Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
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By X.-M. Pan and X.-Q. Sheng

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A hierarchical interpolative decomposition multilevel fast multipole algorithm (ID-MLFMA) is proposed to handle multiscale, dynamic electromagnetic problems. The hierarchical scheme to conduct the ID skeletonization and to implement the matrix vector multiplication is discussed. A strategy to improve the efficiency of ID skeletonization is developed. The hierarchical ID-MLFMA are investigated by numerical experiments on complex targets, demonstrating the capability of the hierarchical ID-MLFMA.

X.-M. Pan and X.-Q. Sheng, "Hierarchical Interpolative Decomposition Multilevel Fast Multipole Algorithm for Dynamic Electromagnetic Simulations," Progress In Electromagnetics Research, Vol. 134, 79-94, 2013.

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

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

3. Yuan, N., T. S. Yeo, X. C. Nie, L. W. Li, and Y. B. Gan, "Analysis of scattering from composite conducting and dielectric targets using the precorrected-FFT algorithm," Journal of Electromagnetic Waves and Applications, Vol. 17, No. 3, 499-515, 2003.

4. Garcia, E., C. Delgado, L. Lozano, I. Gonzalez-Diego, and M. F. Catedra, "An efficient hybrid-scheme combining the characteristic basis function method and the multilevel fast multipole algorithm for solving bistatic RCS and radiation problems," Progress In Electromagnetics Research B, Vol. 34, 327-343, 2011.

5. Lai, B., H. B. Yuan, and C.-H. Liang, "Analysis of nurbs surfaces modeled geometries with higher-order mom based AIM," Journal of Electromagnetic Waves and Applications, Vol. 25, No. 5-6, 683-691, 2011.

6. Pan, X.-M., W.-C. Pi, and X.-Q. Sheng, "On openmp parallelization of the multilevel fast multipole algorithm," Progress In Electromagnetics Research, Vol. 112, 199-213, 2011.

7. Shao, H., H., J. Hu, Z.-P. Nie, G. Han, and S. He, "Hybrid tangential equivalence principle algorithm with MLFMA for analysis of array structures," Progress In Electromagnetics Research, Vol. 113, 127-141, 2011.

8. Ergul, O., "Parallel implementation of MLFMA for homogeneous objects with various material properties," Progress In Electromagnetics Research, Vol. 121, 505-520, 2011.

9. Pan, X. M., W. C. Pi, M. L. Yang, Z. Peng, and X. Q. Sheng, "Solving problems with over one billion unknowns by the MLFMA," IEEE Trans. Antennas Propag., Vol. 60, No. 5, 2012.

10. Schobert, D. T. and T. F. Eibert, "Fast integral equation solution by multilevel Green's function interpolation combined with multilevel fast multipole method," IEEE Trans. Antennas Propag., Vol. 60, No. 9, 4458-4463, 2012.

11. Wulf, D. and R. Bunger, "An efficient implementation of the combined wideband MLFMA/LF-FIPWA," IEEE Trans. Antennas Propag., Vol. 57, No. 12, 467-474, 2009.

12. Bogaert, I., J. Peeters, and F. Olyslager, "A nondirective plane wave MLFMA stable at low frequencies," IEEE Trans. Antennas Propag., Vol. 56, No. 12, 3752-3767, 2008.

13. Pan, X. M., J. G.Wei, Z. Peng, and X. Q. Sheng, "A fast algorithm for multiscale electromagnetic problems using interpolative decomposition and multilevel fast multipole algorithm," Radio Sci., Vol. 47, 2012.

14. Greengard, L., D. Guey┬▒er, P. G. Martinsson, and V. Rokhlin, "Fast direct solvers for integral equations in complex three-dimensional domains," Acta Numerica, Vol. 18, 243-275, 2009.

15. Ho, K. L. and L. Greengard, "A fast direct solver for structured linear systems by recursive skeletonization," SIAM J. Sci. Comput., Vol. 34, No. 5, A2507-A2532, 2012.

16. Rodriguez, J. L., J. M. Taboada, M. G. Araujo, F. O. Basteiro, L. Landesa, and I. Garcia-Tunon, "On the use of the singular value decomposition in the fast multipole method," IEEE Trans. Antennas Propag., Vol. 56, No. 8, 2325-2334, 2008.

17. Liberty, E., F. Woolfe, P. G. Martinsson, V. Rokhlin, and M. Tygert, "Randomized algorithms for the low-rank approximation of matrices," Proc. Natl. Acad. Sci., Vol. 104, 20167-20172, US, 2007.

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