In this paper, the localized pseudo-skeleton approximation (LPSA) method for electromagnetic analysis on electrically large structures is presented. The proposed method seeks the low rank representations of far-field coupling matrices by using pseudo-skeleton approximations (PSA). By using PSA, only part of the original matrix is needed to be calculated and stored which is very similar to the adaptive cross approximation (ACA). Moreover, rank approximation and index finding schemes are given to improve the performance of the method in this paper. Several numerical results are given to demonstrate that the proposed method performs better than the randomized pseudo-skeleton approximation (RPSA) and ACA.
2. Song, J. M. and W. C. Chew, "Multilevel fast-multipole algorithm for solving combined field integral equations of electromagnetic scattering," Microwave Opt. Technol. Lett., Vol. 10, No. 1, 14-19, Sep. 1995.
3. Bebendorf, M., "Approximation of boundary element matrices," Numer. Math., Vol. 86, No. 4, 565-589, 2000.
4. Brick, Y., V. Lomakin, and A. Boag, "Fast direct solver for essentially convex scatterers using multilevel non-uniform grids," IEEE Trans. Antennas Propag., Vol. 62, 4314-4324, 2014.
5. Wei, J.-G., Z. Peng, and J.-F. Lee, "Multiscale electromagnetic computations using a hierarchical multilevel fast multipole algorithm," Radio Science, Vol. 49, 1022-1040, 2014.
6. 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 Science, Vol. 47, RS1011, Feb. 2012.
7. Zhu, X. and W. Lin, "Randomised pseudo-skeleton approximation and its application in electromagnetics," Electronics Letters, Vol. 47, No. 10, 590-592, 2011.
8. Goreinov, S. A., N. L. Zamarashkin, and E. E. Tyrtyshnikov, "Pseudoskeleton approximations by matrices of maximal volume," Math. Notes, Vol. 62, No. 4, 515-519, 1997.
9. Chai, W. and D. Jiao, "Theoretical study on the rank of integral operators for broadband electromagnetic modeling from static to electrodynamic frequencies," IEEE Transactions on Components, Packaging and Manufacturing Technology, Vol. 3.12, 2113-2126, 2013.
10. Rao, S. M., D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas Propag., Vol. 30, 409-418, May 1982.
11. Lee, J, J. Zhang, and C. C. Lu, "Sparse inverse preconditioning of multilevel fast multipole algorithm for hybrid integral equations electromagnetics," IEEE Trans. Antennas Propag., Vol. 52, No. 9, 2277-2287, Sep. 2004.