An efficient higher order MLFMA is developed by using an ``extended-tree''. With this extended-tree, the size of the box at the finest level is reduced, and the cost associated with the aggregation and disaggregation operations is significantly decreased. The sparse approximate inverse (SAI) preconditioner is utilized to accelerate the convergence of iterative solutions. The Cholesky factorization, instead of the often used QR factorization, is employed to construct the SAI preconditioner for cavity scattering analysis, by taking advantage of the symmetry of the matrix arising from electric field integral equation. Numerical experiments show that the higher order MLFMA is more efficient than its low-order counterpart.
"An Efficient High Order Multilevel Fast Multipole Algorithm for Electromagnetic Scattering Analysis," Progress In Electromagnetics Research,
Vol. 126, 85-100, 2012. doi:10.2528/PIER12020203
1. Peterson, A. F., S. L. Ray, and R. Mittra, Computational Methods for Electromagnetics, IEEE Press, Piscataway, NJ, 1998.
2. Rao, S. M., D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas Propag., Vol. 30, No. 3, 409-418, May 1982. doi:10.1109/TAP.1982.1142818
3. Kolundzija, B. M. and B. D. Popovic, "Entire-domain Galerkin method for analysis of metallic antennas and scatterers," IEE Proceedings - H, Vol. 140, No. 1, 1-10, Feb. 1993.
4. Donepudi, K. C., "A novel implementation of multilevel fast multipole algorithm for higher order Galerkin's method," IEEE Trans. Antennas Propag., Vol. 48, 1192-1197, Aug. 2000.
5. Donepudi, K. C., J. M. Jin, S. Velamparambil, J. Song, and W. C. Chew, "A higher order parallelized multilevel fast multipole algorithm for 3-D scattering," IEEE Trans. Antennas Propag., Vol. 49, No. 7, 1069-1078, Jul. 2001. doi:10.1109/8.933487
6. Notaros, B. M., "Higher order frequency-domain computational electromagnetics," IEEE Trans. Antennas Propag., Vol. 56, No. 8, 2251-2276, Aug. 2008. doi:10.1109/TAP.2008.926784
7. Liu, Z.-L. and J. Yang, "Analysis of electromagnetic scattering with higher-order moment method and NURBS model," Progress In Electromagnetics Research, Vol. 96, 83-100, 2009. doi:10.2528/PIER09071704
8. Eibert, T. F., Ismatullah, E. Kaliyaperumal, and C. H. Schmidt, "Inverse equivalent surface current method with hierarchical higher order basis functions, full probe correction and multi-level fast multipole acceleration," Progress In Electromagnetics Research, Vol. 106, 377-394, 2010. doi:10.2528/PIER10061604
9. Zhang, H.-W., X.-W. Zhao, Y. Zhang, D. Garcia-Donoro, W.-X. Zhao, and C.-H. Liang, "Analysis of a large scale narrow-wall slotted waveguide array by parallel MoM out-of-core solver using the higher order basis functions," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 14-15, 1953-1965, 2010.
10. 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. doi:10.1163/156939311794827285
11. Klopf, E. M., S. B. Manic, M. M. Ilic, and B. M. Notaros, "Efficient time-domain analysis of waveguide discontinuities using higher order FEM in frequency domain," Progress In Electromagnetics Research, Vol. 120, 215-234, 2011.
12. Song, J. M., C. C. Lu, and W. C. Chew, "Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects," IEEE Trans. Antennas Propag., Vol. 45, No. 10, 1488-1493, Oct. 1997. doi:10.1109/8.633855
13. Chew, W. C., J. M. Jin, E. Michielssen, and J. Song, Fast E±cient Algorithms in Computational Electromagnetics, Artech House, Boston, MA, 2001.
14. 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 Propag., Vol. 52, No. 9, 2277-2287, Sep. 2004. doi:10.1109/TAP.2004.834084
15. Carpentieri, B., I. S. Duff, L. Griud, and G. Sylvand, "Combing fast multipole techniques and an approximate inverse preconditioner for large electromagnetism calculations," SIAM J. Sci. Comput. , Vol. 27, No. 3, 774-792, 2005. doi:10.1137/040603917
16. 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, 158-175, 2003. doi:10.1016/S0021-9991(02)00052-9
17. Malas, T. and L. Guirel, "Incomplete LU preconditioning with the multilevel fast multipole algorithm for electromagnetic scattering," SIAM J. Sci. Comput., Vol. 29, No. 4, 1476-1494, 2007. doi:10.1137/060659107
18. Pan, X.-M. and X.-Q. Sheng, "A highly efficient parallel approach of multi-level fast multipole algorithm," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 8, 1081-1092, 2006. doi:10.1163/156939306776930321
19. Pan, X. M. and X. Q. Sheng, "A sophisticated parallel MLFMA for scattering by extremely large targets," IEEE Antennas Propag. Mag., Vol. 50, No. 3, 129-138, Jun. 2008. doi:10.1109/MAP.2008.4563583
20. Chow, E., "Parallel implementation and practical use of sparse approximate inverse preconditioners with a priori sparsity patterns," Intl. J. High Perf. Comput. Appl., Vol. 15, No. 1, 56-74, Feb. 2001. doi:10.1177/109434200101500106