共查询到18条相似文献,搜索用时 93 毫秒
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提出用时间调和声散射远场信息来反演二维可穿透目标的一种Linear Sampling方法,通过提取包含可穿透目标的一个样本区域的支集的点列来实现反演的,因为其在区域内与区域外有显著的不同取值,由此而获得区域的逼近.这个算法特别吸引人之处是不需关于障碍物的任何先验信息.并且只需散射场在某个有限孔径中的部分远场信息,即可获得穿透区域的一个逼近.一些数值算例保证了这个反演算法是有效的和实用的. 相似文献
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刚性目标形状反演的一种非线性最优化方法 总被引:1,自引:1,他引:0
发展了从声散射场的远场分布的信息来再现声刚性目标形状反问题的一种非线性最优化方法,它是通过独立地求解一个不适定的线性系统和一个适定的非线性最小化问题来实现的。对反问题的非线性和不适定性的这种分离式数值处理,使所建立方法的数值实现是非常容易和快速的,因为在确定声刚性障碍物形状的非线性最优化步中,只需求解一个只有一个未知函数的小规模的最小平方问题。该方法的另一个特别的性质是,只需要远场分布的一个Fourier系数,即可对未知的刚性目标作物形设别。进而提出了数值实现该方法的一种两步调整迭代算法。对具有各种形状的二维刚性障碍物的数值试验保证了本算法是有效和实用的。 相似文献
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利用远场模式的不完全数据反演声波阻尼系数 总被引:3,自引:0,他引:3
1.引言 对声波反散射理论的研究,已经有大量的研究[1.5].[7]利用散射波的远场模式反演边界条件中的阻尼系数.但是在实际问题中,要在物体的一周测量到远场模式的值是不现实的.因此,利用远场模式的不完全数据来进行反演有明显的物理和实际意义.一些文献将此类问题称为声波反散射理论的“limited aperture problem”.本文利用远场模式的不完全数据,反演边界条件中的声波阻尼系数. 相似文献
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提出一种方法,利用远场模式的完全数据与不完全数据反演声波阻尼区域,证明了方法的收敛性,并给出若干数值例子. 相似文献
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从阻尼边界条件声波散射问题的散射场远场模式的部分数据信息出发给出了反演声波阻尼系数的一种新方法,该问题既是非线性的又是不适定的,这里利用Tikhonov正则化方法将问题转化为一个最优化问题,成功地处理了第一类算子方程的不适定性及该问题的非线性性,给出了具体的数值方法并对其收敛性进行了严格地证明,数值结果表明该方法是非常准确且简单易行的. 相似文献
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该文介绍一类岩性反演问题.从理论上分析LMS估计的结构。在空间齐次假设下,得到不变矩阵α=(αij)的递推计算关系.同时,建立一种计算机模拟岩性的算法,该算法被实践证明是有效的. 相似文献
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用正则化方法求解声波散射反问题 总被引:1,自引:1,他引:0
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. 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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Rainer Kress 《Mathematical Methods in the Applied Sciences》1995,18(4):267-293
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. 相似文献
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Gao Tianling Ma Fuming Zhang Deyue 《高校应用数学学报(英文版)》2007,22(3):259-266
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. 相似文献
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In this paper, the authors describe a new algorithm for solvingthe inverse scattering problem of determining the speed of soundin an inhomogeneous medium from far-field data. Limited testinghas shown that the algorithm has some capacity for reconstructingsimple sound profiles using data over a limited range of frequencies. 相似文献
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Consider the determination of Dirichlet-to-Neumann (D-to-N) map from the far-field pattern in inverse scattering problems, which is the key step in some recently developed inversion schemes such as probe method. Essentially, this problem is related to the reconstruction of the scattered wave from its far-field data. We firstly prove the well-known uniqueness result of the D-to-N map from the far-field pattern using a new scheme based on the mixed reciprocity principle. The advantage of this new proof scheme is that it provides an efficient algorithm for computing the D-to-N map, avoiding the numerical differentiation for the scattered wave. Then combining with the classical potential theory, a simple and feasible regularizing reconstruction scheme for the D-to-N map is proposed. Finally the stability estimate for the reconstruction with noisy input data is rigorously analyzed. 相似文献
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The inverse problem considered is to determine the shape ofan acoustically soft obstacle in R3 from a knowledge of thetime-harmonic incident plane wave and the far-field patternof the scattered wave. To solve this inverse Dirichlet problemin acoustic scattering without requiring the solution of integralequations, a parametric representation is introduced in whichthe parameters are determined by a method of optimization. Directscattering can also be handled by this technique. Comparisonsreveal that results are obtained more easily than, and justas accurately as, in other methods. 相似文献
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针对多裂纹问题,若采用常规的数值求解技术,计算效率较低.为实现多裂纹问题的大规模数值模拟,建立了本征裂纹张开位移(crack opening displacement, COD)边界积分方程及其迭代算法,并引入Eshelby矩阵的定义,将多裂纹分为近场裂纹和远场裂纹来处理裂纹间的相互影响.以采用常单元作为离散单元的快速多极边界元法为参照,对提出的计算模型和迭代算法进行了数值验证.结果表明,本征COD边界积分方程方法在处理多裂纹问题时取得较大的改进,其计算效率显著高于传统的边界元法和快速多极边界元法. 相似文献
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The framework for shape and topology sensitivity analysis in geometrical domains with cracks is established for elastic bodies
in two spatial dimensions. The equilibrium problem for the elastic body with cracks is considered. Inequality type boundary
conditions are prescribed at the crack faces providing a non-penetration between the crack faces. Modelling of such problems
in two spatial dimensions is presented with all necessary details for further applications in shape optimization in structural
mechanics. In the paper, general results on the shape and topology sensitivity analysis of this problem are provided. The
results are of interest of their own. In particular, the existence of the shape and topological derivatives of the energy
functional is obtained. The results presented in the paper can be used for numerical solution of shape optimization and inverse
problems in structural mechanics. 相似文献
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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. 相似文献