洞穴逆散射问题解的惟一性与局部稳定性

时谐电磁波入射到基面内任意形状的开洞上,此过程数学上可由Maxwell方程组来描述.研究了逆散射问题,即利用散射场的信息来确定开洞的形状. 证明了二维TM极化情形时逆散射问题的惟一性和局部稳定性.     

解洞穴逆散射问题的一种正则化Newton方法

We consider the inverse problem to determine the shape of a open cavity embedded in the infinite ground plane from knowledge of the far-field pattern of the scattering of TM polarization.For its approximate solution we propose a regularized Newton iteration scheme.For a foundation of Newton type methods we establish the Fréchet differentiability of solution to the scattering problem with respect to the boundary of the cavity.Some numerical examples of the feasibility of the method are presented.     

解第一类算子方程的一种迭代正则化方法

提出了一种求解第一类算子方程的新的迭代正则化方法,并依据广义Arcangeli方法选取正则参数,建立了正则解的收敛性.与通常的Tikhonov正则化方法相比较,提高了正则解的渐近阶估计.     

求解二维热传导方程侧边值问题的小波正则化方法的误差估计

本文考虑R₊² 上的二维热传导方程的侧边值问题, 这是一个不适定问题. 利用正交多尺度分析 生成Meyer 小波这一工具, 我们提出了一种正则化方法. 这一想法源于Meyer 小波的Fourier 变换具 有紧支集, 这意味着可以使用其防止高频噪声污染问题的解. 本文的主要结果是定理4.2, 它给出了精 确解与截断解(即小波正则解) 之间的误差估计. 这里的截断通过对测量数据f 设定限制以及逐层离 散完成.     

A Regularized Newton Method in Inverse Scattering Problem from Cavities

We consider the inverse problem to determine the shape of a open cavity embedded in the infinite ground plane from knowledge of the far-field pattern of the scattering of TM polarization.For its approximate solution we propose a regularized Newton iteration scheme.For a foundation of Newton type methods we establish the Fréchet differentiability of solution to the scattering problem with respect to the boundary of the cavity.Some numerical examples of the feasibility of the method are presented.     

解带有扰动数据的第一类Volterra积分方程的谱正则化方法

该文的主要目的是通过使用Legendre配置方法和正则化策略来求解带有噪声数据的第一类Volterra积分方程,并给出该方法收敛性分析的严格数学证明.数值实验表明了该方法的有效性.     

A Sampling Method for Solving Inverse Scattering Problems with a Locally Perturbed Half Plane

In this paper,we will consider the scattering of time—harmonic electromagnetic waves by aninfinitely long cylinder with a perfectly conducting boundary.The problem is modelled by aDirichlet problem for the Helmholtz equation.Adopting Cartesion coordinates(Xl,X2,X3)in础we assume that the boundary is the XlX3一plane with the perturbation independent of z3and local with respect to X1.Furthermore,we assume that the elect:tic and magnetic fieldsare invariant with respect to X3 and we restrict …     

Poisson方程反问题的惟一性和稳定性

考虑Poisson方程ψ''''=-e^v-ψ+e^ψ-v-N(x) 的Dirichlet边值问题. 主要研究从一个带有参数的函数类中确定未知函数$N(x)$的反问题, 得到了某些唯一性和稳定性结论.