Open Access
ARTICLE
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
C. Jiang1, Y.C. Bai1, X. Han1,2, H.M. Ning1
CMC-Computers, Materials & Continua, Vol.18, No.1, pp. 21-42, 2010, DOI:10.3970/cmc.2010.018.021
Abstract In this paper, an efficient interval optimization method based on a reliability-based possibility degree of interval (RPDI) is suggested for the design of uncertain structures. A general nonlinear interval optimization problem is studied in which the objective function and constraints are both nonlinear and uncertain. Through an interval order relation and a reliability-based possibility degree of interval, the uncertain optimization problem is transformed into a deterministic one. A sequence of approximate optimization problems are constructed based on the linear approximation technique. Each approximate optimization problem can be changed to a traditional linear programming problem, which can be easily solved by… More >
Open Access
ARTICLE
C.Y. Lin1, M.H. Gu1, D.L. Young1,2
CMC-Computers, Materials & Continua, Vol.18, No.1, pp. 43-68, 2010, DOI:10.3970/cmc.2010.018.043
Abstract The telegraph equations are solved by using the meshless numerical method called the time-marching method of fundamental solutions (TMMFS) in this paper. The present method is based on the method of fundamental solutions, the method of particular solutions and the Houbolt finite difference scheme. The TMMFS is a meshless numerical method, and has the advantages of no mesh building and numerical quadrature. Therefore in this study we eventually solved the multi-dimensional telegraph equation problems in irregular domain. There are totally six numerical examples demonstrated, in order they are one-dimensional telegraph equation, one-dimensional non-decaying telegraph problem, two-dimensional telegraph equation in irregular… More >
Open Access
ARTICLE
A.Z. Lorbiecka1, B. Šarler1,2
CMC-Computers, Materials & Continua, Vol.18, No.1, pp. 69-104, 2010, DOI:10.3970/cmc.2010.018.069
Abstract The aim of this paper is simulation of thermally induced liquid-solid dendritic growth in two dimensions by a coupled deterministic continuum mechanics heat transfer model and a stochastic localized phase change kinetics model that takes into account the undercooling, curvature, kinetic and thermodynamic anisotropy. The stochastic model receives temperature information from the deterministic model and the deterministic model receives the solid fraction information from the stochastic model. The heat transfer model is solved on a regular grid by the standard explicit Finite Difference Method (FDM). The phase-change kinetics model is solved by the classical Cellular Automata (CA) approach and a… More >
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