反演开弧的一种方法A method of reconstructing the open crack
张磊;王连堂;
摘要(Abstract)：
利用最小化方法对含未知边界的不适定方程组进行正则化处理,然后依次迭代更新边界和相应的密度函数,最终得到反演的边界.给出一些数值例子以表明这种方法是有效的和可行的。
关键词(KeyWords)： 牛顿迭代法;最小化;反散射
基金项目(Foundation):
作者(Authors): 张磊;王连堂;
参考文献(References)：
- [1]Kress R.Inverse scattering from an open arc math[J].Methods Appl.Sci.,1995,18(4):267-293.
- [2]Kress R,Serranho P.A hybrid method for two-dimensional crack reconstruction[J].Inverse Problems,2005,21(2):773-784.
- [3]Lee K M.Inverse scattering via nonlinear integral equations for a Neumann crack[J].Inverse Problems,2006,22(6):1989-2000.
- [4]Ivanyshyn O,Johansson T.Boundary integral equations for acoustical inverse sound-soft scattering[J].Journalof Inverse and Ill-Posed Problems,2008,16:65-78.
- [5]Ivanyshyn O,Kress R.Inverse scattering for planar cracks via nonlinear integral equations[J].Math.Meth.Appl.Sci.,2008,31:1221-1232.
- [6]Kress R,Sloan I H.On the numerical solution of a logarithmic integral equation of the first kind for theHelmholtz equation[J].Numer.Math.,1993,66:199-214.
- [7]Colton D,Kress R.Inverse Acoustic and Electromagnetic Scattering Theory[M].Berlin:Springer,1992.
- [8]Kress R.Linear Integral Equations[M].Berlin:Springer,1989.