Mustafa Yidiz¹, Bayram Heydarov², İsmet Gölgeleyen¹

CMES-Computer Modeling in Engineering & Sciences, Vol.62, No.3, pp. 255-264, 2010, DOI:10.3970/cmes.2010.062.255

Abstract We investigate the solvability of an inverse problem for the non-stationary general kinetic equation. We also obtained the approximate solution of this problem by using symbolic computation. A comparison between the approximate solution and the exact solution of the problem is presented. More >

Liviu Marin¹

CMES-Computer Modeling in Engineering & Sciences, Vol.60, No.3, pp. 221-246, 2010, DOI:10.3970/cmes.2010.060.221

Abstract We investigate the implementation of the method of fundamental solutions (MFS), in an iterative manner, for the algorithm of Kozlov, Maz'ya and Fomin (1991) in the case of the Cauchy problem in two-dimensional isotropic linear elasticity. At every iteration, two mixed well-posed and direct problems are solved using the Tikhonov regularization method, while the optimal value of the regularization parameter is chosen according to the generalized cross-validation (GCV) criterion. An efficient regularizing stopping criterion is also presented. The iterative MFS algorithm is tested for Cauchy problems for isotropic linear elastic materials to confirm the numerical convergence, stability and accuracy of… More >

Arif Amirov¹, Zekeriya Ustaoglu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.54, No.3, pp. 283-300, 2009, DOI:10.3970/cmes.2009.054.283

Abstract We present the solvability of a two space dimensional coefficient inverse problem for a transport-like equation and investigate the approximate solution of this problem with the use of centered difference formulas and a symbolic approximation method. Since this inverse problem is overdetermined, which is the main difficulty in studying of its solvability, it is replaced by a related determined one by using some extension of the class of unknown functions. More >

D. C. Knupp¹, A. J. Silva Neto², W. F. Sacco³

CMES-Computer Modeling in Engineering & Sciences, Vol.54, No.2, pp. 121-146, 2009, DOI:10.3970/cmes.2009.054.121

Abstract The inverse analysis of radiative transfer in participating media has several practical applications. In most cases, the inverse problem is formulated implicitly and the solution is given by the minimization of an objective function. Gradient based methods have largely been used for that purpose, but it has been observed in recent years an increasing interest in the use of stochastic methods. In this work, it is proposed the use of the Luus-Jaakola method and the Particle Collision Algorithm. The former is a random search optimization method that has been successfully employed mainly in chemical engineering, and the latter is a… More >

M. Irízar, L. D. Câmara, A. J. Silva Neto, O. Llanes

CMES-Computer Modeling in Engineering & Sciences, Vol.54, No.1, pp. 1-14, 2009, DOI:10.3970/cmes.2009.054.001

Abstract Modeling of Chromatography allows a better understanding and development of new techniques to be applied at industrial level, although it's relatively complex. The models of this process are represented by systems of partial differential equations with non linear parameters difficult to estimate generally, which constitutes an inverse problem. In general there aren't analytical solutions and therefore numerical methods should be used for their direct solutions. Frequently typical boundary conditions are considered, but it's convenient to study different approaches for those. Evolutionary Computation has been used successfully in many problems of diverse areas for searching in complex spaces. Considering previous works… More >

G.S. Li¹, D. Yao², Y.Z. Wang³, H.Y. Jiang²

CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.1, pp. 53-72, 2009, DOI:10.3970/cmes.2009.051.053

Abstract In this paper, an undisturbed soil-column infiltrating experiment is investigated, and a mathematical model describing multi-components solutes transport behaviors in the column is put forward by combing hydro-chemical analysis with advection dispersion mechanisms, which is a group of advection-dispersion-reaction partial differential equations. Since the model involving six reaction coefficients which can not be obtained directly, an optimal perturbation regularization algorithm of determining these parameters is performed, and numerical simulations under different conditions are carried out. Furthermore, the inversion algorithm is applied to solve the real inverse problem by utilizing the measured breakthrough data. The reconstruction data basically coincide with the… More >

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 integral equations are nonsingular and… 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 regularizing stopping criterion which ceases… 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 >