D. L. Young^1,3, K. H. Chen², T. Y. Liu³, L. H. Shen³, C. S. Wu³

CMES-Computer Modeling in Engineering & Sciences, Vol.40, No.3, pp. 225-270, 2009, DOI:10.3970/cmes.2009.040.225

Abstract In this article, a hypersingular meshless method (HMM) is extended to solve 3D potential problems for arbitrary domains after a 2D model was successfully developed (Young et al. 2005a). The solutions are represented by a distribution of the double layer potentials instead of the single layer potentials as generally used in the conventional method of fundamental solutions (MFS). By using the desingularization technique to regularize the singularity and hypersingularity of the double layer potentials, the source points can be located exactly on the real boundary to avoid the sensitivity of locating fictitious boundary for putting… More >

A. Takei¹, S. Yoshimura¹, H. Kanayama²

CMES-Computer Modeling in Engineering & Sciences, Vol.40, No.1, pp. 63-82, 2009, DOI:10.3970/cmes.2009.040.063

Abstract This paper describes a large-scale finite element analysis (FEA) for a high-frequency electromagnetic field of Maxwell equations including the displacement current. A stationary Helmholtz equation for the high-frequency electromagnetic field analysis is solved by considering an electric field and an electric scalar potential as unknown functions. To speed up the analysis, the hierarchical domain decomposition method (HDDM) is employed as a parallel solver. In this study, the Parent-Only type (Parallel processor mode: P-mode) of the HDDM is employed. In the P-mode, Parent processors perform the entire FEA. In this mode, all CPUs can be used More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.40, No.1, pp. 1-28, 2009, DOI:10.3970/cmes.2009.040.001

Abstract We consider an inverse problem of Laplace equation by recoverning boundary value on the inner circle of a two-dimensional annulus from the overdetermined data on the outer circle. The numerical results can be used to determine the Robin coefficient or crack's position inside a disk from the measurements of Cauchy data on the outer boundary. The Fourier series is used to formulate the first kind Fredholm integral equation for the unknown data f(θ) on the inner circle. Then we consider a Lavrentiev regularization, by adding an extra term αf(θ) to obtain the second kind Fredholm integral More >

W. Attaporn¹, H. Koguchi²

CMES-Computer Modeling in Engineering & Sciences, Vol.39, No.3, pp. 237-262, 2009, DOI:10.3970/cmes.2009.039.237

Abstract In the present study, a stress singularity field along free edges meeting at a corner in a three-dimensional joint structure is investigated. The order of stress singularity is determined using an eigen analysis based on a finite element method. Intensities of stress singularity not only at the corner but also along the free edge of interface are determined directly without any post-processing by a new FEM formulation referred to as a three-dimensional enriched FEM. Result in the present analysis is also compared with that in another numerical method. It was slightly larger than the intensity More >

D. S. Liu¹, C.Y. Tsai¹

CMES-Computer Modeling in Engineering & Sciences, Vol.39, No.1, pp. 29-48, 2009, DOI:10.3970/cmes.2009.039.029

Abstract Utilizing a thin copper substrate for illustration purposes, this study presents a novel numerical method for extracting the thermo-mechanical properties of a thin-film. In the proposed approach, molecular dynamics (MD) simulations are performed to establish the load-displacement response of a thin copper substrate nanoindented at temperatures ranging from 300~1400 K. The load data are then input to an artificial neural network (ANN), trained using a finite element model (FEM), in order to extract the material constants of the copper substrate. The material constants are then used to construct the corresponding stress-strain curve, from which the… More >

Nicolas Ali Libre^1,2, Arezoo Emdadi², Edward J. Kansa^3,4, Mohammad Shekarchi², Mohammad Rahimian²

CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.3, pp. 263-284, 2008, DOI:10.3970/cmes.2008.038.263

Abstract We present a wavelet based adaptive scheme and investigate the efficiency of this scheme for solving nearly singular potential PDEs. Multiresolution wavelet analysis (MRWA) provides a firm mathematical foundation by projecting the solution of PDE onto a nested sequence of approximation spaces. The wavelet coefficients then were used as an estimation of the sensible regions for node adaptation. The proposed adaptation scheme requires negligible calculation time due to the existence of the fast Discrete Wavelet Transform (DWT). Certain aspects of the proposed adaptive scheme are discussed through numerical examples. It has been shown that the More >

T. Jarak¹, J. Sorić¹

CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.3, pp. 231-262, 2008, DOI:10.3970/cmes.2008.038.231

Abstract A new mixed meshless formulation based on the interpolation of both strains and displacements has been proposed for the analysis of plate deformation responses. Kinematics of a three dimensional solid is adopted and discretization is performed by the nodes located on the upper and lower plate surfaces. The governing equations are derived by employing the local Petrov-Galerkin approach. The approximation of all unknown field variables is carried out by using the same Moving Least Squares functions in the in-plane directions, while linear polynomials are applied in the transversal direction. The shear locking effect is efficiently More >

X.Y. Cui^1,2, G. R. Liu^2,3, G. Y. Li^1,4, G. Zheng¹

CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.3, pp. 217-230, 2008, DOI:10.3970/cmes.2008.038.217

Abstract In this paper, a gradient smoothed formulation is proposed to deal with a fourth-order differential equation of Bernoulli-Euler beam problems for static and dynamic analysis. Through the smoothing operation, the C¹ continuity requirement for fourth-order boundary value and initial value problems can be easily relaxed, and C⁰ interpolating function can be employed to solve C¹ problems. In present thin beam problems, linear shape functions are employed to approximate the displacement field, and smoothing domains are further formed for computing the smoothed curvature and bending moment field. Numerical examples indicate that very accurate results can be yielded when More >

Briti Sundar Deb¹, Srinivasan Natesan²

CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.2, pp. 179-200, 2008, DOI:10.3970/cmes.2008.038.179

Abstract This paper presents an almost second--order uniformly convergent Richardson extrapolation method for convection- dominated coupled system of boundary value problems. First, we solve the system by using the classical finite difference scheme on the layer resolving Shishkin mesh, and then we construct the Richardson approximation solution using the solutions obtained on N and 2N mesh intervals. Second-order parameter--uniform error estimate is derived. The proposed method is applied to a test example for verification of the theoretical results for the case ε ≤ N⁻¹. More >

C. Zheng¹, S. C. Wu^2,3,4, X.H.Tang¹, J. H. Zhang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.2, pp. 149-178, 2008, DOI:10.3970/cmes.2008.038.149

Abstract A novel meshfree poly-cell Galerkin method is developed for problems of elasticity and fracture. To improve accuracy, a poly-cell support is proposed to ensure the alignment of shape function support and the integration domain. By orthonormalizing basis functions, the improved moving least-square is formulated soundly, in which frequent matrix inversions are avoided. The Nitsche's method is introduced to treat the essential boundary conditions. It is found that computed solutions are more accurate than those obtained using the circle support used in standard MLS. Furthermore, numerical results present the superconvergent property, compared with the theoretical values More >