求解二维多区域声波散射问题的边界元方法

对于多散射区域的声波散射问题的外Neumann边值问题,用单层位势来逼近每个散射域上的散射波,再利用位势理论的跳跃关系将问题转换为第二类边界积分方程组的求解问题,然后用Nystrom方法进行了求解.对多个随机散射区域的声波散射问题,数值例子体现了该求解方法的可行性和准确性.     

利用正则化方法求解浅海声波散射问题

讨论了浅海中波导的声波散射问题，我们将该问题归结为一个第一类边界积分方程，利用正同化方法求解，并证明了该方法的收敛性，数值例子表明了该方法的简单与有效性。     

一个声波散射区域的重建方法与唯一性定理

一个声波散射区域的重建方法与唯一性定理@王连堂...     

关于声波障碍反散射问题

综述了声波障碍反散射问题的历史发展，对时间调和声波的障碍反散射问题，论述了前人的一些成果及需要解决的一些问题。     

直角平面内圆孔对稳态SH波的散射

利用复变函数方法和多极坐标移动技术，研究了直角平面内圆孔在直边分布有反平面稳态载荷时的sH波散射问题．首先构造出直角平面内不含有圆孔时满足边界应力条件的Green函数解；其次提出直角平面内存在圆孔时满足边界应力自由条件的散射波解，并利用叠加原理写出问题的位移总波场．借助于多极坐标移动技术和圆孔边界处应力自由条件，列出求解散射波解中未知系数的无穷代数方程组，在满足计算精度的前提下，通过有限项截断进行求解．作为算例，具体讨论了圆孔边界处的环向动应力随不同波数、圆孔位置及载荷分布位置和分布范围大小的变化情况，算例结果说明了算法的有效实用性．     

表面局部开裂圆柱夹塞物对SH型导波的散射

建立了平板波导中表面局部开裂圆柱夹塞物对SH型导波散射问题的解.用两个垂直于波导表面的虚拟平面将波导分割为3个区域.在包含夹塞物的中间区域,将波场展开为柱面波模式和Chebyshev多项式的叠加;在不含夹塞物的其余两个区域,将波场展开为导波模式的叠加.根据波导表面上应力自由的边界条件及虚拟平面上应力和位移连续的边界条件得到了待求解问题的基础方程组.利用模式匹配技术构造数值计算所需的矩阵方程,从而得到反射及透射系数随圆柱体归一化半径和脱黏区域大小变化的关系曲线.对圆柱表面完好黏结和脱黏区段不同大小的情况作了对比,对结果作了讨论.     

任意形状凸起地形对平面SH波的散射

将具有任意形状的凸起地形对称态SH波散射问题转换为契合问题加以研究,利用求解弹性波动问题的复变函数与保角映射方法,在包括任意形状凸起边界在内的一个区域中,构造一个在凸起边界上应力自由,其他部分位移和应力均为任意的驻波解,然后再将这个驻波解与其余下的区域中的散射波解在两个区域结合面上完成契合过程,由此决定出这两个区域中的驻波和散射波解答,最后对圆弧形和半椭圆形凸起进行了数值计算,并将计算结果与有限元法的数值解进行了比较。     

半空间反射弹性波多参数线性化逆散射

研究了BORN近似条件下的半空间中弹性波方程的多参数反演问题.采用宽带点源表面激发和接收扫描方案,建立了一个同时重构介质密度和拉梅参数的反演方法,证明了表面垂直和水平脉冲激发的散射场可以分解成P→P波、P→S波、S→P波及S→S波4类散射成分,其中包含着重建目标体参数分布所需的信息,所得到的参数重建显示表达式具有滤波反传播的形式.     

利用散射波远场模第P个傅立叶系数重建声波阻尼系数

阐述了利用声波散射远场模Fourier展开的第P个傅立叶系数（声散射远场模的不完全信息）,重建声阻抗系数的一种非线性最优化方法．并给出了该方法收敛性的证明,其数值例子说明这种方法的有效性和可行性．     

具有未知阻尼边界的逆散射问题解的惟一性及重构

考虑R3中的散射体D在阻尼边界条件下由散射波的远场形式重建散射体边界的逆散射问题. 证明了该反问题解的惟一性, 并给出了确定边界形状的精确的反演方法．由于边界阻尼是未知的, 这预示着散射波的远场形式含有散射体的比现在已知的更多的信息.     

