Hui Wei^1,2,3, Wen Chen^1,2,4, HongGuang Sun^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.2, pp. 85-103, 2014, DOI:10.3970/cmes.2014.100.085

Abstract The unknown parameters are critical factors in fractional derivative advection-dispersion equation describing the solute transport in soil. For examples, the fractional derivative order is the index of anomalous dispersion, diffusion coefficient represents the dispersion ability of media and average pore-water velocity denotes the main trend of transport, etc. This paper is to develop a homotopy method to determine the unknown parameters of solute transport with spatial fractional derivative advection-dispersion equation in soil. The homotopy method can be easily developed to solve parameter determination problems of fractional derivative equations whose analytical solutions are difficult to obtain. The sigmoid function is involved… More >

T.A. Elgohary¹, L. Dong², J.L. Junkins³, S.N. Atluri⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.1, pp. 59-84, 2014, DOI:10.3970/cmes.2014.100.059

Abstract In this study, we consider ill-posed time-domain inverse problems for dynamical systems with various boundary conditions and unknown controllers. Dynamical systems characterized by a system of second-order nonlinear ordinary differential equations (ODEs) are recast into a system of nonlinear first order ODEs in mixed variables. Radial Basis Functions (RBFs) are assumed as trial functions for the mixed variables in the time domain. A simple collocation method is developed in the time-domain, with Legendre-Gauss-Lobatto nodes as RBF source points as well as collocation points. The duffing optimal control problem with various prescribed initial and final conditions, as well as the orbital… More >

S,erson L. Gonzaga de Oliveira¹, Jéssica Renata Nogueira¹, João Manuel R. S. Tavares²

CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.1, pp. 31-57, 2014, DOI:10.3970/cmes.2014.100.031

Abstract Triangulations and tetrahedrizations are important geometrical discretization procedures applied to several areas, such as the reconstruction of surfaces and data visualization. Delaunay and Voronoi tessellations are discretization structures of domains with desirable geometrical properties. In this work, a systematic review of algorithms with linear-time behaviour to generate 2D/3D Delaunay and/or Voronoi tessellations is presented. More >

F. Yang¹, C.L. Fu², X.X. Li¹

CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.1, pp. 19-29, 2014, DOI:10.3970/cmes.2014.100.019

Abstract Numerical differentiation is a classical ill-posed problem. The generalized Tikhonov regularization method is proposed to solve this problem. The error estimates are obtained for a priori and a posteriori parameter choice rules, respectively. Numerical examples are presented to illustrate the validity and effectiveness of this method. More >

Xiaoming Zhang¹, Xingxin Xu^1,2, Yuqing Wang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.1, pp. 1-17, 2014, DOI:10.3970/cmes.2014.100.001

Abstract Orthogonal polynomial approach has been used to deal with the wave propagation in structures that have finite dimension in only one direction, such as horizontally infinite flat plates, axially infinite hollow cylinders. In order to solve wave propagation in two-dimensional piezoelectric rod with rectangular cross section, i.e. the piezoelectric plate with finite dimensions in two directions, an extended orthogonal polynomial approach is proposed in this paper. For validation and illustration purposes, the proposed approach is applied to solving the wave propagation in a square steel rod. The results obtained are in good agreement with the results from the semi-analytical finite… More >

R. Messahel¹, M. Souli¹

CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.6, pp. 435-455, 2013, DOI:10.3970/cmes.2013.096.435

Abstract Simulation of Fluid Structure Interaction FSI, problems becomes more and more the focus of computational engineering, where FEM (Finite element Methods) for structural mechanics and Finite Volume for CFD are dominant. New formulations have been developed for FSI applications using mesh free methods as SPH method, (Smooth Particle Hydrodynamic). Up to these days very little has been done to compare different methods and assess which one would be more suitable. For small deformation, FEM Lagrangian formulation can solve structure interface and material boundary accurately; the main limitation of the formulation is high mesh distortion for large deformation and moving structure.… More >

Cheng-Yu Ku¹

CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.6, pp. 409-434, 2013, DOI:10.3970/cmes.2013.096.409

Abstract This paper proposes a novel method, named the dynamical Jacobianinverse free method (DJIFM), with the incorporation of a two-sided equilibrium algorithm for solving ill-conditioned systems of linear equations with extreme physical property contrasts. The DJIFM is based on the construction of a scalar homotopy function for transforming the vector function of linear or nonlinear algebraic equations into a time-dependent scalar function by introducing a fictitious time-like variable. The DJIFM demonstrated great numerical stability for solving linear or nonlinear algebraic equations, particularly for systems involving ill-conditioned Jacobian or poor initial values that cause convergence problems. With the incorporation of a newly… More >

Xuejuan Li^1,2, Jie Ouyang^2,3, Wen Zhou²

CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.6, pp. 379-407, 2013, DOI:10.3970/cmes.2013.096.379

Abstract The three-dimensional (3D) mathematical models for thermal residual stress and warpage are proposed in injection molding, in which the temperature model is rebuilt by considering the phase-change effect to improve the computational accuracy. The 3D thermal residual stress model is transformed into the incremental displacement model so that the boundary conditions can be imposed easily. A modified finite element neural network (FENN) method is used for solving 3D warpage model based on the advantages of finite element method and neural network. The influence of phase-change on temperature is discussed. The numerical simulations of thermal residual stress and warpage are realized,… More >

Mingxu Yi¹, Jun Huang¹, Lifeng Wang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.5, pp. 361-377, 2013, DOI:10.3970/cmes.2013.096.361

Abstract In this paper, operational matrix method based upon the Bernstein polynomials is proposed to solve the variable order fractional integro-differential equations in the Caputo derivative sense. We derive the Bernstein polynomials operational matrix of fractional order integration and introduce the product operational matrix of Bernstein polynomials. A truncated the Bernstein polynomials series together with the polynomials operational matrix are utilized to reduce the variable order fractional integro-differential equations to a system of algebraic equations. Only a small number of Bernstein polynomials are needed to obtain a satisfactory result. Some examples are included to demonstrate the validity and applicability of the… More >

D. C. Knupp^1,2, A. J. Silva Neto³

CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.5, pp. 339-360, 2013, DOI:10.3970/cmes.2013.096.339

Abstract Inverse radiative transfer problems in heterogeneous participating media applications include determining gas properties in combustion chambers, estimating environmental and atmospheric conditions, and remote sensing, among others. In recent papers the spatially variable single scattering albedo has been estimated by expanding this unknown function as a series of known functions, and then estimating the expansion coefficients with parameter estimation techniques. In the present work we assume that there is no prior information on the functional form of the unknown spatially variable albedo and, making use of the Bayesian approach, we propose the development of a posterior probability density, which is explored… More >