Inverse scattering for planar cracks via nonlinear integral equations
Inverse scattering for planar cracks via nonlinear integral equations
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DOI：
10.1002/mma.970
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发表时间：
2008-07
影响因子：
2.9
通讯作者：
O. Ivanyshyn;R. Kress
中科院分区：
文献类型：
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作者：
O. Ivanyshyn;R. Kress
我们提出了一种牛顿型方法，用于从平面波入射的一次谐波散射的远场测量中重建平面声软或完全传导裂纹。我们的方法源于Kress和Rundell （Inv. Probl. 2005; 21(4): 1207-1223）提出的求解拉普拉斯方程反边值问题的方法。它被扩展到声软障碍物的逆散射问题（散射理论和生物医学工程中的数学方法）。世界科学：新加坡，2006；39-50)和声硬裂纹（invv . Probl. 2006; 22(6)）。在这两种情况下，都表明该方法对噪声数据具有准确的重建和合理的稳定性。该方法是基于对未知边界的非线性和不适定积分方程。积分方程通过线性化，即正则牛顿迭代求解。数值重建验证了该方法的可行性。版权所有©2007 John Wiley & Sons， Ltd
We present a Newton‐type method for reconstructing planar sound‐soft or perfectly conducting cracks from far‐field measurements for one time‐harmonic scattering with plane wave incidence. Our approach arises from a method suggested by Kress and Rundell (Inv. Probl. 2005; 21(4):1207–1223) for an inverse boundary value problem for the Laplace equation. It was extended to inverse scattering problems for sound‐soft obstacles (Mathematical Methods in Scattering Theory and Biomedical Engineering. World Scientific: Singapore, 2006; 39–50) and for sound‐hard cracks (Inv. Probl. 2006; 22(6)). In both cases it was shown that the method gives accurate reconstructions with reasonable stability against noisy data. The approach is based on a pair of nonlinear and ill‐posed integral equations for the unknown boundary. The integral equations are solved by linearization, i.e. by regularized Newton iterations. Numerical reconstructions illustrate the feasibility of the method. Copyright © 2007 John Wiley & Sons, Ltd.