Liviu Marin¹, Andreas Karageorghis²

CMC-Computers, Materials & Continua, Vol.10, No.3, pp. 259-294, 2009, DOI:10.3970/cmc.2009.010.259

Abstract We study the stable numerical identification of an unknown portion of the boundary on which a given boundary condition is provided and additional Cauchy data are given on the remaining known portion of the boundary of a two-dimensional domain for problems governed by either the Helmholtz or the modified Helmholtz equation. This inverse geometric problem is solved using the method of fundamental solutions (MFS) in conjunction with the Tikhonov regularization method. The optimal value for the regularization parameter is chosen according to Hansen's L-curve criterion. The stability, convergence, accuracy and efficiency of the proposed method are investigated by considering several… More >

J.H. Tian^1,2, 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 conduction firstly and provides us… More >

B. Šarler¹, R.Vertnik, J. Perko¹

CMC-Computers, Materials & Continua, Vol.2, No.1, pp. 77-84, 2005, DOI:10.3970/cmc.2005.002.077

Abstract The steady-state convective-diffusive solid-liquid phase change problem associated with temperature fields in direct-chill, semi-continuously cast billets and slabs from aluminum alloys has been solved by the Diffuse Approximate Method (DAM). The solution is based on formulation, which incorporates the mixture continuum physical model, nine-noded support, second order polynomial trial functions, and Gaussian window weighting functions. Realistic boundary conditions and temperature variation of material properties are included. Two-dimensional test case solution is shown, verified by comparison with the Finite Volume Method (FVM) results for coarse and fine grid arrangement. More >

T. Tsangaris¹, Y.–S. Smyrlis^{1, 2}, A. Karageorghis^{1, 2}

CMC-Computers, Materials & Continua, Vol.1, No.3, pp. 245-258, 2004, DOI:10.3970/cmc.2004.001.245

Abstract The Method of Fundamental Solutions (MFS) is a boundary-type method for the solution of certain elliptic boundary value problems. In this work, we develop an efficient matrix decomposition MFS algorithm for the solution of biharmonic problems in annular domains. The circulant structure of the matrices involved in the MFS discretization is exploited by using Fast Fourier Transforms. The algorithm is tested numerically on several examples. More >