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PIER PIER B PIER C PIER M PIER Letters
2010-07-22
Solutions of Large-Scale Electromagnetics Problems Using an Iterative Inner-Outer Scheme with Ordinary and Approximate Multilevel Fast Multipole Algorithms
By
Ozgur Ergul,

    Dr. Ozgur Ergul

    Department of Electrical and Electronics Engineering

    Middle East Technical University

    Turkey

    Homepage

Tahir Malas,

    Dr. Tahir Malas

    Department of Electrical and Computer Engineering

    The University of Texas at Austin

    USA

    Homepage

Levent Gurel

    Dr. Levent Gurel

    Department of Electrical and Electronics Engineering

    Bilkent University

    Turkey

    Homepage

Progress In Electromagnetics Research, Vol. 106, 203-223, 2010
doi:10.2528/PIER10061711
Abstract
We present an iterative inner-outer scheme for the efficient solution of large-scale electromagnetics problems involving perfectly-conducting objects formulated with surface integral equations. Problems are solved by employing the multilevel fast multipole algorithm (MLFMA) on parallel computer systems. In order to construct a robust preconditioner, we develop an approximate MLFMA (AMLFMA) by systematically increasing the efficiency of the ordinary MLFMA. Using a flexible outer solver, iterative MLFMA solutions are accelerated via an inner iterative solver, employing AMLFMA and serving as a preconditioner to the outer solver. The resulting implementation is tested on various electromagnetics problems involving both open and closed conductors. We show that the processing time decreases significantly using the proposed method, compared to the solutions obtained with conventional preconditioners in the literature.
Citation
Ozgur Ergul, Tahir Malas, and Levent Gurel, "Solutions of Large-Scale Electromagnetics Problems Using an Iterative Inner-Outer Scheme with Ordinary and Approximate Multilevel Fast Multipole Algorithms," Progress In Electromagnetics Research, Vol. 106, 203-223, 2010.
doi:10.2528/PIER10061711
References

1. Song, J., C.-C. Lu, and W. C. Chew, "Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects," IEEE Trans. Antennas Propagat., Vol. 45, No. 10, 1488-1493, Oct. 1997.

2. Coifman, R., V. Rokhlin, and S. Wandzura, "The fast multipole method for the wave equation: A pedestrian prescription," IEEE Antennas Propag. Mag., Vol. 35, No. 3, 7-12, 1993.

3. Ergul, O. and L. Gurel, "A hierarchical partitioning strategy for efficient parallelization of the multilevel fast multipole algorithm," IEEE Trans. Antennas Propagat., Vol. 57, No. 6, 1740-1750, Jun. 2009.

4. Taboada, J. M., M. G. Araujo, J. M. Bertolo, L. Landesa, F. Obelleiro, and J. L. Rodriguez, "MLFMA-FFT parallel algorithm for the solution of large-scale problems in electromagnetics," Progress In Electromagnetics Research, Vol. 105, 15-30, 2010.

5. Bouras, A. and V. Fraysse, "Inexact matrix-vector products in Krylov methods for solving linear systems: A relaxation strategy," SIAM J. Matrix Anal. Appl., Vol. 26, No. 3, 660-678, 2005.

6. Simoncini, V. and D. B. Szyld, "Flexible inner-outer Krylov subspace methods," SIAM J. Numer. Anal., Vol. 40, No. 6, 2219-2239, 2003.

7. Ding, D. Z., R. S. Chen, and Z. H. Fan, "SSOR preconditioned inner-outer flexible GMRES method for MLFMA analysis of scattering of open objects," Progress In Electromagnetics Research, Vol. 89, 339-357, 2009.

8. Chew, W. C., J.-M. Jin, E. Michielssen, and J. Song, Fast and Efficient Algorithms in Computational Electromagnetics, Artech House, 2001.

9. Rao, S. M., D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas Propagat., Vol. 30, No. 3, 409-418, May 1982.

10. Koc, S., J. M. Song, and W. C. Chew, "Error analysis for the numerical evaluation of the diagonal forms of the scalar spherical addition theorem," SIAM J. Numer. Anal., Vol. 36, No. 3, 906-921, 1999.

