K. Abe¹, H. Fujii¹, S. Yoshimura¹

CMES-Computer Modeling in Engineering & Sciences, Vol.113, No.1, pp. 71-87, 2017, DOI:10.3970/cmes.2017.113.068

Abstract Microscopic traffic simulations are useful for solving various traffic- related problems, e.g. traffic jams and accidents, local and global environmental and energy problems, maintaining mobility in aging societies, and evacuation plan- ning for natural as well as man-made disasters. The origin-destination (OD) matrix is often used as the input to represent traffic demands into traffic simulators. In this study, we propose an indirect method for estimating the OD matrix using a traffic simulator as an internal model. The proposed method is designed to output results that are consistent with the input of the simulator. The method consists of the following… More >

Tao Zhang^1,2, Yiqian He³, Leiting Dong⁴, Shu Li¹, Abdullah Alotaibi⁵, Satya N. Atluri^2,5

CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.6, pp. 509-533, 2014, DOI:10.3970/cmes.2014.097.509

Abstract In this article, the Meshless Local Petrov-Galerkin (MLPG) Mixed Collocation Method is developed to solve the Cauchy inverse problems of Steady- State Heat Transfer In the MLPG mixed collocation method, the mixed scheme is applied to independently interpolate temperature as well as heat flux using the same meshless basis functions The balance and compatibility equations are satisfied at each node in a strong sense using the collocation method. The boundary conditions are also enforced using the collocation method, allowing temperature and heat flux to be over-specified at the same portion of the boundary. For the inverse problems where noise is… 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 >

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 >

Tao Zhang^1,2, Leiting Dong^2,3, Abdullah Alotaibi⁴, Satya N. Atluri^2,5

CMES-Computer Modeling in Engineering & Sciences, Vol.94, No.1, pp. 1-28, 2013, DOI:10.3970/cmes.2013.094.001

Abstract In this paper, a novel Meshless Local Petrov-Galerkin (MLPG) Mixed Collocation Method is developed for solving the inverse Cauchy problem of linear elasticity, wherein both the tractions as well as displacements are prescribed/measured at a small portion of the boundary of an elastic body. The elastic body may be isotropic/anisotropic and simply connected or multiply-connected. In the MLPG mixed collocation method, the same meshless basis function is used to interpolate both the displacement as well as the stress fields. The nodal stresses are expressed in terms of nodal displacements by enforcing the constitutive relation between stress and the displacement gradient… More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.3, pp. 241-269, 2013, DOI:10.32604/cmes.2013.092.241

Abstract In order to solve an ill-posed linear problem, we propose an innovative Jacobian type iterative method by presetting a conditioner before the steepest descent direction. The preconditioner is derived from an invariant manifold approach, which includes two parameters α and γ to be determined. When the weighting parameter α is optimized by minimizing a properly defined objective function, the relaxation parameter γ can be derived to accelerate the convergence speed under a switching criterion. When the switch is turned-on, by using the derived value of γ it can pull back the iterative orbit to the fast manifold. It is the… More >

Chein-Shan Liu¹, Su-Ying Zhang², Satya N. Atluri³

CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.1, pp. 29-48, 2012, DOI:10.3970/cmes.2012.088.029

Abstract With a detailed investigation of n linear algebraic equations Bx=b, we find that the scaled residual dynamics for y∈Sⁿ⁻¹ is equipped with four structures: the Jordan dynamics, the rotation group SO(n), a generalized Hamiltonian formulation, as well as a metric bracket system. Therefore, it is the first time that we can compute the steplength used in the iterative method by a novel algorithm based on the Jordan structure. The algorithms preserving the length of y are developed as the structure preserving algorithms (SPAs), which can significantly accelerate the convergence speed and are robust enough against the noise in the numerical… More >

A.E. Martínez-Castro¹, I.H. Faris¹, R. Gallego¹

CMES-Computer Modeling in Engineering & Sciences, Vol.87, No.3, pp. 177-206, 2012, DOI:10.3970/cmes.2012.087.177

Abstract In this paper, the identification of hidden defects inside a three-dimen -sional layer is set as an Identification Inverse Problem. This problem is solved by minimizing a cost functional which is linearized with respect to the volume defects, leading to a procedure that requires only computations at the host domain free of defects. The cost functional is stated as the misfit between experimental and computed displacements and spherical and/or ellipsoidal cavities are the defects to locate. The identification of these cavities is based on the measured displacements at a set of points due to time-harmonic point loads at an array… More >

F. S. Lobato¹, V. Steffen Jr², A. J. Silva Neto³

CMES-Computer Modeling in Engineering & Sciences, Vol.69, No.1, pp. 1-18, 2010, DOI:10.3970/cmes.2010.069.001

Abstract Differential Evolution Algorithm (DE) has shown to be a powerful evolutionary algorithm for global optimization in a variety of real world problems. DE differs from other evolutionary algorithms in the mutation and recombination phases. Unlike some other meta-heuristic techniques such as genetic algorithms and evolutionary strategies, where perturbation occurs in accordance with a random quantity, DE uses weighted differences between solution vectors to perturb the population. Although the efficiency of DE algorithm has been proven in the literature, studies indicate that the efficiency of the DE methods is sensitive to its control parameters (perturbation rate and crossover rate) and there… More >

Chih-Wen Chang¹, Chein-Shan Liu²

CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.3, pp. 261-276, 2009, DOI:10.3970/cmes.2009.051.261

Abstract The backward advection-dispersion equation (ADE) for identifying the groundwater pollution source identification problems (GPSIPs) is numerically solved by employing a fictitious time integration method (FTIM). The backward ADE is renowned as ill-posed because the solution does not continuously count on the data. We transform the original parabolic equation into another parabolic type evolution equation by introducing a fictitious time coordinate, and adding a viscous damping coefficient to enhance the stability of numerical integration of the discretized equations by employing a group preserving scheme. When several numerical examples are amenable, we find that the FTIM is applicable to retrieve all past… More >