Marco A.A. Kappel¹, Diego C. Knupp¹, Roberto P. Domingos¹, IvanN. Bastos¹

CMC-Computers, Materials & Continua, Vol.49-50, No.1, pp. 13-29, 2015, DOI:10.3970/cmc.2015.049.013

Abstract This work is aimed at the direct and inverse analysis of hydrogen permeation in steels employing a novel anomalous diffusion model. For the inverse analysis, experimental data for hydrogen permeation in a 13% chromium martensitic stainless steel, available in the literature [Turnbull, Carroll and Ferriss (1989)], was employed within the Bayesian framework for inverse problems. The comparison between the predicted values and the available experimental data demonstrates the feasibility of the new model in adequately describing the physical phenomena occurring in this particular problem. 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… 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,… More >

Benjamin Castaneda^∗, Juvenal Ormachea^†, Paul Rodríguez^‡, Kevin J. Parker^§

Molecular & Cellular Biomechanics, Vol.10, No.1, pp. 43-65, 2013, DOI:10.3970/mcb.2013.010.043

Abstract Elasticity imaging can be understood as the intersection of the study of biomechanical properties, imaging sciences, and physics. It was mainly motivated by the fact that pathological tissue presents an increased stiffness when compared to surrounding normal tissue. In the last two decades, research on elasticity imaging has been an international and interdisciplinary pursuit aiming to map the viscoelastic properties of tissue in order to provide clinically useful information. As a result, several modalities of elasticity imaging, mostly based on ultrasound but also on magnetic resonance imaging and optical coherence tomography, have been proposed and… More >

Chein-Shan Liu ¹

CMC-Computers, Materials & Continua, Vol.33, No.2, pp. 175-198, 2013, DOI:10.3970/cmc.2013.033.175

Abstract An optimal m-vector descent iterative algorithm in a Krylov subspace is developed, of which the m weighting parameters are optimized from a properly defined objective function to accelerate the convergence rate in solving an ill-posed linear problem. The optimal multi-vector iterative algorithm (OMVIA) is convergent fast and accurate, which is verified by numerical tests of several linear inverse problems, including the backward heat conduction problem, the heat source identification problem, the inverse Cauchy problem, and the external force recovery problem. Because the OMVIA has a good filtering effect, the numerical results recovered are quite smooth 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… 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… 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. More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.91, No.1, pp. 17-42, 2013, DOI:10.3970/cmes.2013.091.017

Abstract In the present paper, we propose a novel two-side equilibration method to properly reduce the condition number of a given non-singular matrix only through a few operations. Then, two different conditioners together with the conjugate gradient method (CGM) are developed, which can overcome the defect of CGM, being not vulnerable to noisy disturbance exerted on an ill-posed linear system. The twoside CGM (TSCGM) and the pre-conditioning CGM (PrCGM) are convergent fast and accurate in solving linear inverse problems and the linear Hilbert problem under a large random noise. More >

Linjun Wang^1,2, Xu Han³, Youxiang Xie⁴

CMC-Computers, Materials & Continua, Vol.31, No.2, pp. 113-126, 2012, DOI:10.3970/cmc.2012.031.113

Abstract In this paper, a new iterative regularization method (ITR) is presented to solve the reconstruction of multi-source dynamic loads acting on the structure of simple supported plate. Based on a quadratical convergence method, this method is used to compute the the approximate inverse of square matrix. The theoretical proofs and numerical test show that the proposed method is very effective. Finally, the present method is applied to the identification of the multi-source dynamic loads on a surface of simply supported plate. Numerical simulations of two examples demonstrate the effectiveness and robustness of the present method. More >