11. Hastriter, M. L., S. Ohnuki, and W. C. Chew, "Error control of the translation operator in 3D MLFMA," Microwave Opt. Technol., Vol. 37, No. 3, 184-188, Mar. 2003.

12. Ergul, O. and L. Gurel, "Optimal interpolation of translation operator in multilevel fast multipole algorithm," IEEE Trans. Antennas Propagat., Vol. 54, No. 12, 3822-3826, Dec. 2006.

13. Brandt, A., "Multilevel computations of integral transforms and particle interactions with oscillatory kernels," Comp. Phys. Comm., Vol. 65, 24-38, Apr. 1991.

14. Carpentieri, B., I. S. Duff, L. Giraud, and G. Sylvand, "Combining fast multipole techniques and an approximate inverse preconditioner for large electromagnetism calculations," SIAM J. Sci. Comput., Vol. 27, No. 3, 774-792, 2005.

15. Ergul, O. and L. Gurel, "Iterative solutions of hybrid integral equations for coexisting open and closed surfaces," IEEE Trans. Antennas Propag., Vol. 57, No. 6, 1751-1758, Jun. 2009.

16. Araujo, M. G., J. M. Bertolo, F. Obelleiro, and J. L. Rodriguez, "Geometry based preconditioner for radiation problems involving wire and surface basis functions," Progress In Electromagnetics Research, Vol. 93, 29-40, 2009.

17. Benzi, M., "Preconditioning techniques for large linear systems: A survey," J. Comput. Phys., Vol. 182, No. 2, 418-477, Nov. 2002.

18. Malas, T. and L. Gurel, "Incomplete LU preconditioning with the multilevel fast multipole algorithm for electromagnetic scattering," SIAM J. Sci. Comput., Vol. 29, No. 4, 1476-1494, Jun. 2007.

19. Saad, Y., Iterative Methods for Sparse Linear Systems, SIAM, 2003.

20. Lee, J., J. Zhang, and C.-C. Lu, "Incomplete LU preconditioning for large scale dense complex linear systems from electromagnetic wave scattering problems," J. Comput. Phys., Vol. 185, No. 1, 158-175, Feb. 2003.

21. Lee, J., J. Zhang, and C.-C. Lu, "Sparse inverse preconditioning of multilevel fast multipole algorithm for hybrid integral equations in electromagnetics," IEEE Trans. Antennas and Propagat., Vol. 52, No. 9, 2277-2287, Sep. 2004.

22. Malas, T. and L. Gurel, "Accelerating the multilevel fast multipole algorithm with the sparse-approximate-inverse (SAI) preconditioning," SIAM J. Sci. Comput., Vol. 31, No. 3, 1968-1984, Mar. 2009.

23. Ding, D. Z., R. S. Chen, and Z. H. Fan, "An effcient SAI preconditioning technique for higher order hierarchical MLFMA implementation," Progress In Electromagnetics Research, Vol. 88, 255-273, 2008.

24. Gurel, L. and T. Malas, "Iterative near-field (INF) preconditioner for the multilevel fast multipole algorithm," SIAM J. Sci. Comput., accepted for publication.

25. Van den Eshof, J., G. L. G. Sleijpen, and M. B. van Gijzen, "Relaxation strategies for nested Krylov methods," J. Comput. Appl. Math., Vol. 177, No. 2, 347-365, May 2005.

26. Van der Vorst, H. and C. Vuik, "GMRESR: A family of nested GMRES methods," Numer. Linear Algebra Appl., Vol. 1, No. 4, 369-386, Jul. 1994.

27. Balay, S., W. D. Gropp, L. C. McInnes, and B. F. Smith, PETSc Users Manual, Tech. Report ANL-95/11|Revision 2.1.5, Argonne National Laboratory, 2004.

28. Carpentieri, B., I. S. Duff, and L. Giraud, "Experiments with sparse preconditioning of dense problems from electromagnetic applications,", Tech. Report TR/PA/00/04, CERFACS, Toulouse, France, 1999.

29. Gurel, L., H. Bagci, J.-C. Castelli, A. Cheraly, and F. Tardivel, "Validation through comparison: Measurement and calculation of the bistatic radar cross section of a stealth target," Radio Science, Vol. 38, No. 3, 12-1-12-10, Jun. 2003.

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