The boundary element method is considered for solving scattering problems and is accelerated using the hierarchical matrix format. Thus, some matrix blocks chosen by geometrical criteria are approximated by low-rank matrices using a robust compression method. In this paper, we validate the use of the hybrid cross approximation which is quite new in this area, and we apply it to several examples. The validation is done on a conducting sphere, as well as less canonical objects such as the scattering by a rough (Weierstrass) surface or a plane.
2. Poirier, J.-R. and R. Perrussel, "Adaptive cross approximation for scattering by periodic surfaces," Progress In Electromagnetics Research M, Vol. 35, 97-103, 2014.
doi:10.2528/PIERM14011505
3. Borm, S. and Lars Grasedyck, "Hybrid cross approximation of integral operators," Numerische Mathematik, Vol. 101, 221-249, 2005.
doi:10.1007/s00211-005-0618-1
4. Rao, S. M., D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Transactions on Antennas and Propagation, Vol. 30, 409-417, 1982.
doi:10.1109/TAP.1982.1142818
5. Bebendorf, M., "Hierarchical matrices --- A means to efficiently solve elliptic boundary value problems," Lecture Notes in Computational Science and Engineering, Springer, 2008.
6. Bebendorf, M., "Approximation of boundary element matrices," Numerische Mathematik, Vol. 86, 565-589, 2000.
doi:10.1007/PL00005410
7. Grasedyck, L. and W. Hackbusch, "Construction and arithmetics of H-matrices," Computing, Vol. 70, 295-334, 2003.
doi:10.1007/s00607-003-0019-1
8. Bebendorf, M., "A hierarchical LU decomposition-based preconditioners for BEM," Computing, Vol. 74, 225-247, 2005.
doi:10.1007/s00607-004-0099-6
9. Grasedyck, L., "Adaptive recompression of H-matrices for BEM," Computing, Vol. 74, 205-223, 2005.
doi:10.1007/s00607-004-0103-1
10. Siau, J., et al., "Hybrid cross approximation for a magnetostatic formulation," IEEE Transactions on Magnetics, Vol. 51, No. 3, 1-4, 2015.
doi:10.1109/TMAG.2014.2364739
11. Saad, Y. and M. H. Schultz, "GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems," SIAM J. Sci. and Stat. Comput., Vol. 7, No. 3, 856-869, 1985.
doi:10.1137/0907058
12. Berizzi, F. and E. Dalle-Mese, "Fractal analysis of the signal scattered from the sea surface," IEEE Transactions on Antennas and Propagation, Vol. 47, No. 2, 324-338, 1999.
doi:10.1109/8.761073
13. Franceschetti, G., M. Migliaccio, and D. Riccio, "An electromagnetic fractal-based model for the study of fading," Radio Science, Vol. 31, 1749-1759, 1996.
doi:10.1029/96RS02811
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