共查询到20条相似文献,搜索用时 15 毫秒
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Gang Bao Peijun Li 《计算数学(英文版)》2007,25(3):252-265
A regularized recursive linearization method is developed for a two-dimensional in-verse medium scattering problem that arises in near-field optics, which reconstructs the scatterer of an inhomogeneous medium deposited on a homogeneous substrate from data accessible through photon scanning tunneling microscopy experiments. In addition to the ill-posedness of the inverse scattering problems, two difficulties arise from the layered back-ground medium and limited aperture data. Based on multiple frequency scattering data, the method starts from the Born approximation corresponding to the weak scattering at a low frequency, each update is obtained via recursive linearization with respect to the wavenumber by solving one forward problem and one adjoint problem of the Helmholtz equation. Numerical experiments are included to illustrate the feasibility of the proposed method. 相似文献
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刘继军 《高等学校计算数学学报(英文版)》2005,14(3):193-207
The inverse scattering problems are to detect the property of obstacles from the measurements outside the obstacles. One of important research areas in this topic is the recovery of boundary property for impenetrable obstacles. In this paper, we would like to give a brief review about the recently developed singular source methods. There are three different methods in this category, namely, linear sampling method, pointsource method and probe method. We also present some recent new results about the probe method. 相似文献
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§1. Introduction √ Let k ∈R, λ> 0 and i = ?1. We consider an acoustic scattering problem by animpenetrable obstacle D ? R2: ?u k2u = 0, in R2 \ D, … 相似文献
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Jiantao Cheng Tie Zhou 《计算数学(英文版)》2008,(6):876-890
The inverse black body radiation problem, which is to reconstruct the area temperature distribution from the measurement of power spectrum distribution, is a well-known ill-posed problem. In this paper, a variational expectation-maximization (EM) method is developed and its convergence is studied. Numerical experiments demonstrate that the variational EM method is more efficient and accurate than the traditional methods, including the Tikhonov regularization method, the Landweber method and the conjugate gradient method. 相似文献
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朝红阳 《高等学校计算数学学报(英文版)》1993,(2)
In this paper, a new iteration algorithm to solve the coefficient inverse problem is described by using a "basic function" which is specially defined and the idea of regularization. The method is simple and clear.The main advantage of the algorithm is that its computing cost is less than other current algorithms, such as PST and Purlerbalion Methods. Since it has uniform scheme, on the other hand, the method can be easily exleded to other kinds of inverse problems of different leal equations, multidimensional inverse problem and multiparameler inverse problems, etc. 相似文献
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The inverse problem considered in this paper is to determine the
shape and the impedance of crack from a knowledge of the
time-harmonic incident field and the corresponding far field pattern
of the scattered waves in two-dimension. The combined single- and
double-layer potential is used to approach the scattered waves. As
an important feature, this method does not require the solution of $u$ and $\partial u / \partial \nu$ at each iteration. An
approximate method is presented and the convergence of this method
is proven. Numerical examples are given to show that this method is
both accurate and simple to use. 相似文献
