CMES-Vol. 47, No. 2, 2009

Open Access

ARTICLE

Preconditioned Conjugate Gradient Method Enhanced by Deflation of Rigid Body Modes Applied to Composite Materials
T.B Jönsthövel¹, M.B. van Gijzen², C.Vuik², C. Kasbergen¹, A. Scarpas¹
CMES-Computer Modeling in Engineering & Sciences, Vol.47, No.2, pp. 97-118, 2009, DOI:10.3970/cmes.2009.047.097
Abstract The introduction of computed x-ray tomography allows for the construction of high quality, material-per-element based 3D meshes in the field of structural mechanics. The use of these meshes enables a shift from meso to micro scale analysis of composite materials like cement concrete, rocks and asphalt concrete. Unfortunately, because of the extremely long execution time, memory and storage space demands, the majority of commercially available finite element packages are not capable of handling efficiently the most computationally demanding operation of the finite element solution process, that is, the inversion of the structural stiffness matrix. To address this issue, an efficient… More >

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ARTICLE

An Efficient Response Surface Based Optimisation Method for Non-Deterministic Harmonic and Transient Dynamic Analysis
M. De Munck¹, D. Moens², W. Desmet³, D.Vandepitte³
CMES-Computer Modeling in Engineering & Sciences, Vol.47, No.2, pp. 119-166, 2009, DOI:10.3970/cmes.2009.047.119
Abstract Deterministic simulation tools enable a very precise simulation of physical phenomena using numerical models. In many real life situations however, a deterministic analysis is not sufficient to assess the quality of a design. In a design stage, some physical properties of the model may not be determined yet. But even in a design ready for production, design tolerances and production inaccuracies introduce variability and uncertainty. In these cases, a non-deterministic analysis procedure is required, either using a probabilistic or a non-probabilistic approach. The authors developed an intelligent Kriging response surface based optimisation procedure that can be used in combination with… More >

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ARTICLE

A Novel Method for Solving the Cauchy Problem of Laplace Equation Using the Fictitious Time Integration Method
Chih-Chang Chi¹, Weichung Yeih^1,2, Chein-Shan Liu³
CMES-Computer Modeling in Engineering & Sciences, Vol.47, No.2, pp. 167-190, 2009, DOI:10.3970/cmes.2009.047.167
Abstract In this study, a novel method for solving the Cauchy problem of Laplace equation is developed. Through the fictitious time integration method (FTIM), the finding of the root of the resulting linear equations can be transformed into for finding the fixed point of a system of first order ordinary differential equations, in which a fictitious time variable is introduced. In such a sense, the inverse of ill-posed leading matrix is not necessary for the FTIM. This method uses the residual of each equation to control the evolution of unknowns in the fictitious time, and it is different from the conventional… More >

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ARTICLE

Solution of Phase Change Problems by Collocation with Local Pressure Correction
G. Kosec¹, B. Šarler²
CMES-Computer Modeling in Engineering & Sciences, Vol.47, No.2, pp. 191-216, 2009, DOI:10.3970/cmes.2009.047.191
Abstract This paper explores an application of a novel mesh-free Local Radial Basis Function Collocation Method (LRBFCM) [Sarler and Vertnik (2006)] in solution of coupled heat transfer and fluid flow problems with solid-liquid phase change. The melting/freezing of a pure substance is solved in primitive variables on a fixed grid with convection suppression, proportional to the amount of the solid fraction. The involved temperature, velocity and pressure fields are represented on overlapping sub-domains through collocation by using multiquadrics Radial Basis Functions (RBF). The involved first and second derivatives of the fields are calculated from the respective derivatives of the RBF's. The… More >

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