J.L. Morales¹, J.A. Moreno², F. Alhama³

CMES-Computer Modeling in Engineering & Sciences, Vol.76, No.1, pp. 1-18, 2011, DOI:10.3970/cmes.2011.076.001

Abstract Following the rules of the network simulation method, a general purpose network model is designed and numerically solved for linear elastostatic problems formulated by the Navier equations. Coupled and nonlinear terms of the PDE, as well as boundary conditions, are easily implemented in the model by means of general purpose electrical devices named controlled current (or voltage) sources. The complete model is run in the commercial software PSPICE and the numerical results are post-processed by MATLAB to facilitate graphical representation. To demonstrate the reliability and efficiency of the proposed method two applications are presented: a cantilever loaded at one end… More >

Ewa Majchrzak¹

CMES-Computer Modeling in Engineering & Sciences, Vol.69, No.1, pp. 43-60, 2010, DOI:10.3970/cmes.2010.069.043

Abstract Heat transfer processes proceeding in domain of heating tissue are discussed. The typical model of bioheat transfer bases, as a rule, on the well known Pennes equation, this means the heat diffusion equation with additional terms corresponding to the perfusion and metabolic heat sources. Here, the other approach basing on the dual-phase-lag equation (DPLE) is considered in which two time delays τ_q, τ_T (phase lags) appear. The DPL equation contains a second order time derivative and higher order mixed derivative in both time and space. This equation is supplemented by the adequate boundary and initial conditions. To solve the problem… More >

Z. Aksamija^1,2, U. Ravaioli³

CMES-Computer Modeling in Engineering & Sciences, Vol.37, No.1, pp. 45-64, 2008, DOI:10.3970/cmes.2008.037.045

Abstract Finding the scalar potential from the Poisson equation is a common, yet challenging problem in semiconductor modeling. One of the central problems in traditional mesh-based methods is the assignment of charge to the regular mesh imposed for the discretisation. In order to avoid this problem, we create a mesh-free algorithm which starts by assigning each mesh point to each particle present in the problem. This algorithm is based on a Fourier series expansion coupled with point matching. An efficient algorithm for repeatedly solving the Poisson problem for moving charge distributions is presented. We demonstate that this approach is accurate and… More >

Yueting Zhou¹, Xing Li², Dehao Yu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.36, No.2, pp. 147-172, 2008, DOI:10.3970/cmes.2008.036.147

Abstract A problem for bonded plane material with a set of curvilinear cracks, which is under the action of a rigid punch with the foundation of convex shape, has been considered in this paper. Kolosov-Muskhelishvili complex potentials are constructed as integral representations with the Cauchy kernels with respect to derivatives of displacement discontinuities along the crack contours and pressure under the punch. The contact of crack faces is considered. The considered problem has been transformed to a system of complex Cauchy type singular integral equations of first and second kind. The presented approach allows to consider various configurations of cracks and… More >

S.Yu. Reutskiy¹

CMES-Computer Modeling in Engineering & Sciences, Vol.34, No.3, pp. 227-252, 2008, DOI:10.3970/cmes.2008.034.227

Abstract A new numerical technique for solving generalized Sturm--Liouville problem d²w/dx² + q(x, λ )w = 0, b_l[ λ ,w(a)] = b_r[ λ ,w(b)] = 0 is presented. In is presented. In particular, we consider the problems when the coefficient q(x, λ) or the boundary conditions depend on the spectral parameter λ in an arbitrary nonlinear manner. The method presented is based on mathematically modelling of physical response of a system to excitation over a range of frequencies. The response amplitudes are then used to determine the eigenvalues. The same technique can be applied to a very wide class of the… More >

G. C. Bourantas¹, V. C. Loukopoulos²

CMES-Computer Modeling in Engineering & Sciences, Vol.86, No.4, pp. 275-300, 2012, DOI:10.3970/cmes.2012.086.275

Abstract This paper formulates a local Radial Basis Functions (LRBFs) collocation method for the numerical solution of the non-linear dispersive and dissipative KdV-Burger's (KdVB) equation. This equation models physical problems, such as irrotational incompressible flow, considering a shallow layer of an inviscid fluid moving under the influence of gravity and the motion of solitary waves. The local type of approximations used, leads to sparse algebraic systems that can be solved efficiently. The Inverse Multiquadrics (IMQ), Gaussian (GA) and Multiquadrics (MQ) Radial Basis Functions (RBF) interpolation are employed for the construction of the shape functions. Accuracy of the method is assessed in… More >

Ayşe Gül Kaplan¹, Yılmaz Dereli

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.5, pp. 423-438, 2012, DOI:10.3970/cmes.2012.084.423

Abstract In this study, the nonlinear symmetric regularized long wave equation was solved numerically by using radial basis functions collocation method. The single solitary wave solution, the interaction of two positive solitary waves and the clash of two solitary waves were studied. Numerical results and simulations of the wave motions were presented. Validity and accuracy of the method was tested by compared with results in the literature. More >

Ali Shokri¹, Mehdi Dehghan¹

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.4, pp. 333-358, 2012, DOI:10.3970/cmes.2012.084.333

Abstract The Ginzburg-Landau equation has been used as a mathematical model for various pattern formation systems in mechanics, physics and chemistry. In this paper, we study the complex Ginzburg-Landau equation in two spatial dimensions with periodical boundary conditions. The method numerically approximates the solution by collocation method based on radial basis functions (RBFs). To improve the numerical results we use a predictor-corrector scheme. The results of numerical experiments are presented, and are compared with analytical solutions to confirm the accuracy and efficiency of the presented method. More >

Yiming Chen, Mingxu Yi, Chen Chen, Chunxiao Yu

CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.6, pp. 639-654, 2012, DOI:10.3970/cmes.2012.083.639

Abstract In this paper, Bernstein polynomials method is proposed for the numerical solution of a class of space-time fractional convection-diffusion equation with variable coefficients. This method combines the definition of fractional derivatives with some properties of Bernstein polynomials and are dispersed the coefficients efficaciously. The main characteristic behind this method is that the original problem is translated into a Sylvester equation. Only a small number of Bernstein polynomials are needed to obtain a satisfactory result. Numerical examples show that the method is effective. More >

Hsiang-Wen Tang, Cha’o-Kung Chen¹, Chen-Yu Chiang

CMES-Computer Modeling in Engineering & Sciences, Vol.65, No.1, pp. 95-106, 2010, DOI:10.3970/cmes.2010.065.095

Abstract Up to now, solving some nonlinear differential equations is still a challenge to many scholars, by either numerical or theoretical methods. In this paper, the method of the maximum principle applied on differential equations incorporating the Residual Correction Method is brought up and utilized to obtain the upper and lower approximate solutions of nonlinear heat transfer problem of the non-Fourier fin. Under the fundamental of the maximum principle, the monotonic residual relations of the partial differential governing equation are established first. Then, the finite difference method is applied to discretize the equation, converting the differential equation into the mathematical programming… More >