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三维Helmholtz方程外问题的自然边界元与有限元耦合法 总被引:4,自引:0,他引:4
1.引言 设Γ0是空间闭曲面,Ω是Γ0外部的无界区域,考虑三维Helmholtz 方程外Neumann问题其中 是波数,w是频率,c0为波在均匀介质中的传播速度,v是区域Ω的边界Γ0的外法线方向,即指向由 Γ0包围的内部区域, 为 Γ0上的已知函数.为了保证问题(1.1)和(1.2)的解的存在唯一性,必须附加上无穷远边界条件,即所谓的 Sommerfeld辐射条件其中i是虚数单位, . 许多数学物理问题,例如时间调和声波对不可穿透的障碍物的散射,海洋水下声波的传播,电磁波的绕射与辐… 相似文献
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本文用声波远场模式的完全与不完全数据对声波散射区域进行了反演。其前提条件是整体场满足齐次Dirichlet边界条件,对于这个问题,文中给出一种对任意波数k(k〉0)的组合方法。方法的收敛性得到证明,数值例子表明了方法是可行的和精确的。 相似文献
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二维逆散射问题探测方法的数值实现 总被引:1,自引:1,他引:0
探测方法是最近发展起来的逆散射问题的一种重要的求解方法,其主要思想是由散射波测量数据构造一个带有散射体外面参数点的指示函数,当参数点靠近散射体的边界时,指示函数爆破,由此重建散射体的边界.本文对具有Sound-soft边界的二维散射体给出了探测方法的数值实现.在给出标志函数的构造的基础上,进一步提出了利用模拟数据实现探测法的一个改进的逼近方法.为了更清楚地检验所提出的方法的数值结果,我们直接从Ω边界上的 D-to-N映射来研究探测方法的数值解. 相似文献
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We consider an inverse quadratic programming (IQP) problem in which the parameters in the objective function of a given quadratic programming (QP) problem are adjusted as little as possible so that a known feasible solution becomes the optimal one. This problem can be formulated as a minimization problem with a positive semidefinite cone constraint and its dual (denoted IQD(A, b)) is a semismoothly differentiable (SC^1) convex programming problem with fewer variables than the original one. In this paper a smoothing Newton method is used for getting a Karush-Kuhn-Tucker point of IQD(A, b). The proposed method needs to solve only one linear system per iteration and achieves quadratic convergence. Numerical experiments are reported to show that the smoothing Newton method is effective for solving this class of inverse quadratic programming problems. 相似文献
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Wen-huan Yu 《计算数学(英文版)》1998,(4)
1.IntroductionQuasi-Newtonmethodsplayanimportantroleinnumericallysolvingnon--linearsystemsofequationsontheEuclideanspaces.Blltitseemsthatthequasi-Newtonmethodshavenotbeenapplieddirectlytosolvinginverseproblemsinpartialdifferentialequations(PDE)uptonowifwe… 相似文献
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In this paper, we investigate the use of ultra weak variational formulation to solve a wave scattering problem in near field optics. In order to capture the sub-scale features of waves, we utilize evanescent wave functions together with plane wave functions to approximate the local properties of the field. We analyze the global convergence and give an error estimation of the method. Numerical examples are also presented to demonstrate the effectiveness of the strategy. 相似文献
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INVERSESCATTERINGTRANSFORMATIONFORTHEVARIABLECOEFFICIENTSINE-GORDONTYPEEQUATIONXUBAOZHIANDZHAOSHENQIAbstract:Inthispaper,thev... 相似文献
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一个扩散问题的自然边界元法与有限元法组合 总被引:7,自引:0,他引:7
李瑞遐 《高校应用数学学报(A辑)》1998,13(3):333-341
本文讨论由Helmholtz方程描述的扩散问题的自然边界元法与有限元法的组合.取一个圆作为公共边界,用Fourier展开建立边界积分方程,将无界区域上的问题化为有界区域上的非局部边值问题.在变分方程中公共边界上的未知量只包含函数本身而不包含其法向导数,从而减少了未知数的数目,并且边界元剐度矩阵只有极少量不同的元素,有利于数值计算.这种组台方法优越于建立在直接边界元法基础上的组合方法.文中证明了变分解的唯一性,数值解的收敛性和误差估计.最后讨论了数值技术并给出一个算倒. 相似文献
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In this paper, a new collocation BEM for the Robin boundary value problem of the conductivity equation ▽(γ▽u) = 0 is discussed, where the 7 is a piecewise constant function. By the integral representation formula of the solution of the conductivity equation on the boundary and interface, the boundary integral equations are obtained. We discuss the properties of these integral equations and propose a collocation method for solving these boundary integral equations. Both the theoretical analysis and the error analysis are presented and a numerical example is given. 相似文献
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