Arif Amirov¹, Fikret Gölgeleyen¹, Ayten Rahmanova²

CMES-Computer Modeling in Engineering & Sciences, Vol.43, No.2, pp. 131-148, 2009, DOI:10.3970/cmes.2009.043.131

Abstract This paper has two purposes. The first is to prove existence and uniqueness theorems for the solution of an inverse problem for the general linear kinetic equation with a scattering term. The second one is to develop a numerical approximation method for the solution of this inverse problem for two dimensional case using finite difference method. More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.40, No.1, pp. 1-28, 2009, DOI:10.3970/cmes.2009.040.001

Abstract We consider an inverse problem of Laplace equation by recoverning boundary value on the inner circle of a two-dimensional annulus from the overdetermined data on the outer circle. The numerical results can be used to determine the Robin coefficient or crack's position inside a disk from the measurements of Cauchy data on the outer boundary. The Fourier series is used to formulate the first kind Fredholm integral equation for the unknown data f(θ) on the inner circle. Then we consider a Lavrentiev regularization, by adding an extra term αf(θ) to obtain the second kind Fredholm integral equation. The termwise separable… More >

Liviu Marin¹

CMES-Computer Modeling in Engineering & Sciences, Vol.30, No.2, pp. 99-122, 2008, DOI:10.3970/cmes.2008.030.099

Abstract The application of the method of fundamental solutions (MFS) to inverse boundary value problems associated with the steady-state heat conduction in isotropic media in the presence of sources, i.e. the Poisson equation, is investigated in this paper. Based on the approach of Alves and Chen (2005), these problems are solved in two steps, namely by finding first an approximate particular solution of the Poisson equation and then the numerical solution of the resulting inverse boundary value problem for the Laplace equation. The resulting MFS discretised system of equations is ill-conditioned and hence it is solved by employing the singular value… More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.30, No.2, pp. 65-76, 2008, DOI:10.3970/cmes.2008.030.065

Abstract Trefftz method (TM) is one of widely used meshless numerical methods in elliptic type boundary value problems, of which the approximate solution is expressed as a linear combination of T-complete bases, and the unknown coefficients are determined from boundary conditions by solving a linear equations system. However, the accuracy of TM is severely limited by its ill-conditioning. This paper is a continuation of the work of Liu (2007a). The collocation TM is modified and applied to the direct and inverse problems of biharmonic equation in a simply connected plane domain. Due to its well-conditioning of the resulting linear equations system,… More >

S. D. Harris¹, R. Mustata², L. Elliott², D. B. Ingham², D. Lesnic²

CMES-Computer Modeling in Engineering & Sciences, Vol.25, No.2, pp. 69-80, 2008, DOI:10.3970/cmes.2008.025.069

Abstract Two homogeneous anisotropic materials are butted together to form a contact surface within a single composite material (the specimen). An inverse boundary element method (BEM) is developed to determine the components of the hydraulic conductivity tensor of each material and the position of the contact surface. A steady state flow is forced through the specimen by the application of a constant pressure differential on its opposite faces. Experimental measurements (simulated) of pressure and average hydraulic flux at exposed boundaries are then used in a modified least squares functional. This functional minimises the gap between the above measured (simulated) values and… More >

Liviu Marin¹, Henry Power¹, Richard W. Bowtell², Clemente Cobos Sanchez², Adib A. Becker¹, Paul Glover²，Arthur Jones¹

CMES-Computer Modeling in Engineering & Sciences, Vol.23, No.3, pp. 149-174, 2008, DOI:10.3970/cmes.2008.023.149

Abstract We investigate the reconstruction of a divergence-free surface current distribution from knowledge of the magnetic flux density in a prescribed region of interest in the framework of static electromagnetism. This inverse problem is motivated by the design of gradient coils for use in magnetic resonance imaging (MRI) and is formulated using its corresponding integral representation according to potential theory. A novel boundary element method (BEM) which employs linear interpolation on quadratic surfaces and also satisfies the continuity equation for the current density, i.e. a divergence-free BEM, is presented. Since the discretised BEM system is ill-posed and hence the associated least-squares… More >

Cheng-Hung Huang^1,2, Chih-Chun Shih¹

CMES-Computer Modeling in Engineering & Sciences, Vol.21, No.3, pp. 239-254, 2007, DOI:10.3970/cmes.2007.021.239

Abstract An inverse forced vibration problem, based on the Conjugate Gradient Method (CGM), (or the iterative regularization method), is examined in this study to estimate simultaneously the unknown time-dependent applied force and moment for an Euler-Bernoulli beam by utilizing the simulated beam displacement measurements. The accuracy of this inverse problem is examined by using the simulated exact and inexact displacement measurements. The numerical experiments are performed to test the validity of the present algorithm by using different types of applied force and moment, sensor locations and measurement errors. Results show that excellent estimations on the applied force and moment can be… More >

Leevan Ling¹, Tomoya Takeuchi²

CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.2, pp. 99-110, 2007, DOI:10.3970/cmes.2007.020.099

Abstract We aim to identify the unknown source locations in a two-dimensional heat equation from scattered measurements. In [Inverse Problems, 22(4):1289--1305, 2006], we proposed a numerical procedure that identifies the unknown source locations of 2D heat equation solely based on three measurement points. Due to the nonlinearity and complexity of the problem, the quality of the resulting estimations is often poor especially when the number of unknown is large. In this paper, we purpose a linear refinement scheme that takes the outputs of the existing nonlinear algorithm as initial guesses and iteratively improves on the accuracy of the estimations; the convergence… More >

Chein-Shan Liu¹, Li-Wei Liu², Hong-Ki Hong²

CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.1, pp. 1-18, 2007, DOI:10.3970/cmes.2007.017.001

Abstract In this paper we are concerned with the parameters identification of the inverse heat conduction problems governed by linear parabolic partial differential equations (PDEs). It is the first time that one can construct a closed-form estimation method for the inverse thermal problems of estimating the spatial-dependent thermophysical parameters. The key points hinge on an establishment of a one-step group preserving scheme (GPS) for the semi-discretization of PDEs, as well as a closed-form solution of the resulting algebraic equations. The new method, namely the Lie-group estimation method, has four advantages: it does not require any prior information on the functional forms… More >

Ru-Min Chao, Yen-Ji Chen, F.C. Lin¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.1, pp. 73-86, 2001, DOI:10.3970/cmes.2001.002.073

Abstract The two-dimensional elasticity problem of an isotropic material, containing a centered-crack with unknown boundary traction is studied by the inverse procedure. The dual boundary integral equations are used to analyze the problem. While solving the ill-posed inverse problem, both of the conjugate gradient method and the regularization method are used. A scaling factor depending upon the material constant μ is introduced into the sensitivity matrix in order to keep the order of magnitude the same throughout the formulation. The result by using the displacement measurement will be compared with those by stress measurement, and an extensive discussion will be given.… More >