Analysis of Direct and Inverse Cavity Scattering Problems

Consider the scattering of a time-harmonic electromagnetic plane wave by an arbitrarily shaped and filled cavity embedded in a perfect electrically conducting infinite ground plane.A method of symmetric coupling of finite element and boundary integral equations is presented for the solutions of electromagnetic scattering in both transverse electric and magnetic polarization cases.Given the incident field,the direct problem is to determine the field distribution from the known shape of the cavity; while the inverse problem is to determine the shape of the cavity from the measurement of the field on an artificial boundary enclosing the cavity.In this paper,both the direct and inverse scattering problems are discussed based on a symmetric coupling method.Variational formulations for the direct scattering problem are presented,existence and uniqueness of weak solutions are studied,and the domain derivatives of the field with respect to the cavity shape are derived.Uniqueness and local stability results are established in terms of the inverse problem.     

用正则化方法求解声波散射反问题

研究了从声波散射场的远场模式的信息来再现散射物边界形状的反问题.首先构造表达散射物特征的指示函数,然后利用该函数之特性,建立求解该类反问题的基本方程,从而确定散射物的边界形状.在这个算法中,不需预先知道散射物的边界类型和形状等知识,从T ikhonov正则化方法进行的数值计算结果表明了该方法是有效的和实用的.     

Reconstruction and uniqueness of an inverse scattering problem with impedance boundary

Consider an inverse scattering problem for a scatterer D ⊂ R³ with impedance type boundary condition. By defining the scatterer shape in a completely new way, we give a constructive method to recover the scatterer shape with unknown impedance coefficient. The uniqueness for this inverse problem is also obtained.     

The factorization method for cracks in inhomogeneous media

We consider the inverse scattering problem of determining the shape and location of a crack surrounded by a known inhomogeneous media. Both the Dirichlet boundary condition and a mixed type boundary conditions are considered. In order to avoid using the background Green function in the inversion process, a reciprocity relationship between the Green function and the solution of an auxiliary scattering problem is proved. Then we focus on extending the factorization method to our inverse shape reconstruction problems by using far field measurements at fixed wave number. We remark that this is done in a non intuitive space for the mixed type boundary condition as we indicate in the sequel.     

Inverse scattering from an orthotropic medium

We consider the inverse scattering problem of determining the shape of an orthotropic homogeneous medium from a knowledge of the far field pattern corresponding to incident time harmonic plane waves. We solve the direct problem by potential theory, show the uniqueness of the inverse problem and then use a ‘simple’ method recently developed by Colton and Kirsch (1996) and Colton and Monk (1997) to solve the inverse problem. Numerical examples are given showing the practicality of our method for solving the inverse problem.     

Inverse scattering from an open arc

A Newton method is presented for the approximate solution of the inverse problem to determine the shape of a sound-soft or perfectly conducting arc from a knowledge of the far-field pattern for the scattering of time-harmonic plane waves. Fréchet differentiability with respect to the boundary is shown for the far-field operator, which for a fixed incident wave maps the boundary arc onto the far-field pattern of the scattered wave. For the sake of completeness, the first part of the paper gives a short outline on the corresponding direct problem via an integral equation method including the numerical solution.     

Mathematical basis of the linear sampling method for partially coated obstacles

We consider the inverse scattering problem of determining the shape of a partially coated obstacle D. To this end, we solve a scattering problem for the Helmholtz equation where the scattered field satisfies mixed Dirichlet–Neumann-impedance boundary conditions on the Lipschitz boundary of the scatterer D. Based on the analysis of the boundary integral system to the direct scattering problem, we propose how to reconstruct the shape of the obstacle D by using the linear sampling method.     

RECOVERY OF THE SINGULARITIES OF A POTENTIAL FROM FIXED ANGLE SCATTERING DATA

We study the inverse scattering problem for Schroedinger equation. We prove that for non-smooth potential the main singularities of the potential are contained in the Born approximation which can be obtained from measurement of the scattering amplitude in a single outgoing direction. We measure singularities in the scale of Sobolev spaces.     

The inverse scattering problem for a partially coated cavity with interior measurements

We consider the interior inverse scattering problem of recovering the shape and the surface impedance of an impenetrable partially coated cavity from a knowledge of measured scatter waves due to point sources located on a closed curve inside the cavity. First, we prove uniqueness of the inverse problem, namely, we show that both the shape of the cavity and the impedance function on the coated part are uniquely determined from exact data. Then, based on the linear sampling method, we propose an inversion scheme for determining both the shape and the boundary impedance. Finally, we present some numerical examples showing the validity of our method.     

ANALYSIS OF TWO-DIMENSIONAL ELECTROMAGNETIC SCATTERING BY A PERFECTLY CONDUCTING OBSTACLE IN A HOMOGENEOUS CHIRAL ENVIRONMENT

The time-harmonic electromagnetic plane waves incident on a perfectly conducting obstacle in a homogeneous chiral environment are considered.A two-dimensional direct scat- tering model is established and the existence and uniqueness of solutions to the problem are discussed by an integral equation approach.The inverse scattering problem to find the shape of scatterer with the given far-field data is formulated.Result on the uniqueness of the inverse problem is proved.