关键词：
Helmholtz equation;Inverse scattering;locally rough interface;the Kirsch-Kress approach;transmission problem
摘要：
This paper is concerned with the inverse problem of reconstructing an infinite, locally rough interface from the scattered field measured on line segments above and below the interface in two dimensions. We extend the Kirsch-Kress method originally developed for inverse obstacle scattering problems to the above inverse transmission problem with unbounded interfaces. To this end, we reformulate our inverse problem as a nonlinear optimization problem with a Tikhonov regularization term. We prove the convergence of the optimization problem when the regularization parameter tends to zero. Finally, numerical experiments are carried out to show the validity of the inversion algorithm.
作者机构：
[Sie Long Kek] Center for Research on Computational Mathematics, Universiti Tun Hussein Onn Malaysia, Batu Pahat, Malaysia;[Jiao Li] School of Mathematics and Computing Science, Changsha University of Science and Technology, Changsha, China;[Kok Lay Teo] Department of Mathematics and Statistics, Curtin University of Technology, Perth, Australia
摘要：
In this paper, an efficient computational approach is proposed to solve the discrete time nonlinear stochastic optimal control problem. For this purpose, a linear quadratic regulator model, which is a linear dynamical system with the quadratic criterion cost function, is employed. In our approach, the model-based optimal control problem is reformulated into the input-output equations. In this way, the Hankel matrix and the observability matrix are constructed. Further, the sum squares of output error is defined. In these point of views, the least squares optimization problem is introduced, so as the differences between the real output and the model output could be calculated. Applying the first-order derivative to the sum squares of output error, the necessary condition is then derived. After some algebraic manipulations, the optimal control law is produced. By substituting this control policy into the input-output equations, the model output is updated iteratively. For illustration, an example of the direct current and alternating current converter problem is studied. As a result, the model output trajectory of the least squares solution is close to the real output with the smallest sum squares of output error. In conclusion, the efficiency and the accuracy of the approach proposed are highly presented.
作者：
Sie Long Kek;Jiao Li;Wah June Leong;Mohd Ismail Abd Aziz;PDF
期刊：
最优化(英文),2017年06(03):85-100 ISSN：2325-7105
作者机构：
[Sie Long Kek] Center for Research on Computational Mathematics, Universiti Tun Hussein Onn Malaysia, Batu Pahat, Malaysia;[Jiao Li] School of Mathematics and Computing Science, Changsha University of Science and Technology, Changsha, China;[Wah June Leong] Department of Mathematics, Universiti Putra Malaysia, Serdang, Malaysia;[Mohd Ismail Abd Aziz] Department of Mathematical Sciences, Universiti Teknologi Malaysia, Skudai, Malaysia
摘要：
Output measurement for nonlinear optimal control problems is an interesting issue. Because the structure of the real plant is complex, the output channel could give a significant response corresponding to the real plant. In this paper, a least squares scheme, which is based on the Gauss-Newton algorithm, is proposed. The aim is to approximate the output that is measured from the real plant. In doing so, an appropriate output measurement from the model used is suggested. During the computation procedure, the control trajectory is updated iteratively by using the Gauss-Newton recursion scheme. Consequently, the output residual between the original output and the suggested output is minimized. Here, the linear model-based optimal control model is considered, so as the optimal control law is constructed. By feed backing the updated control trajectory into the dynamic system, the iterative solution of the model used could approximate to the correct optimal solution of the original optimal control problem, in spite of model-reality differences. For illustration, current converted and isothermal reaction rector problems are studied and the results are demonstrated. In conclusion, the efficiency of the approach proposed is highly presented.
