CMES-Vol. 38, No. 1, 2008

Open Access

ARTICLE

A Numerical Meshfree Technique for the Solution of the MEW Equation
Sirajul Haq¹, Siraj-ul-Islam², Arshed Ali³
CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.1, pp. 1-24, 2008, DOI:10.3970/cmes.2008.038.001
Abstract In this paper we propose a meshfree technique for the numerical solution of the modified equal width wave (MEW) equation. Combination of collocation method using the radial basis functions (RBFs) with first order accurate forward difference approximation is employed for obtaining meshfree solution of the problem. Different types of RBFs are used for this purpose. Performance of the proposed method is successfully tested in terms of various error norms. In the case of non-availability of exact solution, performance of the new method is compared with the results obtained from the existing methods. Propagation of a solitary wave, interaction of two… More >

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A New Mathematical Modeling of Maxwell Equations: Complex Linear Operator and Complex Field
Chein-Shan Liu¹
CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.1, pp. 25-38, 2008, DOI:10.3970/cmes.2008.038.025
Abstract In this paper a complex matrix operator and a complex field are used to express the Maxwell equations, of which the complex field embraces all field variables and the matrix operator embraces the time and space differential operators. By left applying the operator on the complex field one can get all the four Maxwell equations, which are usually expressed by the vector form. The new formulation matches the Lorenz gauge condition, and its mathematical advantage is that it can incorporate the Maxwell equations into a single equation. The introduction of four-potential is possible only under the Lorenz gauge. In terms… More >

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Application of the Generalized Finite Difference Method to improve the approximated solution of pdes
J.J. Benito¹, F. Ureňa², L. Gavete³, B. Alonso³
CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.1, pp. 39-58, 2008, DOI:10.3970/cmes.2008.038.039
Abstract One of the most universal and effective methods, in wide use today, for solving equations of mathematical physics approximately is the finite difference method (FDM). The Generalized finite difference method (GFDM) is evolved fron classical (FDM), which can be applied over general or irregular clouds of points.
This paper starts by showing the GFDM. In this paper, this meshless method is used for solving second-order partial (pde's) with constant coefficients in any type of domain. The method gives the values of derivatives in the nodes using the direct application of the formulae in differences obtained.
The following points describe… More >

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A Method Based on Wavelets for Band Structure Analysis of Phononic Crystals
Zhi-Zhong Yan^1,2, Yue-Sheng Wang^1,3, Chuanzeng Zhang²
CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.1, pp. 59-88, 2008, DOI:10.3970/cmes.2008.038.059
Abstract In this paper, a numerical method based on the wavelet theory is developed for calculating band structures of 2D phononic crystals consisting of general anisotropic materials. After systematical consideration of the appropriate choice of wavelets, two types of wavelets, the Haar wavelet and Biorthogonal wavelet, are selected. Combined with the supercell technique, the developed method can be then applied to compute the band structures of phononic crystals with point or line defects. We illustrate the advantages of the method both mathematically and numerically. Particularly some representative numerical examples are presented for various material combinations (solid-solid, solid-fluid and fluid-fluid) with complex… More >

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