An Improved Combination of IE-ODDM and MLFMA
Keywords:
Improved combined method, method of moments, multilevel fast multipole algorithm, overlapped domain decomposition method of integral equationsAbstract
Domain decomposition methods are efficient for analyzing scattering problems with large-scale structures. In the present paper, an improved combination of Overlapped Domain Decomposition Method of Integral Equations (IEODDM) and Multilevel Fast Multi-pole Algorithm (MLFMA) is developed. Amount of independent MLFMA progresses of sub-domains are departed and re-integrated, such that the total CPU time of coupled effects in IE-ODDM can be saved. The proposed method developed minimal-completed sub-trees of sub-domains to reduce redundant aggregations of the MLFMA process blended in IEODDM. Numerical results and comparisons with the original method are provided, which suggest that the proposed combination integrates MLFMA with IE-ODDM better than the original combined method, and it can greatly improve the computational efficiency of coupled effects in IEODDM.
Downloads
References
R. F. Harrington, “Field computation by moment method,” New York: McMillan, 1968.
N. Engheta, W. D. Murphy, V. Rokhlin, et.al., “The fast multipole method (FMM) for electromagnetic scattering problems,” IEEE Trans. Antennas Propag., vol. 40, pp. 634-641, 1992.
J. M. Song and W. C. Chew, “Multilevel fast multipole algorithm for solving combined field integral equations of electromagnetic scattering,” Microwave Opt. Technol. Lett., vol. 10, pp. 14-19, 1995.
J. M. Song, C. C. Lu, and W. C. Chew, “Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects,” IEEE Trans. Antennas Propag., vol. 45, pp. 1488-1493, 1997.
E. Bleszybski, M, Bleszynski, and T. Jaroszewicz, “AIM: adaptive integral method for solving largescale electromagnetic scattering and radiation problems,” Radio Science, vol. 31, pp. 1225-1251, 1996.
Y. Zhang, D. Huang, and J. Chen, “Combination of asymptotic phase basis functions and matrix interpolation method for fast analysis of monostatic RCS,” Applied Computational Electromagnetics Society (ACES) Journal, vol. 28, pp. 49-56, 2013.
N. Carpentieri, Y. F. Jing, T. Z. Huang, W. C. Pi, and X. Q. Sheng, “Combining the CORS and BiCORSTAB iterative methods with MLFMA and SAI preconditioning for solving large linear systems in electromagnetics,” Applied Computational Electromagnetics Society (ACES) Journal, vol. 27, pp. 102-111, 2012.
Z. N. Jiang, R. S. Chen, Z. H. Fan, S. G. Shen, and X. Q. Hu, “Efficient multilevel compressed block decomposition for large-scale electromagnetic problems using asymptotic phasefront extraction,” Applied Computational Electromagnetics Society (ACES) Journal, vol. 26, pp. 876-885, 2011.
M. Chen, R. Chen, Z. Fan, and D. Ding, “Accelerating the multilevel fast multipole method with parallel preconditioner for large-scale scattering problems,” Applied Computational Electromagnetics Society (ACES) Journal, vol. 26, pp. 815-822, 2011.
Z. N. Jiang, Z. H. Fan, D. Z. Ding, R. S. Chen, and K. W. Leung, “Preconditioned MDA-SVDMLFMA for analysis of multi-scale problems,” Applied Computational Electromagnetics Society (ACES) Journal, vol. 25, pp. 914-925, 2010.
H. Fangjing, N. Zaiping, and H. Jun, “An efficient parallel multilevel fast multipole algorithm for large-scale scattering problems,” Applied Computational Electromagnetics Society (ACES) Journal, vol. 25, pp. 381-387, 2010.
M. R. Pino, et al., “The generalized forwardbackward method for analyzing the scattering from targets on ocean-like rough surfaces,” IEEE Trans. Antennas Propag., vol. 47, pp. 961-969, 1999.
C. Brennan, P. Cullen, and M. Condon, “A novel iterative solution of three dimensional electric field integral equation,” IEEE Trans. Antennas Propag., vol. 52, pp. 2781-2784, 2004.
W. D. Li, W. Hong, and H. X. Zhou, “Integral equation-based overlap domain decomposition method for the analysis of electromagnetic scattering of 3D conducting object,” Microwave Opt. Technol. Lett., vol. 49, pp. 265-274, 2007.
J. Hu, W. Hong, H. X. Zhou, W. D. Li, and Z. Song, “An overlapped domain decomposition method for solving electromagnetic surface integral equations,” International Conference on Computational Problem-Solving (ICCP), Lijiang, pp. 1-4, 2010.
W. D. Li, W. Hong, and H. X. Zhou, “An IEODDM-MLFMA scheme with DILU preconditioner for analysis of electromagnetic scattering from large complex objects,” IEEE Trans. Antennas Propag., vol. 56, pp. 1368-1380, 2008.
W. D. Li, W. Hong, and H. X. Zhou, “A cube-based scheme of IE-ODDM-MLFMA for electromagnetic scattering problems,” IEEE Antennas and Wireless Propagation Letters, vol. 8, pp. 630-633, 2009.
J. Chen, S. Li, and Y. Song, “Analysis of electromagnetic scattering problems by means of a VSIE-ODDM-MLFMA method,” Applied Computational Electromagnetics Society (ACES) Journal, vol. 27, pp. 660-667, 2012.
A. A. Kucharski, “Efficient solution of integralequation based electromagnetic problems with the use of macromodels,” IEEE Trans. on Antennas Propag., vol. 56, pp. 1482-1487, 2008.
L. Carin, “Fast electromagnetic solvers for largescale naval scattering problem,” Final Report for Office of Naval Research, September 2008.
P. Yla-Oijala and M. Taskinen, “Electromagnetic scattering by large and complex structures with surface equivalence principle algorithm,” Waves in Random and Complex Media, vol. 19, pp. 105-125, 2009.
L. M. Jaime, “Técnicas de descomposición de dominios con ecuación integral para el análisis eficiente de problemsas electromagnéticos,” Tesis Doctoral, Universidad De Oviedo, April 2010.
J. A. Kong, “Electromagnetic wave theory,” New York: Wiley, 1981.
S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag., vol. 3, pp. 409-418, 1982.