摘要：
In this paper, we consider a type of fractional diffusion equation (FDE) with variable coefficients on a finite domain. Firstly, we utilize a second-order scheme to approximate the Riemann-Liouville fractional derivative and present the finite difference scheme. Specifically, we discuss the Crank-Nicolson scheme and solve it in matrix form. Secondly, we prove the stability and convergence of the scheme and conclude that the scheme is unconditionally stable and convergent with the second -order accuracy of theta(tau(2) + h(2)). Furthermore, we develop a fast accurate iterative method for the Crank-Nicolson scheme, which only requires storage of theta(m) and computational cost of theta(m log m) while retaining the same accuracy and approximation property as Gauss elimination, where m = 1/h is the partition number in space direction. Finally, several numerical examples are given to show the effectiveness of the numerical method, and the results are in excellent agreement with the theoretical analysis. (C) 2016 Elsevier Ltd. All rights reserved.
作者机构：
[J. Li] School of Mathematics and Statistics, Changsha University of Science and Technology, China;[Pi Hua Wen; C. Shi] School of Engineering and Materials Science, Queen Mary University of London, London, United Kingdom
会议名称：
16th International Conference on Fracture and Damage Mechanics, 2017
作者：
Li, J.;Liu, J. Z.*;Korakianitis, T.;Wen, P. H.*
期刊：
Engineering Analysis with Boundary Elements,2017年82:57-67 ISSN：0955-7997
通讯作者：
Liu, J. Z.;Wen, P. H.
作者机构：
[Li, J.] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha, Hunan, Peoples R China.;[Liu, J. Z.] Hunan Inst Technol, Sch Math & Phys, Hengyang, Hunan, Peoples R China.;[Korakianitis, T.] St Louis Univ, Pk Coll Engn Aviat & Technol, St Louis, MO 63103 USA.;[Wen, P. H.] Queen Mary Univ London, Sch Engn & Mat Sci, London E1 4NS, England.
通讯机构：
[Liu, J. Z.] H;[Wen, P. H.] Q;Hunan Inst Technol, Sch Math & Phys, Hengyang, Hunan, Peoples R China.;Queen Mary Univ London, Sch Engn & Mat Sci, London E1 4NS, England.
关键词：
Finite block method;Mapping technique and differential matrix;Lagrange series interpolation;Mixed-mode stress intensity factors;Functionally graded material;Anisotropy
摘要：
The finite block method (FEM) is developed to determine stress intensity factors with orthotropic functionally graded materials under static and dynamic loads in this paper. By employing the Lagrange series, the first order partial differential matrix for one block is derived with arbitrary distribution of nodes. The higher order derivative matrix for two dimensional problems can be constructed directly. For linear elastic fracture mechanics, the COD and J-integral techniques to determine the stress intensity factors are formulated. For the dynamic problems, the Laplace transform method and Durbin's inverse technique are employed. Several examples are given and comparisons have been made with both the finite element method and analytical solutions in order to demonstrate the accuracy and convergence of the finite block method. (C) 2017 Elsevier Ltd. All rights reserved.
期刊：
Mathematical Problems in Engineering,2017年2017:1-2 ISSN：1024-123X
通讯作者：
Huang, Chuangxia(cxiahuang@126.com)
作者机构：
[Huang, Chuangxia] College of Mathematics and Computing Science, Changsha University of Science and Technology, Changsha, 410114, China;[He, Shaoyi] Department of Information and Decision Sciences, College of Business and Public Administration, California State University, Long Beach, CA, United States;[Yi, Taishan] Department of Applied Mathematics, University of Western Ontario, London, ON, N6A 5B7, Canada;[Lin, Xiaodong] Rutgers Business School, Rutgers University, Piscataway, NJ, 08854, United States;[Li, Jianping] Institute of Policy and Management, Chinese Academy of Science (CAS), Beijing, 100190, China
通讯机构：
College of Mathematics and Computing Science, Changsha University of Science and Technology, Changsha, China
摘要：
Consider the scattering of a time-harmonic point source from an unbounded rough surface. The surface is assumed to be different from a plane surface over a finite interval, which leads to the situation that the model problem can be reduced to an equivalent boundary value problem with compactly supported boundary data. Well-posedness is thus proved by employing the variational method with classical Fredholm theory. By constructing a modified near-field equation, we then propose a novel sampling-type method for reconstructing the shape and location of the local rough surface, yielding a fast imaging algorithm. Numerical experiments are presented to illustrate the effectiveness of the method.
