decient nature of the coupling matrices, corresponding to scatterer 1 (the object) and scatterer 2 (the rough surface) interactions, to further reduce the complexity of the method by using the Adaptive Cross Approximation (ACA).
1. Guo, L.-X., A.-Q. Wang, and J. Wang, "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
2. Liu, P. and Y. Q. Jin, "The finite-element method with domain decomposition for electromagnetic bistatic scattering from the comprehensive model of a ship on and a target above a large-scale rough sea surface," IEEE Transactions on Geoscience and Remote Sensing, Vol. 12, No. 5, 950-956, 2004.
3. Ye, H. and Y. Q. Jin, "A hybrid analytic-numerical algorithm of scattering from an object above a rough surface," IEEE Transactions on Geoscience and Remote Sensing, Vol. 45, No. 5, 1174-1180, 2007. doi:10.1109/TGRS.2007.892609
4. Dechamps, N., N. De Beaucoudrey, C. Bourlier, and S. Toutain, "Fast numerical method for electromagnetic scattering by rough layered interfaces: Propagation-inside-layer expansion method," Journal of the Optical Society of America A, Vol. 23, No. 2, 359-369, 2006. doi:10.1364/JOSAA.23.000359
5. Kouali, M., G. Kubick, and C. Bourlier, "Electromagnetic scattering from two-scatterers using the extended propagation-inside-layer expansion method," General Assembly and Scientific Symposium, 1-4, 2011.
7. Kubick, G. and C. Bourlier, "A fast hybrid method for scattering from a large object with dihedral effects above a large rough surface," IEEE Transactions on Antennas and Propagation, Vol. 59, No. 2, 189-198, 2011. doi:10.1109/TAP.2010.2090470
8. Pino, M. R., L. Landesa, J. L. Rodriguez, F. Obelleiro, and R. J. Burkholder, "The generalized forward-backward method for analyzing the scattering from targets on ocean-like rough surfaces," IEEE Transactions on Antennas and Propagation, Vol. 47, No. 6, 961-969, 1999. doi:10.1109/8.777118
9. Ye, H. and Y. Q. Jin, "Fast iterative approach to difference scattering from the target above a rough surface," IEEE Transactions on Geoscience and Remote Sensing, Vol. 44, No. 1, 108-115, 2006. doi:10.1109/TGRS.2005.859955
10. Ye, H. and Y. Q. Jin, "A hybrid KAMoM algorithm for computation of scattering from a 3D PEC target above a dielectric rough surface," Radio Science, Vol. 43, No. 3, 1-15, 2008. doi:10.1029/2007RS003702
11. Guan, B., J. F. Zhang, X. Y. Zhou, and T. J. Cui, "Electromagnetic scattering from objects above a rough surface using the method of moments with half-space Green’s function," IEEE Transactions on Geoscience and Remote Sensing, Vol. 47, No. 10, 3399-3405, 2009. doi:10.1109/TGRS.2009.2022169
12. Johnson, J. T., "A numerical study of scattering from an object above a rough surface," IEEE Transactions on Antennas and Propagation, Vol. 50, No. 10, 1361-1367, 2002. doi:10.1109/TAP.2002.802152
13. Johnson, J. T. and R. J. Burkholder, "Coupled canonical grid/discrete dipole approach for computing scattering from objects above or below a rough interface," IEEE Transactions on Geoscience and Remote Sensing, Vol. 39, No. 6, 1214-1220, 2001. doi:10.1109/36.927443
14. Johnson, J. T., "A study of the four path model for scattering from an object above a half space," Microwave and Optical Technology Letters, Vol. 20, No. 30, 130-134, 2001. doi:10.1002/mop.1242
15. Guo, L. X., J. Li, and H. Zeng, "Bistatic scattering from a three-dimensional object above a two-dimensional randomly rough surface modeled with the parallel FDTD approach," JOSA A, Vol. 26, No. 11, 2383-2392, 2009. doi:10.1364/JOSAA.26.002383
16. Kuang, L. and Y. Q. Jin, "Bistatic scattering from a three-dimensional object over a randomly rough surface using the FDTD algorithm," IEEE Transactions on Antennas and Propagation, Vol. 55, No. 8, 2302-2312, 2007. doi:10.1109/TAP.2007.901846
17. Kouali, M., G. Kubick, and C. Bourlier, "Extended propagation-inside-layer expansion method combined with the forward-backward method to study the scattering from an object above a rough surface," Optics Letters, Vol. 37, No. 14, 2985-2987, 2012. doi:10.1364/OL.37.002985
18. Boag, A. and R. Mittra, "Complex multipole beam approach to electromagnetic scattering problems," IEEE Transactions on Antennas and Propagation, Vol. 42, No. 3, 366-372, 1994. doi:10.1109/8.280723
19. Tap, K., P. H. Pathak, and R. J. Burkholder, "Complex source beam-moment method procedure for accelerating numerical integral equation solutions of radiation and scattering problems," IEEE Transactions on Antennas and Propagation, Vol. 62, No. 4, 2052-2062, 2014. doi:10.1109/TAP.2014.2298536
20. Canning, F. X., "The impedance matrix localization (IML) method for moment-method calculations," IEEE Antennas and Propagation Magazine, Vol. 32, No. 5, 18-30, 1990. doi:10.1109/74.80583
21. Zhao, K., M. N. Vouvakis, and J. F. Lee, "The adaptive cross approximation algorithm for accelerated method of moments computations of EMC problems," IEEE Transactions on Electromagnetic Compatibility, Vol. 47, No. 4, 763-773, 2005. doi:10.1109/TEMC.2005.857898
22. Kubicke, G., C. Bourlier, S. Bellez, and H. Li, "A fast EPILE+FBSA method combined with adaptive cross approximation for the scattering from a target above a large ocean-like surface," Progress In Electromagnetics Research M, Vol. 37, 175-182, 2014. doi:10.2528/PIERM14052503
23. Yang, W. and C. Qi, "A bi-iteration model for electromagnetic scattering from a 3D object above a 2D rough surface," Electromagnetics, Vol. 35, No. 3, 190-204, 2015. doi:10.1080/02726343.2015.1005203
24. Kouali, M., G. Kubick, and C. Bourlier, "Scattering from an object above a rough surface using the extended PILE method hybridized with PO approximation," Antennas and Propagation Society International Symposium (APSURSI), 1-2, 2012.
25. Kouali, M., G. Kubick, and C. Bourlier, "Electromagnetic interactions analysis between two 3-D scatterers using the E-PILE method combined with the PO approximation," Progress In Electromagnetic Research B, Vol. 58, 123-138, 2014. doi:10.2528/PIERB14011204