J.C. Michel¹, H. Moulinec, P. Suquet

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.2, pp. 79-88, 2000, DOI:10.3970/cmes.2000.001.239

Abstract An iterative numerical method based on Fast Fourier Transforms has been proposed by \cite{MOU98} to investigate the effective properties of periodic composites. This iterative method is based on the exact expression of the Green function for a linear elastic, homogeneous reference material. When dealing with linear phases, the number of iterations required to reach convergence is proportional to the contrast between the phases properties, and convergence is therefore not ensured in the case of composites with infinite contrast (those containing voids or rigid inclusions or highly nonlinear materials). It is proposed in this study to… More >

H. Okumura¹, M. Kawahara¹

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.2, pp. 71-78, 2000, DOI:10.3970/cmes.2000.001.231

Abstract This paper presents a new approach to a shape optimization problem of a body located in the unsteady incompressible viscous flow field based on an optimal control theory. The optimal state is defined by the reduction of drag and lift forces subjected to the body. The state equation used is the transient incompressible Navier--Stokes equations. The shape optimization problem can be formulated to find out geometrical coordinates of the body to minimize the performance function that is defined to evaluate forces subjected to the body. The fractional step method with the implicit temporal integration and More >

Igor Patlashenko¹, Dan Givoli²

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.2, pp. 61-70, 2000, DOI:10.3970/cmes.2000.001.221

Abstract The method of Absorbing Boundary Conditions (ABCs) is considered for the numerical solution of a class of nonlinear exterior wave scattering problems. Recently, a scheme based on the exact nonlocal Dirichlet-to-Neumann (DtN) ABC has been proposed for such problems. Although this method is very accurate, it is also highly expensive computationally. In this paper, the nonlocal ABC is replaced by a low-order local ABC, which is obtained by localizing the DtN condition in a certain "optimal'' way. The performance of the new local scheme is compared to that of the nonlocal scheme via numerical experiments More >

H. Lin, S.N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.2, pp. 45-60, 2000, DOI:10.3970/cmes.2000.001.205

Abstract Due to the very general nature of the Meshless Local Petrov-Galerkin (MLPG) method, it is very easy and natural to introduce the upwinding concept (even in multi-dimensional cases) in the MLPG method, in order to deal with convection-dominated flows. In this paper, several upwinding schemes are proposed, and applied to solve steady convection-diffusion problems, in one and two dimensions. Even for very high Peclet number flows, the MLPG method, with upwinding, gives very good results. It shows that the MLPG method is very promising to solve the convection-dominated flow problems, and fluid mechanics problems. More >

D. Boffi¹, C. Chinosi², L. Gastaldi³

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.2, pp. 31-44, 2000, DOI:10.3970/cmes.2000.001.191

Abstract In this paper we are dealing with the approximation of the grad-div operator in nonconvex polygonal domains. A penalization strategy is considered in order to obtain a formulation of the original eigenproblem which is associated with an elliptic operator. However the presence of singular eigensolutions, in the case of nonconvex domains, is the origin of major troubles in the numerical approximation of the problem. A mixed-type approximation, based on a projection procedure, is introduced and analyzed from the theoretical and numerical point of view. Several numerical experiments confirm that in presence of singularities the projection More >

V. Carvelli², G. Maier², A. Taliercio²

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.2, pp. 19-30, 2000, DOI:10.3970/cmes.2000.001.179

Abstract Homogenization of periodic fiber-reinforced ductile composite materials is performed as for the material strength, i.e. the carrying capacity with respect to macroscopic (average) stresses. Rigid-plastic limit analysis is formulated by the kinematic theorem applied to the representative volume with periodicity boundary conditions and von Mises yield criterion. The iterative procedure adopted for the numerical solution of the minimization problem is comparatively discussed on the basis of applications to various ductile heterogeneous media. More >

Fernando A. Rochinha¹, Rubens Sampaio²

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.2, pp. 7-18, 2000, DOI:10.3970/cmes.2000.001.167

Abstract The dynamics of flexible systems, such as robot manipulators, mechanical chains or cables, is becoming increasingly important in engineering. The main question arising from the numerical modelling of large overall motions of multibody systems is an appropriate treatment for the large rotations. In the present work an alternative approach is proposed leading to a time-stepping numerical algorithm which achieves stable solutions combined with high precision. In particular, in order to check the performance of the proposed approach, two examples having preserved constants of the motion are presented. More >

T. Ozawa¹, N. Ishigami¹, Y. Hayakawa², T. Koyama², M. Kumagawa²

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.2, pp. 1-6, 2000, DOI:10.3970/cmes.2000.001.161

Abstract To investigate the solution convection in the rotational Bridgman method, both flow patterns and temperature distributions were calculated by solving three equations in 3-dimensional analysis: Navier-Stokes, continuity and energy. We focused on the relationship between ampoule rotational rate and temperature distribution in the growth solution reservoir. In the 3-dimensional model, In-Ga-Sb solution was put between GaSb seed and feed crystals, where seed and feed crystals were cylindrical in shape, and the In-Ga-Sb solution was semi-cylindrical. The ampoule rotational rate was changed in a range of 0 to 100 rpm. By increasing the ampoule rotational rate, the More >

Conor Rafferty¹, R. Kent Smith

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.1, pp. 151-160, 2000, DOI:10.3970/cmes.2000.001.151

Abstract The PROPHET simulator is a software system for solving partial differential equations (PDEs) in time and 1,2 or 3 space dimensions. When equipped with appropriate modules, it can be configured as a process simulator or a device simulator, with application to modeling semiconductor fabrication processes and transistor behavior. The simulator is designed with three main goals: efficiency, geometric flexibility, equation extensibility. The first two distinguish it from canned packages such as Mathematica, which do not easily allow the use of arbitrary shapes or grids and are not tuned to solve systems with 10⁵ or 10⁶ unknowns. More >

Anand L. Pardhanani¹, Graham F. Carey¹

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.1, pp. 141-150, 2000, DOI:10.3970/cmes.2000.001.141

Abstract Rapid prototyping tools that combine powerful numerics with a flexible applications interface can play a significant role in micro-scale modeling and simulation. We demonstrate this idea using the PROPHET simulator. In the first part of the investigations we extend the simulator's capability to allow analysis of carrier transport in deep submicron MOSFETs using a hydrodynamic model. The model is numerically implemented within PROPHET's dial-an-operator framework by adding certain "flux'' routines. Once implemented, the model becomes available for use in any number of spatial dimensions. We present results for MOSFET type test problems in one and More >