Numerical simulation for the shape reconstruction of a cavity

We consider the inverse problem of reconstructing the interior boundary curve of a cavity from the knowledge of the measurements on the exterior boundary. The domain derivative of the corresponding operator is presented, and this allows the investigation of the regularized Newton method for the solution of the ill‐posed and nonlinear problem. Numerical examples indicate the feasibility of our method. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009     

结构动力学逆特征值问题的同伦解法

将结构动力学反问题视为拟乘法逆特征值问题,利用求解非线性方程组的同伦方法来解决结构动力学逆特征值问题,这种方法由于沿同伦路径求解,对初值的选取没有本质的要求,算例说明了这种方法是可行的．     

半定规划的限制逆问题与广义逆问题

本文提出了半定规划的限制逆问题与广义逆问题，利用半定规划的最优性条件，分别给出了其在l∞，l1,l2模意义下的数学模型，它们仍为半定规划问题。     

Shape inverse problem for the two‐dimensional unsteady Stokes flow

In this article, the shape inverse problem for the two‐dimensional unsteady Stokes flow has been presented. We employ Piola transformation to bypass the divergence free condition for the flow and prove the differentiability of the solution to the initial boundary value problem. For the approximate solution of the ill‐posed and nonlinear problem, we propose a regularized Gauss‐Newton method. The numerical examples show that our theory is useful for practical purpose and the proposed algorithm is feasible. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010     

A Solution of Inverse Eigenvalue Problems for Unitary Hessenberg Matrices

Let H∈Cn×n be an n×n unitary upper Hessenberg matrix whose subdiagonal elements are all positive. Partition H as H=[H11 H12 H21 H22],(0.1) where H11 is its k×k leading principal submatrix; H22 is the complementary matrix of H11. In this paper, H is constructed uniquely when its eigenvalues and the eigenvalues of (H|^)11 and (H|^)22 are known. Here (H|^)11 and (H|^)22 are rank-one modifications of H11 and H22 respectively.     

On the Solution of Inverse Problems for Generalized Oxygen Consumption

We present the solution of some inverse problems for one-dimensional free boundary problems of oxygen consumption type, with a semilinear convection-diffusion-reaction parabolic equation. Using a fixed domain transformation (Landau's transformation) the direct problem is reduced to a system of ODEs. To minimize the objective functionals in the inverse problems, we approximate the data by a finite number of parameters with respect to which automatic differentiation is applied.     

凸二次规划问题逆问题的模型与解法

本文分别考虑带非负约束和不带大量负约束凸二次规划问题逆问题。首先得到各个逆问题的数学模型,然后对不同的模型给出不同的求解方法。     

两个反问题的数学模型

本文考察了两个工业中的反问题 ,讨论了如何建立起这些问题的偏微分方程模型 ,并最终归结为变分问题 ,简述了这些模型的求解方法 .     

决策方法在反问题研究中的应用

本文讨论了决策方法在反问题研究中的应用.首先阐述在反问题研究中应用决策方法的必要性,然后以一个具体的反问题为例论述了如何确立决策目标.     

基于时域精细积分算法的瞬态传热多宗量反演

基于有限元法和精细积分算法,提出了一种求解瞬态热传导多宗量反演问题的新方法．采用有限元法和精细积分算法分别对空间、时间变量进行离散,可以得到正演问题高精度的半解析数值模型,由此建立了多宗量反演的计算模式,并给出敏度分析的计算公式．对一维和二维的热物性参数、热源项、边界条件等进行了单宗量和多宗量的反演求解,初步考虑了初值和噪音等对反演结果的影响,数值算例验证了该方法的有效性．     

关于工科“线性代数”课程中的反问题

讨论了工科"线性代数"课程中涉及到的几类简单的反问题,给出了解的存在条件与一般解法.     

波动方程反演问题的一种新的逼近方法

本文给出了一种求解波动方程反演问题的“多目标函数法”.这种方法简单、有效,并具有明确的物理意义.对于三维问题的程序化它有很强的优越性.     

Shape reconstruction for the time‐dependent Navier‐Stokes flow

This article deals with the shape reconstruction of a bounded domain with a viscous incompressible fluid driven by the time‐dependent Navier‐Stokes equations. For the approximate solution of the ill‐posed and nonlinear problem we propose a regularized Newton method. A theoretical foundation for the Newton method is given by establishing the differentiability of the initial boundary value problem with respect to the interior boundary curve in the sense of the domain derivative. Numerical examples indicate the feasibility of our method. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008     

两个DEA的逆问题的解法的探讨

文[1]提出了两个DEA的逆问题，并用搜索法来解．而本文根据所证的定理，对每个问题一般只要解二、三个线性规划问题就能得到答案．     

非完整动力学逆问题的一种提法和解法*

本文给出非完整动力学逆问题的一种提法和解法:已知某些积分,来求施加在系统上的非完整约束的形式;进而在已知系统动能表达式的情况下,来求加在系统上的广义约束反力;最后,给出例子说明解法的应用.     

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.     

A Stability Estimate for a Solution to a Three-Dimensional Inverse Problem for the Maxwell Equations

We consider the problem of determining dielectric permittivity and conductivity in the Maxwell equations. As additional information we prescribe the traces of the tangential components of the electromagnetic field on the lateral surface of a cylindric domain. We establish a stability estimate for a solution to the inverse problem and a uniqueness theorem.     

Meyer-KnigandZeller算子的保形问题

讨论了 Meyer-Knig and Zeller算子的保形逼近问题 ,我们用基于算子特殊结构的分析方法得到了该算子的保单调性 .保凸性以及保形逆定理等保形性质 .     

Shape inverse problem of thermodynamic equations based on domain derivative method

In this paper, we consider the shape inverse problem of a body immersed in the incompressible fluid governed by thermodynamic equations. By applying the domain derivative method, we obtain the explicit representation of the derivative of solution with respect to the boundary, which plays an important role in the inverse design framework. Moreover, according to the boundary parametrization technique, we present a regularized Gauss–Newton algorithm for the shape reconstruction problem. Finally, numerical examples indicate the proposed algorithm is feasible and effective for the low Reynolds numbers. Copyright © 2017 John Wiley & Sons, Ltd.     

一类线性流形上矩阵方程X^TAX=B的反问题

设Ω={A∈ASR^nxn｜Ax=C，↓Ax∈RT（S），SS^＋C=0，T2^TC2=-C2^TT2，C2T2^＋72=C2}，考虑问题Ⅰ：给定X∈R^nxm，B∈R^mxm求A∈Ω，使得f（A）=｜｜X^TAX—B｜｜=min；问题Ⅱ：给定A^＋∈R^nxm，求A∈SE，使得｜｜A^＋-A｜｜=minA∈SE｜｜A^＋-A｜｜，SE是问题Ⅰ的解集。本文给出了问题Ⅰ、Ⅱ的解的通式，并给出了问题Ikf（A）=0成立的充分必要条件。