Home / Journals / CMES / Vol.100, No.5, 2014
Table of Content
  • Open Access

    ARTICLE

    Boundary Layer Effect in Regularized Meshless Method for Laplace Equation

    Weiwei Li1, Wen Chen1,2
    CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.5, pp. 347-362, 2014, DOI:10.3970/cmes.2014.100.347
    Abstract This paper presents an efficient strategy for the accurate evaluation of near-boundary solutions in the regularized meshless method (RMM), also known as the boundary layer effect associated with the boundary element method. The RMM uses the double layer potentials as its interpolation basis function. When the field point is close to the boundary, the basis function will present nearly strongand hyper-singularities, respectively, for potentials and its derivative. This paper represents the first attempt to apply a nonlinear transformation, based on sinh function, to the accurate evaluation of nearly singular kernels associated with the RMM. The accuracy and efficiency of the… More >

  • Open Access

    ARTICLE

    Parallel Control-volume Method Based on Compact Local Integrated RBFs for the Solution of Fluid Flow Problems

    N. Pham-Sy1, C.-D. Tran1, N. Mai-Duy1, T. Tran-Cong1
    CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.5, pp. 363-397, 2014, DOI:10.3970/cmes.2014.100.363
    Abstract In this paper, a high performance computing method based on the Integrated Radial Basis Function (IRBF), Control Volume (CV) and Domain Decomposition technique for solving Partial Differential Equations is presented. The goal is to develop an efficient parallel algorithm based on the Compact Local IRBF method using the CV approach, especially for problems with non-rectangular domain. The results showed that the goal is achieved as the computational efficiency is quite significant. For the case of square lid driven cavity problem with Renoylds number 100, super-linear speed-up is also achieved. The parallel algorithm is implemented in the Matlab environment using Parallel… More >

  • Open Access

    ARTICLE

    Numerical Solution of System of N–Coupled Nonlinear Schrödinger Equations via Two Variants of the Meshless Local Petrov–Galerkin (MLPG) Method

    M. Dehghan1, M. Abbaszadeh2, A. Mohebbi3
    CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.5, pp. 399-444, 2014, DOI:10.3970/cmes.2014.100.399
    Abstract In this paper three numerical techniques are proposed for solving the system of N-coupled nonlinear Schrödinger (CNLS) equations. Firstly, we obtain a time discrete scheme by approximating the first-order time derivative via the forward finite difference formula, then for obtaining a full discretization scheme, we use the Kansa’s approach to approximate the spatial derivatives via radial basis functions (RBFs) collocation methodology. We introduce the moving least squares (MLS) approximation and radial point interpolation method (RPIM) with their shape functions, separately. It should be noted that the shape functions of RPIM unlike the shape functions of the MLS approximation have kronecker… More >

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