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PIER PIER B PIER C PIER M PIER Letters PIER Photonics
2018-10-31
Hybrid Cross Approximation for the Electric Field Integral Equation
By
Priscillia Daquin,

    Dr. Priscillia Daquin

    University of Toulouse

    France

    Homepage

Ronan Perrussel,

    Dr. Ronan Perrussel

    Universite de Toulouse

    France

    Homepage

Jean-René Poirier

    Dr. Jean-René Poirier

    University of Toulouse

    France

    Homepage

Progress In Electromagnetics Research M, Vol. 75, 79-90, 2018
doi:10.2528/PIERM18052803 | Google Scholar

Abstract
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.
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Citation
Priscillia Daquin, Ronan Perrussel, and Jean-René Poirier, "Hybrid Cross Approximation for the Electric Field Integral Equation," Progress In Electromagnetics Research M, Vol. 75, 79-90, 2018.
doi:10.2528/PIERM18052803
References

1. Darve, E., "The fast multipole method: Numerical implementation," Journal of Computational Physics, Vol. 160, 195-240, 2000.
doi:10.1006/jcph.2000.6451        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

5. Bebendorf, M., "Hierarchical matrices --- A means to efficiently solve elliptic boundary value problems," Lecture Notes in Computational Science and Engineering, Springer, 2008.        Google Scholar

6. Bebendorf, M., "Approximation of boundary element matrices," Numerische Mathematik, Vol. 86, 565-589, 2000.
doi:10.1007/PL00005410        Google Scholar

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        Google Scholar

8. Bebendorf, M., "A hierarchical LU decomposition-based preconditioners for BEM," Computing, Vol. 74, 225-247, 2005.
doi:10.1007/s00607-004-0099-6        Google Scholar

9. Grasedyck, L., "Adaptive recompression of H-matrices for BEM," Computing, Vol. 74, 205-223, 2005.
doi:10.1007/s00607-004-0103-1        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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