J. Sladek¹, V. Sladek¹, P.H. Wen², Y.C. Hon³

CMES-Computer Modeling in Engineering & Sciences, Vol.48, No.2, pp. 191-218, 2009, DOI:10.3970/cmes.2009.048.191

Abstract The meshless local Petrov-Galerkin (MLPG) method is used to solve the inverse heat conduction problem of predicting the distribution of the heat transfer coefficient on the boundary of 2-D and axisymmetric bodies. Using this method, nodes are randomly distributed over the numerical solution domain, and surrounding each of these nodes, a circular sub-domain is introduced. By choosing a unit step function as the test function, the local integral equations (LIE) on the boundaries of these sub-domains are derived. To eliminate the time variation in the governing equation, the Laplace transform technique is applied. The local… More >

Liviu Marin¹

CMES-Computer Modeling in Engineering & Sciences, Vol.48, No.2, pp. 121-154, 2009, DOI:10.3970/cmes.2009.048.121

Abstract We investigate the numerical implementation of the alternating iterative algorithm originally proposed by ` 12 ` 12 `$12 `&12 `#12 `^12 `_12 `%12 `~12 *Kozlov91 in the case of the Cauchy problem for the two-dimensional Laplace equation using a meshless method. The two mixed, well-posed and direct problems corresponding to every iteration of the numerical procedure are solved using the method of fundamental solutions (MFS), in conjunction with the Tikhonov regularization method. For each direct problem considered, the optimal value of the regularization parameter is chosen according to the generalized cross-validation (GCV) criterion. An efficient More >

Weichung Yeih^1,2, Chein-Shan Liu³

CMES-Computer Modeling in Engineering & Sciences, Vol.46, No.2, pp. 107-128, 2009, DOI:10.3970/cmes.2009.046.107

Abstract We consider an inverse problem for estimating an unknown time dependent heat source H(t) in a heat conduction equation u_t(x,t) = u_xx(x,t) + H(t). First this inverse problem is formulated as a three-point boundary value problem (BVP) for ODEs discretized from the transformed homogeneous governing equation. To treat this three-point BVP we develop a two-stage Lie-group shooting method (TSLGSM). The novel approach is examined through numerical examples to convince that it is rather accurate and efficient; the estimation error is small even for identifying discontinuous and oscillatory heat sources under noise. More >

Mustafa Yildiz¹

CMES-Computer Modeling in Engineering & Sciences, Vol.45, No.2, pp. 141-154, 2009, DOI:10.3970/cmes.2009.045.141

Abstract The solvability conditions of an inverse problem for the non-stationary kinetic equation is formulated and a new numerical method is developed to obtain the approximate solution of the problem. A comparison between the approximate solution and the exact solution of the problem is presented. More >

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 More >

Chein-Shan Liu¹, Chih-Wen Chang², Jiang-Ren Chang^2,3

CMC-Computers, Materials & Continua, Vol.9, No.2, pp. 111-136, 2009, DOI:10.3970/cmc.2009.009.111

Abstract In this paper, we take the advantage of an analytical method to solve the advection-dispersion equation (ADE) for identifying the contamination problems. First, the Fourier series expansion technique is employed to calculate the concentration field C(x, t) at any time t< T. Then, we consider a direct regularization by adding an extra term αC(x,0) on the final condition to carry off a second kind Fredholm integral equation. The termwise separable property of the kernel function permits us to transform itinto a two-point boundary value problem. The uniform convergence and error estimate of the regularized solution C^α(x,t) are provided More >

B. Tomas Johansson¹, Liviu Marin²

CMC-Computers, Materials & Continua, Vol.13, No.2, pp. 153-190, 2009, DOI:10.3970/cmc.2009.013.153

Abstract We propose two algorithms involving the relaxation of either the given Dirichlet data or the prescribed Neumann data on the over-specified boundary, in the case of the alternating iterative algorithm of Kozlov, Maz'ya and Fomin(1991) applied to Cauchy problems for the modified Helmholtz equation. A convergence proof of these relaxation methods is given, along with a stopping criterion. The numerical results obtained using these procedures, in conjunction with the boundary element method (BEM), show the numerical stability, convergence, consistency and computational efficiency of the proposed methods. More >

LiviuMarin ¹

CMC-Computers, Materials & Continua, Vol.12, No.1, pp. 71-100, 2009, DOI:10.3970/cmc.2009.012.071

Abstract In this paper, the alternating iterative algorithm originally proposed by Kozlov, Maz'ya and Fomin (1991) is numerically implemented for the Cauchy problem in anisotropic heat conduction using a meshless method. Every iteration of the numerical procedure consists of two mixed, well-posed and direct problems which are solved using the method of fundamental solutions (MFS), in conjunction with the Tikhonov regularization method. For each direct problem considered, the optimal value of the regularization parameter is chosen according to the generalized cross-validation (GCV) criterion. An efficient regularizing stopping criterion which ceases the iterative procedure at the point More >

B.K.Raghuprasad¹, N.Lakshmanan², N.Gopalakrishnan², K.Muthumani²

Structural Durability & Health Monitoring, Vol.4, No.3, pp. 117-144, 2008, DOI:10.3970/sdhm.2008.004.117

Abstract The reduction in natural frequencies, however small, of a civil engineering structure, is the first and the easiest method of estimating its impending damage. As a first level screening for health-monitoring, information on the frequency reduction of a few fundamental modes can be used to estimate the positions and the magnitude of damage in a smeared fashion. The paper presents the Eigen value sensitivity equations, derived from first-order perturbation technique, for typical infra-structural systems like a simply supported bridge girder, modelled as a beam, an end-bearing pile, modelled as an axial rod and a simply… More >