计算电大尺寸目标物理光学散射场的快速算法
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摘要
针对电大尺寸目标高频散射场的仿真,采用物理光学(physics optics,PO)算法来求解.由于PO积分为高振荡积分,传统的数值求积方法非常耗时,文中提出了数值最速下降路径(numerical steepest descent path method,NSDP)算法来计算.首先,通过对振幅函数和相位函数二次拉格朗日函数插值,得到二次曲面片上PO积分标准形式.其次,通过变换积分路径,将高振荡PO积分转化为最速下降路径上的积分,大大减少了计算复杂度.NSDP算法进一步将PO积分转变为驻相点、谐振点和顶点的贡献,具有鲜明的物理意义.数值算例证明了NSDP算法具有精度误差可控和频率无关的特性.
In this paper,we adopt the physical optics(PO)method to obtain the high frequency scattered fields from electrically large scatterers.Because the PO integral is highly oscillatory,the conventional quadrature rules like Gauss quadrature rule is very time-consuming.Hence,we propose a numerical steepest descent path method(NSDP)to handle this problem.We use the Lagrange interpolation method to get the quadratic amplitude and phase functions.Then,we transform the highly oscillatory integrand into a smooth and rapidly decreasing function by distorting the integral paths.This method greatly reduce the computational workload than brute force method.The NSDP method could divide the PO integral into several critical points contributions like stationary phase points,resonance points and vertex points in physical insights.The numerical results demonstrate that this method has advantages of error-controllable and frequency-independent.
In this paper,we adopt the physical optics(PO)method to obtain the high frequency scattered fields from electrically large scatterers.Because the PO integral is highly oscillatory,the conventional quadrature rules like Gauss quadrature rule is very time-consuming.Hence,we propose a numerical steepest descent path method(NSDP)to handle this problem.We use the Lagrange interpolation method to get the quadratic amplitude and phase functions.Then,we transform the highly oscillatory integrand into a smooth and rapidly decreasing function by distorting the integral paths.This method greatly reduce the computational workload than brute force method.The NSDP method could divide the PO integral into several critical points contributions like stationary phase points,resonance points and vertex points in physical insights.The numerical results demonstrate that this method has advantages of error-controllable and frequency-independent.
引文
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[16]邹宁,杨杨,吴语茂.光滑曲面上测地线射线寻迹算法及爬行波计算[J].太赫兹科学与电子信息学报,2017,15(5):745-751.ZOU N,YANG Y,WU Y M.Geodesic ray tracing algorithm and calculation of traveling wave on smooth surface[J].Journal of Terahertz science and electronic information technology,2017,15(5):745-751.(in Chinese)
[17]杨杨,朱劼,邹宁,等.电大凸目标电磁散射的数值路径变换算法研究[J].电波科学学报,2017,32(2):199-206.YANG Y,ZHU J,ZOU N,et al.Numerical contour deformation method for calculating the scattered field from the electrically large convex scatterers[J].Chinese journal of radio science,2017,32(2):199-206.(in Chinese)
[18]UFIMTSEV P.Fundamentals of the physical theory of diffraction[M].Hoboken:Wiley,2007.
[2]PENNEY C W,LUEBBERS R J,SCHUSTER J W.Scattering from coated targets using a frequency-dependent,surface impedance boundary condition in FDTD[J].IEEE transactions on antennas and propagation,1996,44(4):434-443.
[3]JIN J M.The finite element method in electromagnetics[M].Hoboken:John Wiley&Sons,2015.
[4]KLINE M,KAY I.Electromagnetic theory and geometrical optics[M].New York:Interscience,1965.
[5]KELLER J B.Geometrical theory of diffraction[J].JOSA,1962,52(2):116-130.
[6]KOUYOUMJIAN R G,PATHAK P H.A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface[J].Proceedings of the IEEE,1974,62(11):1448-1461.
[7]UFIMTSEV P.New insight into the classical macdonald physical optics approximation[J].IEEE antennas&propagation magazine,2008,50(3):11-20.
[8]UFIMTSEV P.Elementary edge waves and the physical theory of diffraction[J].Electromagnetics,1991,11(2):125-160.
[9]GORDON W B.Far-field approximations to the Kirchoff-Helmholtz representations of scattered fields[J].IEEE transactions on antennas and propagation,1975,23(4):590-592.
[10]LUDWING A.Computation of radiation patterns involving numerical double integration[J].IEEE transactions on antennas and propagation,2002,16(6):767-769.
[11]KOUYOUMJIAN R G.Asymptotic high-frequency methods[J].Proceedings of the IEEE,1965,53(8):864-876.
[12]MCCLURE J P,WONG R.Two-dimensional stationary phase approximation:stationary point a a corner[J].SIAM journal on mathematical analysis,1991,22(1):500-523.
[13]BOUCHE D,MOLINET F,MITTRA R.Asymptotic methods in electromagnetics[M].Berlin:Springer,1997.
[14]RIUS J M,FERRANDO M,JOFRE L.GRECO:graphical electromagnetic computing for RCS prediction in real time[J].IEEE transactions on antennas and propagation,1993,35(2):7-17.
[15]MACDONALD H M.The effect produced by an obstacle on a train of electric waves[J].Philosophical transactions of the Royal Society of London,1913,212(484-496):299-337.
[16]邹宁,杨杨,吴语茂.光滑曲面上测地线射线寻迹算法及爬行波计算[J].太赫兹科学与电子信息学报,2017,15(5):745-751.ZOU N,YANG Y,WU Y M.Geodesic ray tracing algorithm and calculation of traveling wave on smooth surface[J].Journal of Terahertz science and electronic information technology,2017,15(5):745-751.(in Chinese)
[17]杨杨,朱劼,邹宁,等.电大凸目标电磁散射的数值路径变换算法研究[J].电波科学学报,2017,32(2):199-206.YANG Y,ZHU J,ZOU N,et al.Numerical contour deformation method for calculating the scattered field from the electrically large convex scatterers[J].Chinese journal of radio science,2017,32(2):199-206.(in Chinese)
[18]UFIMTSEV P.Fundamentals of the physical theory of diffraction[M].Hoboken:Wiley,2007.