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  • 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,… 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) More >

  • Open Access

    ARTICLE

    An Iterative and Adaptive Lie-Group Method for Solving the Calderón Inverse Problem

    Chein-Shan Liu1, Satya N. Atluri2

    CMES-Computer Modeling in Engineering & Sciences, Vol.64, No.3, pp. 299-326, 2010, DOI:10.3970/cmes.2010.064.299

    Abstract We solve the Calderón inverse conductivity problem [Calderón (1980, 2006)], for an elliptic type equation in a rectangular plane domain, to recover an unknown conductivity function inside the domain, from the over-specified Cauchy data on the bottom of the rectangle. The Calderón inverse problem exhibitsthree-fold simultaneous difficulties: ill-posedness of the inverse Cauchy problem, ill-posedness of the parameter identification, and no information inside the domain being available on the impedance function. In order to solve this problem, we discretize the whole domain into many sub-domains of finite strips, each with a small height. Thus the Calderón… More >

  • Open Access

    ARTICLE

    On the Solution of an Inverse Problem for an Integro-differential Transport Equation

    Ismet Gölgeleyen1

    CMES-Computer Modeling in Engineering & Sciences, Vol.64, No.1, pp. 71-90, 2010, DOI:10.3970/cmes.2010.064.071

    Abstract In this paper, the solvability conditions for an inverse problem for an integro-differential transport equation are obtained and a numerical approximation method based on the finite difference method is developed. A comparison between the numerical solution and the exact solution of the problem is presented. Experimental results show that proposed method is robust to data noises. More >

  • Open Access

    ARTICLE

    Self-Adaptive Differential Evolution Based on the Concept of Population Diversity Applied to Simultaneous Estimation of Anisotropic Scattering Phase Function, Albedo and Optical Thickness

    F. S. Lobato1, V. Steffen Jr2, A. J. Silva Neto3

    CMES-Computer Modeling in Engineering & Sciences, Vol.69, No.1, pp. 1-18, 2010, DOI:10.3970/cmes.2010.069.001

    Abstract Differential Evolution Algorithm (DE) has shown to be a powerful evolutionary algorithm for global optimization in a variety of real world problems. DE differs from other evolutionary algorithms in the mutation and recombination phases. Unlike some other meta-heuristic techniques such as genetic algorithms and evolutionary strategies, where perturbation occurs in accordance with a random quantity, DE uses weighted differences between solution vectors to perturb the population. Although the efficiency of DE algorithm has been proven in the literature, studies indicate that the efficiency of the DE methods is sensitive to its control parameters (perturbation rate More >

  • Open Access

    ARTICLE

    Evolutionary Algorithms Applied to Estimation of Thermal Property by Inverse Problem

    V.C. Mariani1, V. J. Neckel2, L. S. Coelho3

    CMES-Computer Modeling in Engineering & Sciences, Vol.68, No.2, pp. 167-184, 2010, DOI:10.3970/cmes.2010.068.167

    Abstract In this study an inverse heat conduction problem using two optimization methods to estimate apparent thermal diffusivity at different drying temperatures is solved. Temperature and moisture versus time were obtained numerically using heat and mass transfer equations with drying temperatures in the range between 20°C to 70°C. The solution of the partial differential equation is made with a finite difference method coupled to optimization techniques of Differential Evolution (DE) and Particle Swarm Optimization (PSO) used in inverse problem. Statistical analysis shows no significant differences between reported and estimated curves, and no remarkable differences between results More >

  • Open Access

    ARTICLE

    Solvability of an Inverse Problem for the Kinetic Equation and a Symbolic Algorithm

    Arif Amirov1, Fikret Gölgeleyen1

    CMES-Computer Modeling in Engineering & Sciences, Vol.65, No.2, pp. 179-192, 2010, DOI:10.3970/cmes.2010.065.179

    Abstract In this work, we derive the solvability conditions for an inverse problem for the kinetic equation and develop a new symbolic algorithm to obtain the approximate solution of the problem. The computational experiments show that proposed method provides highly accurate numerical solutions even subjecting to a large noise in the given data. More >

  • Open Access

    ARTICLE

    Approximate Solution of an Inverse Problem for a Non-Stationary General Kinetic Equation

    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 >

  • Open Access

    ARTICLE

    Reconstruction of Boundary Data in Two-Dimensional Isotropic Linear Elasticity from Cauchy Data Using an Iterative MFS Algorithm

    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 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 More >

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