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  • Open Access

    ARTICLE

    An Inverse Boundary Element Method for Determining the Hydraulic Conductivity in Anisotropic Rocks

    R. Mustata1, S. D. Harris2, L. Elliott1, D. Lesnic1, D. B. Ingham1

    CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.3, pp. 107-116, 2000, DOI:10.3970/cmes.2000.001.409

    Abstract An inverse boundary element method is developed to characterise the components of the hydraulic conductivity tensor K of anisotropic materials. Surface measurements at exposed boundaries serve as additional input to a Genetic Algorithm (GA) using a modified least squares functional that minimises the difference between observed and BEM-predicted boundary pressure and/or hydraulic flux measurements under current hydraulic conductivity tensor component estimates. More >

  • Open Access

    ARTICLE

    Analysis of Hydrogen Permeation in Metals by Means of a New Anomalous Diffusion Model and Bayesian Inference

    Marco A.A. Kappel1, Diego C. Knupp1, Roberto P. Domingos1, IvanN. Bastos1

    CMC-Computers, Materials & Continua, Vol.49-50, No.1, pp. 13-29, 2015, DOI:10.3970/cmc.2015.049.013

    Abstract This work is aimed at the direct and inverse analysis of hydrogen permeation in steels employing a novel anomalous diffusion model. For the inverse analysis, experimental data for hydrogen permeation in a 13% chromium martensitic stainless steel, available in the literature [Turnbull, Carroll and Ferriss (1989)], was employed within the Bayesian framework for inverse problems. The comparison between the predicted values and the available experimental data demonstrates the feasibility of the new model in adequately describing the physical phenomena occurring in this particular problem. 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 and a… More >

  • Open Access

    ARTICLE

    The Lie-Group Shooting Method for Thermal Stress Evaluation Through an Internal Temperature Measurement

    Chein-Shan Liu1

    CMC-Computers, Materials & Continua, Vol.8, No.1, pp. 1-16, 2008, DOI:10.3970/cmc.2008.008.001

    Abstract In the present work we study numerical computations of inverse thermal stress problems. The unknown boundary conditions of an elastically deformable heat conducting rod are not given a priori and are not allowed to measure directly, because the boundary may be not accessible to measure. However, an internal measurement of temperature is available. We treat this inverse problem by using a semi-discretization technique, of which the time domain is divided into many sub-intervals and the physical quantities are discretized at these node points of discrete times. Then the resulting ordinary differential equations in the discretized space are numerically integrated towards… More >

  • Open Access

    ARTICLE

    An LGEM to Identify Time-Dependent Heat Conductivity Function by an Extra Measurement of Temperature Gradient

    Chein-Shan Liu1,2

    CMC-Computers, Materials & Continua, Vol.7, No.2, pp. 81-96, 2008, DOI:10.3970/cmc.2008.007.081

    Abstract We consider an inverse problem for estimating an unknown heat conductivity parameter α(t) in a heat conduction equation Tt(x,t) = α(t)Txx(x,t) with the aid of an extra measurement of temperature gradient on boundary. Basing on an establishment of the one-step Lie-group elements G(r) and G(l) for the semi-discretization of heat conduction equation in time domain, we can derive algebraic equations from G(r) = G(l). The new method, namely the Lie-group estimation method (LGEM), is examined through numerical examples to convince that it is highly accurate and efficient; the maximum estimation error is smaller than 10-5 for smooth parameter and for… More >

  • Open Access

    ARTICLE

    Solution of Inverse Boundary Optimization Problem by Trefftz Method and Exponentially Convergent Scalar Homotopy Algorithm

    Hsin-Fang Chan1, Chia-Ming Fan1,2, Weichung Yeih1

    CMC-Computers, Materials & Continua, Vol.24, No.2, pp. 125-142, 2011, DOI:10.3970/cmc.2011.024.125

