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  • Open Access


    A Fictitious Time Integration Method for Multi-Dimensional Backward Heat Conduction Problems

    Chih-Wen Chang1

    CMC-Computers, Materials & Continua, Vol.19, No.3, pp. 285-314, 2010, DOI:10.3970/cmc.2010.019.285

    Abstract In this article, we propose a new numerical approach for solving these multi-dimensional nonlinear and nonhomogeneous backward heat conduction problems (BHCPs). A fictitious time t is employed to transform the dependent variable u(x, y, z, t) into a new one by (1+t)u(x, y, z, t)=: v(x, y, z, t, t), such that the original nonlinear and nonhomogeneous heat conduction equation is written as a new parabolic type partial differential equation in the space of (x, y, z, t, t). In addition, a fictitious viscous damping coefficient can be used to strengthen the stability of numerical More >

  • Open Access


    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 More >

  • Open Access


    A Quasi-Boundary Semi-Analytical Approach for Two-Dimensional Backward Heat Conduction Problems

    Chih-Wen Chang1, Chein-Shan Liu2, Jiang-Ren Chang3

    CMC-Computers, Materials & Continua, Vol.15, No.1, pp. 45-66, 2010, DOI:10.3970/cmc.2010.015.045

    Abstract In this article, we propose a semi-analytical method to tackle the two-dimensional backward heat conduction problem (BHCP) by using a quasi-boundary idea. First, the Fourier series expansion technique is employed to calculate the temperature field u(x, y, t) at any time t < T. Second, we consider a direct regularization by adding an extra termau(x, y, 0) to reach a second-kind Fredholm integral equation for u(x, y, 0). The termwise separable property of the kernel function permits us to obtain a closed-form regularized solution. Besides, a strategy to choose the regularization parameter is suggested. When several numerical examples were More >

  • Open Access


    Heat Transfer in Composite Beams using Combined Cellular Automaton and Fibre Model

    W.F.Yuan1, K.H.Tan 1

    CMC-Computers, Materials & Continua, Vol.13, No.1, pp. 49-62, 2009, DOI:10.3970/cmc.2009.013.049

    Abstract A simple cellular automaton (CA) scheme is proposed to simulate heat conduction in anisotropic domains. The CA is built on random nodes rather than an irregular grid. The local rule used in the CA is defined by physical concepts instead of differential equations. The accuracy of the proposed approach is verified by classical examples. As an application of the proposed method, the CA approach is incorporated into fibre model which is widely used in finite element analysis to calculate the temperature distribution on the cross-section of composite beams. Numerical examples demonstrate that the proposed scheme More >

  • Open Access


    Three-Dimensional Solutions of Functionally Graded Piezo-Thermo-Elastic Shells and Plates Using a Modified Pagano Method

    Chih-Ping Wu1,2, Shao-En Huang2

    CMC-Computers, Materials & Continua, Vol.12, No.3, pp. 251-282, 2009, DOI:10.3970/cmc.2009.012.251

    Abstract A modified Pagano method is developed for the three-dimensional (3D) coupled analysis of simply-supported, doubly curved functionally graded (FG) piezo-thermo-elastic shells under thermal loads. Four different loading conditions, applied on the lateral surfaces of the shells, are considered. The material properties of FG shells are regarded as heterogeneous through the thickness coordinate, and then specified to obey an exponent-law dependent on this. The Pagano method, conventionally used for the analysis of multilayered composite elastic plates/shells, is modified to be feasible for the present analysis of FG piezo-thermo-elastic plates/shells. The modifications include that a displacement-based formulation More >

  • Open Access


    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 >

  • Open Access


    An Analysis of the Heat Conduction Problem for Plates with the Functionally Graded Material Using the Hybrid Numerical Method

    J.H. Tian1,2, X. Han2, S.Y. Long3, G.Q. Xie4

    CMC-Computers, Materials & Continua, Vol.10, No.3, pp. 229-242, 2009, DOI:10.3970/cmc.2009.010.229

    Abstract A heat conduction analysis of the functionally graded material (FGM) plates has been investigated based on the hybrid numerical method (HNM). HNM combines the layer element method with the method of Fourier transforms and proves to be efficient and reliable. The FGM plates are infinite large and the material properties vary continuously through thickness. The heat source continually acted one the FGM plates. The temperature distribution of the FGM plates is obtained in different time and different position. Some useful results for heat conduction problems are shown in figures. This article applies HNM to heat More >

  • Open Access


    Transient Non-linear Heat Conduction Solution by a Dual Reciprocity Boundary Element Method with an Effective Posteriori Error Estimator

    Eduardo Divo1, Alain J. Kassab2

    CMC-Computers, Materials & Continua, Vol.2, No.4, pp. 277-288, 2005, DOI:10.3970/cmc.2005.002.277

    Abstract A Dual Reciprocity Boundary Element Method is formulated to solve non-linear heat conduction problems. The approach is based on using the Kirchhoff transform along with lagging of the effective non-linear thermal diffusivity. A posteriori error estimate is used to provide effective estimates of the temporal and spatial error. A numerical example is used to demonstrate the approach. More >

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