CMES-Vol. 86, No. 2, 2012

Open Access

ARTICLE

Numerical Reconstruction of a Space-Dependent Heat Source Term in a Multi-Dimensional Heat Equation
C. Shi¹, C. Wang¹, T. Wei^1,2
CMES-Computer Modeling in Engineering & Sciences, Vol.86, No.2, pp. 71-92, 2012, DOI:10.3970/cmes.2012.086.071
Abstract In this paper, we consider a typical ill-posed inverse heat source problem, that is, we determine a space-dependent heat source term in a multi-dimensional heat equation from a pair of Cauchy data on a part of boundary. By a simple transformation, the inverse heat source problem is changed into a Cauchy problem of a homogenous heat conduction equation. We use the method of fundamental solutions (MFS) coupled with the Tikhonov regularization technique to solve the ill-conditioned linear system of equations resulted from the MFS discretization. The generalized cross-validation rule for determining the regularization parameter is More >

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ARTICLE

Simulation of Multi-Option Pricing on Distributed Computing
J.E. Lee¹and S.J. Kim²
CMES-Computer Modeling in Engineering & Sciences, Vol.86, No.2, pp. 93-112, 2012, DOI:10.3970/cmes.2012.086.093
Abstract As the option trading nowadays has become popular, it is important to simulate efficiently large amounts of option pricings. The purpose of this paper is to show valuations of large amount of options, using network distribute computing resources. We valuated 108 options simultaneously on the self-made cluster computer system which is very inexpensive, compared to the supercomputer or the GPU adopting system. For the numerical valuations of options, we developed the option pricing software to solve the Black-Scholes partial differential equation by the finite element method. This yielded accurate values of options and the Greeks More >

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Static and Dynamic BEM Analysis of Strain Gradient Elastic Solids and Structures
S.V. Tsinopoulos¹, D. Polyzos², D.E. Beskos^3,4
CMES-Computer Modeling in Engineering & Sciences, Vol.86, No.2, pp. 113-144, 2012, DOI:10.3970/cmes.2012.086.113
Abstract This paper reviews the theory and the numerical implementation of the direct boundary element method (BEM) as applied to static and dynamic problems of strain gradient elastic solids and structures under two- and three- dimensional conditions. A brief review of the linear strain gradient elastic theory of Mindlin and its simplifications, especially the theory with just one constant (internal length) in addition to the two classical elastic moduli, is provided. The importance of this theory in successfully modeling microstructural effects on the structural response under both static and dynamic conditions is clearly described. The boundary… More >

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ARTICLE

A LBIE Method for Solving Gradient Elastostatic Problems
E.J. Sellountos¹, S.V. Tsinopoulos², D. Polyzos³
CMES-Computer Modeling in Engineering & Sciences, Vol.86, No.2, pp. 145-170, 2012, DOI:10.3970/cmes.2012.086.145
Abstract A Local Boundary Integral Equation (LBIE) method for solving two dimensional problems in gradient elastic materials is presented. The analysis is performed in the context of simple gradient elasticity, the simplest possible case of Mindlin's Form II gradient elastic theory. For simplicity, only smooth boundaries are considered. The gradient elastic fundamental solution and the corresponding boundary integral equation for displacements are used for the derivation of the LBIE representation of the problem. Nodal points are spread over the analyzed domain and the moving least squares (MLS) scheme for the approximation of the interior and boundary More >

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