精确快速计算时域积分方程中奇异性积分的新方法

赵延文; 徐建华; 聂在平; 武胜波

精确快速计算时域积分方程中奇异性积分的新方法

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出版历程
- 收稿日期: 2004-05-26
- 修回日期: 2004-11-15
- 刊出日期: 2005-11-19

A New Scheme for Accurate and Efficient Evaluation of Singular Integral of Time-Domain Integral Equation

摘要

摘要: 该文首先利用参数坐标和广义Duffy坐标变换将时域电场积分方程(TDEFIE)的奇异性积分转换成非奇异性积分，然后根据时间基函数的特点将该积分转换成可以快速精确计算的分区域积分。数值计算实例表明，该方法可以大幅度提高求解TDEFIE的后时稳定性和解的精度，而不必采用任何求平均的过程。该方法适用于任意类型的时间基函数并可方便地推广到高阶曲面拟合和高阶空间基函数情形。
- 时域电磁散射;时域积分方程;时间步进算法;奇异性积分
Abstract: In this article, the transformations of the parametric coordinates (i.e. area coordinates) and general Duffycoordinates are employed to transform the singular integrals of the Time-Domain Electric Field Integral Equation (TDEFIE) into non-singular integrals, which can be accurately and efficiently evaluated by dividing the transformed domain of integration into sub-domains. Simulation results demonstrate that this approach seems to drastically improve stability and accuracy of the numerical results without resort to any averaging processes. The proposed method is suitable to any causal temporal basis functions and can be extended to curvilinear patch and high-order spatial basis functions in a straightforward way.

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参考文献(1)

Vechinski D, Rao S M. A stable procedure to calculate the transient scattering by conducting surfaces of arbitrary shape. IEEE Trans. on AP, 1992, AP-40(6): 661-665.[2]Davies P J, Duncan D B. Averaging techniques for time-marching schemes for retarded potential integral equations[J].Appl. Numer. Math.1997, 23:291-310[3]Weile D S, Pisharody G , Chen N W, Shanker B, Michielssen E. A novel schemes for the solution of the time domain integral equations of electromagnetics[J].IEEE Trans. on AP.2004, 52(1):283-295[4]Manara G, Monorchio A, Reggiannini R. A space-time discretization criterion for a stable time-marching solution of the electric field integral equation. IEEE Trans. on AP, 1997, AP-45(3): 527-532.[5]Hu J L, Chan C H. A new temporal basis function for the time-domain integral equation method[J].IEEE Wireless Components Letters.2001, 11(11):465-466[6]Bluck M J, Walker S P. Time-domain BIE analysis of large three-dimensional electromagnetic scattering problems. IEEE Trans. on AP, 1997, 45(5): 894-901.[7]Lu M, Michielsson E. Closed form evaluation of time domain fields due to Rao-Wilton-Glisson sources for use in matching-on- in-time based EFIE solvers. IEEE APS Int. Symp. Dig., San Antonio, 2002: 74-77.[8]Shanker B, Ergin A A, Aygun K, Michielsson E. Analysis of transient electromagnetic scattering from closed surfaces using a combined field integral quation. IEEE Trans. on AP, 2000, AP-48(7): 1064-1074.[9]Rao S M, Wilton D R. Transient scattering by conducting surfaces of arbitrary shape. IEEE Trans. on AP, 1991, AP-39(1): 56-61.[10]Graglia R D. On the numerical integration of the linear shape functions times the 3-D Greens function or its gradient on a plane triangle. IEEE Trans. on AP, 1993, AP-41(10): 1448-1455.[11]Duffy M G. Quadrature over a pyramid or cube of integrands with a singularity at a vertex[J].SIAM J. Numer. Anal.1982, 19(6):1260-1262[12]Vechinski D A, Rao S M, Sarkar T K. Transient scattering from three-dimensional arbitrary shaped dielectric bodies. J. Opt.Soc[13]Amer. A, Opt. Image Sci., 1994, 11(4): 1458-1470.

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