The rigorous evaluation of the NRCS (Normalized Radar Cross Section) of an object above a one-dimensional sea surface (2D case) needs to numerically solve a set of discretized integral equations involving a large number of unknowns. Thus, the direct solution of the impedance matrix equation via LU decomposition becomes the most expensive step in the MoM (Method of Moments) procedure. So, in order to minimize the computation cost, the iterative domain decomposition method called EPILE (Extended Propagation-Inside-Layer Expansion) was used and then was combined with the FBSA (Forward-Backward with Spectral Acceleration) to calculate the local interactions on the rough sea surface. The resulting fast method is called EPILE+FBSA. In this paper, we take advantage of the rank-deficient nature of the coupling matrices, corresponding to the object-surface interactions, to further reduce the complexity of the method by using the ACA (Adaptive Cross Approximation). Thus, the coupling matrices are strongly compressed without a loss of accuracy and the memory requirement is then strongly reduced. For a cylinder above a rough sea surface, the results show the efficiency of the accelerated EPILE+FBSA+ACA method.
2. Bourlier, C., N. Pinel, and G. Kubicke, Method of Moments for 2D Scattering Problems. Basic Concepts and Applications, FOCUS SERIES in WAVES, Ed. WILEY-ISTE, 2013.
3. 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.
4. Kubicke, G., C. Bourlier, and J. Saillard, "Scattering by an object above a randomly rough surface from a fast numerical method: Extended PILE method combined with FB-SA," Waves in Random and Complex Media, Vol. 18, No. 3, 495-519, 2008.
5. Kubicke, G., C. Bourlier, and J. Saillard, "Scattering from canonical objects above a sea-like one-dimensional rough surface from a rigorous fast method," Waves in Random and Complex Media, Vol. 20, No. 1, 156-178, 2010.
6. Chou, H. T. and J. T. Johnson, "A novel acceleration algorithm for the computation of scattering from rough surfaces with the forward-backward method," Radio Science, Vol. 33, No. 5, 1277-1287, 1998.
7. Bebendorf, M., "Approximation of boundary element matrices," Numerische Mathematik, Vol. 86, No. 4, 565-589, 2000.
8. Bebendorf, M. and S. Rjasanow, "Adaptive low-rank approximation of collocation matrices," Computing, Vol. 70, No. 1, 1-24, 2003.
9. Kurz, S., O. Rain, and S. Rjasanow, "The adaptive cross-approximation technique for the 3-D boundary element method," IEEE Transactions on Magnetics, Vol. 38, No. 2, 421-424, 2002.
10. Zhao, K., M. N. Vouvakis, and J.-F. Lee, "The adaptive cross approximation algorithm for accelerated method of moments computation of EMC problem," IEEE Transactions on Electromagnetic Compatibility, Vol. 47, No. 4, 763-773, 2005.
11. Shaeffer, J., "LU factorization and solve of low rank electrically large MoM problems for monostatic scattering using the adaptive cross approximation for problem sizes to 1 025 101 unknowns on a PC workstation," Proc. IEEE Antennas Propag. Soc. Int. Symp., 1273-1276, Sep. 9-15, 2007.
12. Shaeffer, J., "Direct solve of electrically large integral equations for problem sizes to 1M unknowns," IEEE Transactions on Antennas and Propagation, Vol. 56, No. 8, 2306-2313, 2008.
13. Tamayo, J. M., A. Heldring, and J. M. Rius, "Multilevel adaptive cross approximation (MLACA)," IEEE Transactions on Antennas and Propagation, Vol. 59, No. 12, 4600-4608, 2011.
14. Elfouhaily, T., B. Chapron, K. Katsaros, and D. Vandermark, "A unified directional spectrum for long and short wind-driven waves," Journal of Geophysical Research, Vol. 102, No. C7, 781-796, 1997.
15. Thorsos, E. I., "The validity of the Kirchho® approximation for rough surface scattering using a Gaussian roughness spectrum," Journal of the Acoustical Society of America, Vol. 83, 78-92, 1988.
16. Hackbusch, W., "A sparse matrix arithmetic based on H-matrices. Part I. Introduction to H-matrices," Computing, Vol. 62, No. 2, 89-108, 1999.
17. Grasedyck, L. and W. Hackbusch, "Construction and arithmetics of H-matrices," Computing, Vol. 70, No. 4, 295-344, 2003.