Maxwell方程反演的小波多尺度方法

丁亮; 韩波; 刘家琦

doi:10.3879/j.issn.1000-0887.2009.08.010

Maxwell方程反演的小波多尺度方法

doi: 10.3879/j.issn.1000-0887.2009.08.010

哈尔滨工业大学理学院数学系, 哈尔滨 150001

详细信息

作者简介:
丁亮(1979- ),男,黑龙江泰来人,博士生(Tel:+86-451-82113465;E-mail:iamashen@yahoo.com.cn);韩波,教授,博士(联系人.E-mail:bohan@hit.edu.cn).

中图分类号: O157.2;O357
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出版历程
- 收稿日期: 2008-12-27
- 修回日期: 2009-06-29
- 刊出日期: 2009-08-15

Wavelet Multiscale Method for the Inversion of Maxwell’s Equation

Department of Mathematics, School of Science, Harbin Institute of Technology, Harbin 150001, P. R. China

摘要

摘要: 研究Maxwell方程电导率的识别问题．主要的难点是目标函数中存在一些局部极小值．将小波多尺度方法应用到Maxwell方程反演过程，通过小波变换，反问题被分解到多个尺度上，于是原反问题可以在子一级的尺度上，由大尺度到小尺度逐级求解．在每个尺度上我们采用稳定、快速的Gauss-Newton迭代法．数值算例的结果显示了这种方法大范围收敛、计算效率高、结果准确，是一种可行的计算方法．
- Maxwell方程 /
- 小波多尺度方法 /
- 反演 /
- 正则Gauss-Newton方法 /
- 时域有限差分(FDTD)方法
Abstract: The estimation of the electrical conductivity in Maxwell's equation is concerned with. The primary difficulty is the presence of numerous local minima in the objective functional. A wavelet multiscale method was introduced and applied to the inversion of Maxwell equations. The inverse problem was then decomposed to multiple scales by wavelet transform and hence the original inverse problem was reformulated to a set of subinverse problems corresponding to different scales solved successively according to the size of scale from the shortest to the longest. On each scale, the stable and fast regularized Gauss-Newton method was carried out. The results of numerical simulation showed that this method is an available method, especially on aspects of wide convergence, computational efficiency and precision.
- Maxwell’s equation /
- wavelet multiscale method /
- inversion /
- regularized Gauss-Newton method /
- FDTD(finite difference time domain) method

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参考文献(18)

[1]	Alumbaugh D L,Newman G A.3D massively parallel electromagnetic inversion—part B:analysis of a cross well experiment[J].Geophys J Int,1997,128:355-363. doi: 10.1111/j.1365-246X.1997.tb01560.x
[2]	Newman G A,Recher S,Tezkan B,et al.3D inversion of a scalar radio magnetotelluric field data set[J].Geophys,2003,68(3):782-790. doi: 10.1190/1.1581031
[3]	Ascher U M,Haber E.A multigrid method for distributed parameter estimation problem[J].Electron Trans Numer Anal,2003,15:1-17.
[4]	Baboolal S,Bharuthram R.Two-scale numerical solution of the electromagnetic two-fluid plasma-Maxwell equations:shock and soliton simulation[J].Mathematics and Computers in Simulation,2007,76(1/3):3-7. doi: 10.1016/j.matcom.2007.01.004
[5]	Haber E.Quasi-Newton methods for large-scale electromagnetic inverse problems[J].Inverse Problems,2005,21(1):305-323. doi: 10.1088/0266-5611/21/1/019
[6]	HE Sai-ling,Weston V H.Wave-splitting and absorbing boundary condition for Maxwell's equations on a curved surface[J].Mathematics and Computers in Simulation,1999,50(5/6):435-455. doi: 10.1016/S0378-4754(99)00097-X
[7]	Dorn O,Aguirre H B,Berryman J G,et al.A nonlinear inversion method for 3D electromagnetic imaging using adjoint fields[J].Inverse Problems,1999,15(6):1523-1558. doi: 10.1088/0266-5611/15/6/309
[8]	Farquharson C G.,Oldenburg D W,Li Y G.An approximate inversion algorithm for time-domain electromagnetic surveys[J].Journal of Applied Geophysics,1999,42(2):71-80. doi: 10.1016/S0926-9851(99)00023-3
[9]	Cohen A,Hoffmann M,Reiss M.Adaptive wavelet Galerkin methods for linear inverse problems[J].SIAM J Numer Anal,2004,42(4):1749-1501.
[10]	Dicken V,Maass P.Wavelet Galerkin methods for ill-posed problems[J].J Inverse and Ill-Posed Problems,1996,4(3):203-222.
[11]	FU Chun-li,ZHU You-bin,QIU Chun-yu.Wavelet regularization for an inverse heat conduction problem[J].J Math Anal Appl,2003,288(1):212-222. doi: 10.1016/j.jmaa.2003.08.003
[12]	LIU Jun.A multiresolution method for distributed parameter estimation[J].SIAM J Sci Comput,1993,14(2):389-405. doi: 10.1137/0914024
[13]	FU Hong-sun,HAN Bo.A wavelet multiscale method for the inverse problems of a two-dimentional wave equation[J].Inverse Problems in Science and Engineering,2004,12:643-656. doi: 10.1080/10682760410001694203
[14]	Bunks C,Saleck F M,Zaleski S,et al.Multiscale seismic waveform inversion[J].Geophysics,1995,60(5):1457-1473. doi: 10.1190/1.1443880
[15]	Yee K S.Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media[J].IEEE Transactions on Antennas and Propagation,1996,14(3):302-308.
[16]	Farquharson C,Oldenburg D.Non-linear inversion using general measures of data misfit and model structure[J].Geophysics,1998,134(1):213-227.
[17]	Huber P J.Robust estimation of a location parameter[J].Ann Math Stats,1964,35(1):73-101. doi: 10.1214/aoms/1177703732
[18]	Haber E,Ascher U,Oldenburg D.On optimization techniques for solving non-linear inverse problems[J].Inverse Problems,2000,16(5):1263-1280. doi: 10.1088/0266-5611/16/5/309