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  • Open Access

    ARTICLE

    Numerical Inversion of Multi-Parameters in Multi-Components Reactive Solutes Transportation in an Undisturbed Soil-Column Experiment

    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 More >

  • Open Access

    ARTICLE

    The Inverse Problem of Determining Heat Transfer Coefficients by the Meshless Local Petrov-Galerkin Method

    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 >

  • Open Access

    ARTICLE

    An iterative MFS algorithm for the Cauchy problem associated with the Laplace equation

    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 >

  • Open Access

    ARTICLE

    A Three-Point BVP of Time-Dependent Inverse Heat Source Problems and Solving by a TSLGSM

    Weichung Yeih1,2, 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 ut(x,t) = uxx(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 >

  • Open Access

    ARTICLE

    On the Solution of a Coefficient Inverse Problem for the Non-stationary Kinetic Equation

    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 >

  • Open Access

    ARTICLE

    An Inverse Problem for the General Kinetic Equation and a Numerical Method

    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 >

  • Open Access

    ARTICLE

    Solving the Inverse Problems of Laplace Equation to Determine the Robin Coefficient/Cracks' Position Inside a Disk

    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 >

  • Open Access

    ARTICLE

    A Quasi-Boundary Semi-Analytical Method for Backward in Time Advection-Dispersion Equation

    Chein-Shan Liu1, Chih-Wen Chang2, Jiang-Ren Chang2,3

    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 Cα(x,t) are provided More >

  • Open Access

    ARTICLE

    Relaxation of Alternating Iterative Algorithms for the Cauchy Problem Associated with the Modified Helmholtz Equation

    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 >

  • Open Access

    ARTICLE

    An Alternating Iterative MFS Algorithm for the Cauchy Problem in Two-Dimensional Anisotropic Heat Conduction

    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 >

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