Yixiong Wei¹, Qifu Wang^1,2, Yingjun Wang¹, Yunbao Huang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.86, No.3, pp. 241-274, 2012, DOI:10.3970/cmes.2012.086.241

Abstract In this study, we propose a novel method to accelerate the process of elastodynamic analysis in 3D problems with BEM (boundary element method). With applying the DRBEM (dual reciprocity boundary element method) to form new integral equations for reducing complexity;the modified FMM (fast multipole method)is introduced to simplify the computation process and save storage space by avoiding intermediate coefficientmatrices. At the same time, FMM-DRBEM is reprogrammed in parallel byapplying GPU with CUDA (Compute Unified Device Architecture)for improving efficiency further.The main features in this paper are: ( 1 )with respect to defects of classical method for More >

J.H. Wu¹, L.Y. Zhu², J.T. Tang³

CMES-Computer Modeling in Engineering & Sciences, Vol.86, No.3, pp. 225-240, 2012, DOI:10.3970/cmes.2012.086.225

Abstract Magnetic induction hyperthermia is one of hopeful methods for tumor therapy. In this method, several ferromagnetic seeds are needed to be implanted into the tumor. The seeds would produce energy, and cause the nearby tumor to die. Temperature prediction is significant before treatment. In addition, in clinical treatment, the tumor temperature has to be monitored in realtime. However, using as few thermometers as possible is the basic principle. Fortunately, the numerical simulation can contribute to realtime measurement. The seed temperature is modeled based on the Haider's method, which is treated as the thermal boundary in More >

L. Chen¹ J. H. Lee¹, C.-f. Chen¹

CMES-Computer Modeling in Engineering & Sciences, Vol.86, No.3, pp. 199-224, 2012, DOI:10.3970/cmes.2012.086.199

Abstract This paper presents a numerical procedure to model surface tension using the Generalized Interpolation Material Point (GIMP) method which employs a background mesh in solving the equations of motion. The force due to surface tension is formulated at the mesh grid points by using the continuum surface force (CSF) model and then added to the equations of motion at each grid point. In GIMP, we use the grid mass as the color function in CSF and apply a moving average smoothing scheme to the grid mass to improve the accuracy in calculating the surface interface. More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.86, No.3, pp. 171-198, 2012, DOI:10.3970/cmes.2012.086.171

Abstract In the optimal control theory, the Hamiltonian formalism is a famous one to find an optimal solution. However, when the performance index is complicated or for a degenerate case with a non-convexity of the Hamiltonian function with respect to the control force the Hamiltonian method does not work to find the solution. In this paper we will address this important issue via a quite different approach, which uses the optimal control problem of nonlinear Duffing oscillator as a demonstrative example. The optimally controlled vibration problem of nonlinear oscillator is recast into a nonlinear inverse problem… More >

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 >

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 >

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 >

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 >

Yixian Du^1,2, De Chen^1,3

CMES-Computer Modeling in Engineering & Sciences, Vol.86, No.1, pp. 53-70, 2012, DOI:10.3970/cmes.2012.086.053

Abstract This study proposes a new topology optimization method for continuum structures, which includes modified heuristic optimality criteria in conjunction with the SIMP scheme to suppress gray-scale elements occurred in topology optimization of continua through smoothed Heaviside function. In the process of numerical implementation, the gray scale elements are suppressed to approach the binary bounds of 0 or 1 by utilizing the proposed approach and the corresponding convergence criterion. Two typical numerical examples are used to demonstrate the effectiveness of the proposed method in suppressing the gray-scale elements with intermediate densities, as well as the efficiency More >

H. Çerdik Yaslan¹

CMES-Computer Modeling in Engineering & Sciences, Vol.86, No.1, pp. 29-38, 2012, DOI:10.3970/cmes.2012.086.029

Abstract This paper presents the approximate analytical solutions to the time fractional differential equations of elasticity for 3D quasicrystals with initial conditions. These equations are written in the form of a vector partial differential equation of the second order. The time fractional vector partial differential equations with initial conditions are solved by variational iteration method (VIM). The fractional derivatives are described in the Caputo sense. Numerical example shows that the proposed method is quite effective and convenient for solving kinds of time fractional system of partial differential equations. More >