S. Callsen¹, O. von Estorff¹, O. Zaleski²

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.5, pp. 421-430, 2004, DOI:10.3970/cmes.2004.006.421

Abstract In standard boundary element formulations, singular integrals need to be solved as soon as the considered sources coincide with the collocation points at the boundary. Using a desingularized boundary element approach, the sources are distributed on a surface outside the acoustic domain which means that they are never located at the boundary. Consequently, all the resulting kernels are nonsingular which reduces the complexity of the numerical treatment of the boundary integral equations considerably. In the current contribution a desingularized formulation is given for both, the direct and the indirect boundary element method used to solve More >

Nam Mai-Duy¹

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.2, pp. 209-226, 2004, DOI:10.3970/cmes.2004.006.209

Abstract This paper is concerned with the use of the indirect radial basis function network (RBFN) method in solving partial differential equations (PDEs) with scattered points. Indirect RBFNs (Mai-Duy and Tran-Cong, 2001a), which are based on an integration process, are employed to approximate the solution of PDEs via point collocation mechanism in the set of randomly distributed points. The method is tested with the solution of Poisson's equations and the Navier-Stokes equations (Boussinesq material). Good results are obtained using relatively low numbers of data points. For example, the natural convection flow in a square cavity at More >

Z.Y. Qian¹, Z.D. Han¹, S.N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.1, pp. 115-122, 2004, DOI:10.3970/cmes.2004.006.115

Abstract This article has no abstract. More >

F. Reitich¹, K. K. Tamma²

CMES-Computer Modeling in Engineering & Sciences, Vol.5, No.4, pp. 287-294, 2004, DOI:10.3970/cmes.2004.005.287

Abstract This article has no abstract. More >

N. Mai-Duy, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.1, pp. 85-102, 2003, DOI:10.3970/cmes.2003.004.085

Abstract This paper reports a mesh-free Indirect Radial Basis Function Network method (IRBFN) using Thin Plate Splines (TPSs) for numerical solution of Differential Equations (DEs) in rectangular and curvilinear coordinates. The adjustable parameters required by the method are the number of centres, their positions and possibly the order of the TPS. The first and second order TPSs which are widely applied in numerical schemes for numerical solution of DEs are employed in this study. The advantage of the TPS over the multiquadric basis function is that the former, with a given order, does not contain the… More >

Enzo TONTI¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 237-258, 2001, DOI:10.3970/cmes.2001.002.237

Abstract We present a new numerical method for the solution of field equations. The essence of the method is to directly provide a discrete formulation of field laws, without using and requiring a differential formulation. It is proved that, for linear interpolation, the stiffness matrix so obtained coincides with the one of the Finite Element Method. For quadratic interpolation, however, the present stiffness matrix differs from that of FEM; moreover it is unsymmetric. It is shown that by using a parabolic interpolation, a convergence of the fourth order is obtained. This is greater than the one More >

W.W. Liou¹, Y.C. Fang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.4, pp. 119-128, 2000, DOI:10.3970/cmes.2000.001.571

Abstract A simple implicit treatment for the low speed inflow and outflow boundary conditions for the direct simulation Monte Carlo (DSMC) of the flows in microelectromechanical systems (MEMS) is proposed. The local mean flow velocity, temperature, and number density near the subsonic boundaries were used to determine the number of molecules entering the computational domain and their corresponding velocities at every sample average step. The proposed boundary conditions were validated against micro-Poiseuille flows and micro-Couette flows. The results were compared with analytical solutions derived from the Navier-Stokes equations using first-order and second order slip-boundary conditions. The More >

J. Sladek¹, V. Sladek¹, V. Kompis², R. Van Keer³

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.4, pp. 1-8, 2000, DOI:10.3970/cmes.2000.001.453

Abstract This paper presents an application of a direct Trefftz method with domain decomposition to the two-dimensional elasticity problem. Trefftz functions are substituted into Betti's reciprocity theorem to derive the boundary integral equations for each subdomain. The values of displacements and tractions on subdomain interfaces are tailored by continuity and equilibrium conditions, respectively. Since Trefftz functions are regular, much less requirements are put on numerical integration than in the traditional boundary integral method. Then, the method can be utilized to analyse also very narrow domains. Linear elements are used for modelling of the boundary geometry and More >

A.N. Gulluoglu¹, C.T. Tsai²

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.1, pp. 85-90, 2000, DOI:10.3970/cmes.2000.001.085

Abstract Twins in growing crystals are due to excessive thermal stresses induced by the temperature gradients developed during the growth process. Twinning is an important defect in advanced semiconductor crystals such as GaAS and InP. The objective of this study is to develop a computational model to predict the twin formation in the Gallium Arsenide (GaAs) crystals grown by the vertical gradient freeze method (VGF). A quantitative quasi-steady state thermal stress model is developed here for predicting the twinning formation in GaAs grown by VGF. The thermoelastic stresses in VGF grown crystal are calculated from a More >