Chein-Shan Liu¹, Satya N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.64, No.3, pp. 299-326, 2010, DOI:10.3970/cmes.2010.064.299

Abstract We solve the Calderón inverse conductivity problem [Calderón (1980, 2006)], for an elliptic type equation in a rectangular plane domain, to recover an unknown conductivity function inside the domain, from the over-specified Cauchy data on the bottom of the rectangle. The Calderón inverse problem exhibitsthree-fold simultaneous difficulties: ill-posedness of the inverse Cauchy problem, ill-posedness of the parameter identification, and no information inside the domain being available on the impedance function. In order to solve this problem, we discretize the whole domain into many sub-domains of finite strips, each with a small height. Thus the Calderón inverse problem is reduced to… More >

Weiming Tao¹, Xingwang Yang¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.12, No.3, pp. 83-84, 2009, DOI:10.3970/icces.2009.012.083

Abstract Laser controlled separation of brittle materials like glass is a promising non-conven\discretionary {-}{}{}tional cutting method. It is an application of the crack propagation driven by thermal stresses induced by laser irradiation. In order to induce and control a crack propagating accurately along predetermined asymmetric trajectory in a brittle plate, an iterative method for effective laser scanning path was presented, and the effect of control parameters on the convergence was investigated. The iterative formulation for laser scanning path was based on PID control theory, which was composed of deviation of the crack from predetermined trajectory and its integral and differential. To… More >

Chein-Shan Liu¹, Chih-Wen Chang²

CMC-Computers, Materials & Continua, Vol.25, No.2, pp. 107-134, 2011, DOI:10.3970/cmc.2011.025.107

Abstract We consider two inverse problems for estimating radiative coefficients α(x) and α(x, y), respectively, in T_t(x, t) = T_xx(x, t)-α(x)T(x, t), and T_t(x, y, t) = T_xx(x, y, t) + T_yy(x, y, t)-α(x, y)T(x, y, t), where a are assumed to be continuous functions of space variables. A Lie-group adaptive method is developed, which can be used to find a at the spatially discretized points, where we only utilize the initial condition and boundary conditions, such as those for a typical direct problem. This point is quite different from other methods, which need the overspecified final time data. Three-fold advantages… More >

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 >

Yasunori Yusa¹, Shinobu Yoshimura¹

CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.1, pp. 87-104, 2014, DOI:10.3970/cmes.2014.099.087

Abstract To speed up the elastic–plastic analysis of a large-scale model with a crack in which plasticity is observed near the crack, the partitioned coupling method is applied. In this method, the entire analysis model is decomposed into two non-overlapped domains (i.e., global and local domains), and the two domains are analyzed with an iterative method. The cracked local domain is modeled as an elastic–plastic body, whereas the large-scale global domain is modeled as an elastic body. A subcycling technique is utilized for incremental analysis to reduce the number of global elastic analyses. For a benchmark problem with 6 million degrees… More >

Yasunori Yusa¹, Shinobu Yoshimura¹

CMES-Computer Modeling in Engineering & Sciences, Vol.91, No.6, pp. 445-461, 2013, DOI:10.3970/cmes.2013.091.445

Abstract For large-scale fracture mechanics simulation, a partitioned iterative coupling method is investigated. In this method, an analysis model is decomposed into two domains, which are analyzed separately. A crack is introduced in one small domain, whereas the other large domain is a simple elastic body. Problems concerning fracture mechanics can be treated only in the small domain. In order to satisfy both geometric compatibility and equilibrium on the domain boundary, the two domains are analyzed repeatedly using an iterative solution technique. A benchmark analysis was performed in order to validate the method and evaluate its computational performance. The computed stress… More >

Chein-Shan Liu^1,2, Satya N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.80, No.3&4, pp. 275-298, 2011, DOI:10.3970/cmes.2011.080.275

Abstract To solve an ill-conditioned system of linear algebraic equations (LAEs): Bx - b = 0, we define an invariant-manifold in terms of r := Bx - b, and a monotonically increasing function Q(t) of a time-like variable t. Using this, we derive an evolution equation for dx / dt, which is a system of Nonlinear Ordinary Differential Equations (NODEs) for x in terms of t. Using the concept of discrete dynamics evolving on the invariant manifold, we arrive at a purely iterative algorithm for solving x, which we label as an Optimal Iterative Algorithm (OIA) involving an Optimal Descent Vector… More >

Minghui Wang¹, Musheng Wei², Shanrui Hu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.77, No.3&4, pp. 173-182, 2011, DOI:10.3970/cmes.2011.077.173

Abstract The mapping from the symmetric solution set to its independent parameter space is studied and an iterative method is proposed for the least-squares minimum-norm symmetric solution of AXB = E. Numerical results are reported that show the efficiency of the proposed methods. More >

Liviu Marin¹

CMES-Computer Modeling in Engineering & Sciences, Vol.60, No.3, pp. 221-246, 2010, DOI:10.3970/cmes.2010.060.221

Abstract We investigate the implementation of the method of fundamental solutions (MFS), in an iterative manner, for the algorithm of Kozlov, Maz'ya and Fomin (1991) in the case of the Cauchy problem in two-dimensional isotropic linear elasticity. At every iteration, two mixed well-posed and direct problems are solved using the Tikhonov regularization method, while the optimal value of the regularization parameter is chosen according to the generalized cross-validation (GCV) criterion. An efficient regularizing stopping criterion is also presented. The iterative MFS algorithm is tested for Cauchy problems for isotropic linear elastic materials to confirm the numerical convergence, stability and accuracy of… More >

Chein-Shan Liu¹, Weichung Yeih², Chung-Lun Kuo³, Satya N. Atluri⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.53, No.1, pp. 47-72, 2009, DOI:10.3970/cmes.2009.053.047

Abstract Iterative algorithms for solving a system of nonlinear algebraic equations (NAEs): F_i(x_j) = 0, i, j = 1,... ,n date back to the seminal work of Issac Newton. Nowadays a Newton-like algorithm is still the most popular one to solve the NAEs, due to the ease of its numerical implementation. However, this type of algorithm is sensitive to the initial guess of solution, and is expensive in terms of the computations of the Jacobian matrix ∂F_i/∂x_j and its inverse at each iterative step. In addition, the Newton-like methods restrict one to construct an iteration procedure for n-variables by using n-equations,… More >