    Abstract The inverse boundary optimization problem, governed by the Helmholtz equation, is analyzed by the Trefftz method (TM) and the exponentially convergent scalar homotopy algorithm (ECSHA). In the inverse boundary optimization problem, the position for part of boundary with given boundary condition is unknown, and the position for the rest of boundary with additionally specified boundary conditions is given. Therefore, it is very difficult to handle the boundary optimization problem by any numerical scheme. In order to stably solve the boundary optimization problem, the TM, one kind of boundary-type meshless methods, is adopted in this study, since it can avoid the… More >

  • Open Access

    ARTICLE

    Using a Lie-Group Adaptive Method for the Identification of a Nonhomogeneous Conductivity Function and Unknown Boundary Data

    Chein-Shan Liu1

    CMC-Computers, Materials & Continua, Vol.21, No.1, pp. 17-40, 2011, DOI:10.3970/cmc.2011.021.017

    Abstract Only the left-boundary data of temperature and heat flux are used to estimate an unknown parameter function α(x) in Tt(x,t) = ∂(α(x)Tx)/∂x + h(x,t), as well as to recover the right-boundary data. When α(x) is given the above problem is a well-known inverse heat conduction problem (IHCP). This paper solves a mixed-type inverse problem as a combination of the IHCP and the problem of parameter identification, without needing to assume a function form of α(x) a priori, and without measuring extra data as those used by other methods. We use the one-step Lie-Group Adaptive Method (LGAM) for the semi-discretizations of… More >

  • Open Access

    ARTICLE

    A Lie-Group Adaptive Method for Imaging a Space-Dependent Rigidity Coefficient in an Inverse Scattering Problem of Wave Propagation

    Chein-Shan Liu1

    CMC-Computers, Materials & Continua, Vol.18, No.1, pp. 1-20, 2010, DOI:10.3970/cmc.2010.018.001

    Abstract We are concerned with the reconstruction of an unknown space-dependent rigidity coefficient in a wave equation. This problem is known as one of the inverse scattering problems. Based on a two-point Lie-group equation we develop a Lie-group adaptive method (LGAM) to solve this inverse scattering problem through iterations, which possesses a special character that by using onlytwo boundary conditions and two initial conditions, as those used in the direct problem, we can effectively reconstruct the unknown rigidity function by aself-adaption between the local in time differential governing equation and the global in time algebraic Lie-group equation. The accuracy and efficiency… More >

  • Open Access

    ARTICLE

    On Solving the Direct/Inverse Cauchy Problems of Laplace Equation in a Multiply Connected Domain, Using the Generalized Multiple-Source-Point Boundary-Collocation Trefftz Method &Characteristic Lengths

    Weichung Yeih1, Chein-Shan Liu2, Chung-Lun Kuo3, Satya N. Atluri4

    CMC-Computers, Materials & Continua, Vol.17, No.3, pp. 275-302, 2010, DOI:10.3970/cmc.2010.017.275

    Abstract In this paper, a multiple-source-point boundary-collocation Trefftz method, with characteristic lengths being introduced in the basis functions, is proposed to solve the direct, as well as inverse Cauchy problems of the Laplace equation for a multiply connected domain. When a multiply connected domain with genus p (p>1) is considered, the conventional Trefftz method (T-Trefftz method) will fail since it allows only one source point, but the representation of solution using only one source point is impossible. We propose to relax this constraint by allowing many source points in the formulation. To set up a complete set of basis functions, we… More >

  • Open Access

    ARTICLE

    Stable Boundary and Internal Data Reconstruction in Two-Dimensional Anisotropic Heat Conduction Cauchy Problems Using Relaxation Procedures for an Iterative MFS Algorithm

    Liviu Marin1

    CMC-Computers, Materials & Continua, Vol.17, No.3, pp. 233-274, 2010, DOI:10.3970/cmc.2010.017.233

    Abstract We investigate two algorithms involving the relaxation of either the given boundary temperatures (Dirichlet data) or the prescribed normal heat fluxes (Neumann data) on the over-specified boundary in the case of the iterative algorithm of Kozlov91 applied to Cauchy problems for two-dimensional steady-state anisotropic heat conduction (the Laplace-Beltrami equation). 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)… More >

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