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  • Open Access


    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 equation. The termwise separable… More >

  • Open Access


    The Method of Fundamental Solutions for Inverse Problems Associated with the Steady-State Heat Conduction in the Presence of Sources

    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 >

  • Open Access


    A Highly Accurate MCTM for Direct and Inverse Problems of Biharmonic Equation in Arbitrary Plane Domains

    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 >

  • Open Access


    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


    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 >

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