Ying-Hsiu Shen¹, Chein-Shan Liu^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.2, pp. 157-178, 2011, DOI:10.3970/cmes.2011.071.157

Abstract When the local differential quadrature (LDQ) has been successfully applied to solve two-dimensional problems, the global method of DQ still has a problem by requiring to solve the inversions of ill-posed matrices. Previously, when one uses (n-1)th order polynomial test functions to determine the weighting coefficients with n grid points, the resultant n ×n Vandermonde matrix is highly ill-conditioned and its inversion is hard to solve. Now we use (m-1)th order polynomial test functions by n grid points that the size of Vandermonde matrix is m×n, of which m is much less than n. We find that the (m-1)th order… More >

A. Idesman ¹

CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.2, pp. 111-148, 2011, DOI:10.3970/cmes.2011.071.111

Abstract The paper deals with the following issues of existing time-integration methods for a semi-discrete system of elastodynamics equations: a) the quantification and the suppression of spurious high frequencies; b) the selection of the amount of numerical dissipation for a time-integration method; and c) accurate time integration of low modes. The finite element method used in the paper or other methods can be applied for the space discretization. A new two-stage time-integration procedure consisting of basic computations and the filtering stage is developed. For accurate integration of all frequencies, a time-integration method with zero (or small) numerical dissipation is applied for… More >

Shuncai Li^1,2,3, Zhengzhu Dong², Dan Ma²

CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.2, pp. 93-110, 2011, DOI:10.3970/cmes.2011.071.093

Abstract Weak local support is a very common phenomenon in roadway support engineering. It is a problem that needs to be studied thoroughly at the theoretical level. So far, the literature on stress field theory of rock surrounding a roadway is largely restricted to analytical solutions of stress for roadways with a uniform support or no support at all. The corresponding stress solution under conditions of local or weak local support has not been provided. Based on a mechanical model of weak local support at the boundary of a circular roadway and the boundary element method on boundary value problems of… More >

S. Abbasbandy^1,2, V. Sladek³, A. Shirzadi¹, J. Sladek³

CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.1, pp. 15-38, 2011, DOI:10.3970/cmes.2011.071.015

Abstract This paper deals with the development of a new method for solution of initial-boundary value problems governed by a couple of nonlinear diffusion equations occurring in the theory of self-organization in non-equilibrium systems. The time dependence is treated by linear interpolation using the finite difference method and the semi-discrete partial differential equations are considered in a weak sense by using the local integral equation method with approximating 2-d spatial variations of the field variables by the Moving Least Squares. The evaluation techniques are discussed and the applicability of the presented method is demonstrated on two illustrative examples with exact solutions… More >

K. Le-Cao¹, N. Mai-Duy¹, C.-D. Tran¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.67, No.3, pp. 265-294, 2010, DOI:10.3970/cmes.2010.067.265

Abstract In this paper, radial basis functions are utilised for numerical prediction of the bulk properties of particulate suspensions under simple shear conditions. The suspending fluid is Newtonian and the suspended particles are rigid. Results obtained are compared well with those based on finite elements in the literature. More >

Hua Zou¹, Hua Li^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.67, No.1, pp. 55-78, 2010, DOI:10.3970/cmes.2010.067.055

Abstract A novel meshless technique termed the Random Integral Quadrature (RIQ) method is developed in this paper for solving the generalized integral equations. By the RIQ method, the governing equations in the integral form are discretized directly with the field nodes distributed randomly or uniformly, which is achieved by discretizing the integral governing equations with the generalized integral quadrature (GIQ) technique over a set of background virtual nodes, and then interpolating the function values at the virtual nodes over a set of field nodes with Local Kriging method, where the field nodes are distributed either randomly or uniformly. The RIQ method… More >

Marcin Maździarz¹

CMES-Computer Modeling in Engineering & Sciences, Vol.66, No.1, pp. 1-24, 2010, DOI:10.3970/cmes.2010.066.001

Abstract The paper presents unified approach to 3D isoparametric Lagrange brick, tetra, and prism finite elements. All shape functions, linear, quadratic and cubic, are depicted in one Cartesian orthogonal coordinate system x,y,z regardless of the type of element. This allows one to use a single transformation rule to calculate global derivatives and a second for integration. Proper numerical Gauss quadratures for these isoparametric elements in a unified approach are presented additionally. More >

Montri Maleewong¹, Sirod Sirisup²

CMES-Computer Modeling in Engineering & Sciences, Vol.65, No.2, pp. 193-216, 2010, DOI:10.3970/cmes.2010.065.193

Abstract In this paper, we describe our investigation of an "on-line" POD-assisted projective integration method for solving a nonlinear PDE. Using the on-line method, we have computed the representative POD modes without assuming knowledge of the underlying slow manifold along the integration process. This approach is based on the "equation-free" framework where the governing PDE does not need to be projected onto the POD bases in order to build a reduced-order model. The main objectives of this study were to investigate the effectiveness of the method in reducing the computational time required for numerically solving a nonlinear PDE. Here, the one-dimensional… More >