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  • Open Access


    An Optimal Multi-Vector Iterative Algorithm in a Krylov Subspace for Solving the Ill-Posed Linear Inverse Problems

    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 with small error, even under… More >

  • Open Access


    Artificial Neural Network Methods for the Solution of Second Order Boundary Value Problems

    Cosmin Anitescu1, Elena Atroshchenko2, Naif Alajlan3, Timon Rabczuk3,*

    CMC-Computers, Materials & Continua, Vol.59, No.1, pp. 345-359, 2019, DOI:10.32604/cmc.2019.06641

    Abstract We present a method for solving partial differential equations using artificial neural networks and an adaptive collocation strategy. In this procedure, a coarse grid of training points is used at the initial training stages, while more points are added at later stages based on the value of the residual at a larger set of evaluation points. This method increases the robustness of the neural network approximation and can result in significant computational savings, particularly when the solution is non-smooth. Numerical results are presented for benchmark problems for scalar-valued PDEs, namely Poisson and Helmholtz equations, as well as for an inverse… More >

  • Open Access


    A New Iterative Regularization Method for Solving the Dynamic Load Identification Problem

    Linjun Wang1,2, 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 >

  • Open Access


    Optimally Generalized Regularization Methods for Solving Linear Inverse Problems

    Chein-Shan Liu1

    CMC-Computers, Materials & Continua, Vol.29, No.2, pp. 103-128, 2012, DOI:10.3970/cmc.2012.029.103

    Abstract In order to solve ill-posed linear inverse problems, we modify the Tikhonov regularization method by proposing three different preconditioners, such that the resultant linear systems are equivalent to the original one, without dropping out the regularized term on the right-hand side. As a consequence, the new regularization methods can retain both the regularization effect and the accuracy of solution. The preconditioned coefficient matrix is arranged to be equilibrated or diagonally dominated to derive the optimal scales in the introduced preconditioning matrix. Then we apply the iterative scheme to find the solution of ill-posed linear inverse problem. Two theorems are proved… More >

  • Open Access


    A Combined Sensitive Matrix Method and Maximum Likelihood Method for Uncertainty Inverse Problems

    W. Zhang1, X. Han1,2, J. Liu1, Z. H. Tan1

    CMC-Computers, Materials & Continua, Vol.26, No.3, pp. 201-226, 2011, DOI:10.3970/cmc.2011.026.201

    Abstract The uncertainty inverse problems with insufficiency and imprecision in the input and/or output parameters are widely existing and unsolved in the practical engineering. The insufficiency refers to the partly known parameters in the input and/or output, and the imprecision refers to the measurement errors of these ones. In this paper, a combined method is proposed to deal with such problems. In this method, the imprecision of these known parameters can be described by probability distribution with a certain mean value and variance. Sensitive matrix method is first used to transform the insufficient formulation in the input and/or output to a… More >

  • Open Access


    A Computational Inverse Technique to Determine the Dynamic Constitutive Model Parameters of Concrete

    R. Chen1, X. Han1,2, J. Liu1, W. Zhang1

    CMC-Computers, Materials & Continua, Vol.25, No.2, pp. 135-158, 2011, DOI:10.3970/cmc.2011.025.135

    Abstract In this paper, a computational inverse technique is presented to determine the constitutive parameters of concrete based on the penetration experiments. In this method, the parameter identification problem is formulated as an inverse problem, in which the parameters of the constitutive model can be characterized through minimizing error functions of the penetration depth measured in experiments and that computed by forward solver LS-DYNA. To reduce the time for forward calculation during the inverse procedure, radial basis function approximate model is used to replace the actual computational model. In order to improve the accuracy of approximation model, a local-densifying method combined… More >

  • Open Access


    A Lie-Group Adaptive Method to Identify the Radiative Coefficients in Parabolic Partial Differential Equations

    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 Tt(x, t) = Txx(x, t)-α(x)T(x, t), and Tt(x, y, t) = Txx(x, y, t) + Tyy(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 >

  • Open Access


    Data Mining and Machine Learning Methods Applied to 3 A Numerical Clinching Model

    Marco Götz1,*, Ferenc Leichsenring1, Thomas Kropp2, Peter Müller2, Tobias Falk2, Wolfgang Graf1, Michael Kaliske1, Welf-Guntram Drossel2

    CMES-Computer Modeling in Engineering & Sciences, Vol.117, No.3, pp. 387-423, 2018, DOI:10.31614/cmes.2018.04112

    Abstract Numerical mechanical models used for design of structures and processes are very complex and high-dimensionally parametrised. The understanding of the model characteristics is of interest for engineering tasks and subsequently for an efficient design. Multiple analysis methods are known and available to gain insight into existing models. In this contribution, selected methods from various fields are applied to a real world mechanical engineering example of a currently developed clinching process. The selection of introduced methods comprises techniques of machine learning and data mining, in which the utilization is aiming at a decreased numerical effort. The methods of choice are basically… More >

  • Open Access


    A Virtual Boundary Element Method for Three-Dimensional Inverse Heat Conduction Problems in Orthotropic Media

    Xu Liu1, Guojian Shao1, Xingxing Yue2,*, Qingbin Yang3, Jingbo Su4

    CMES-Computer Modeling in Engineering & Sciences, Vol.117, No.2, pp. 189-211, 2018, DOI:10.31614/cmes.2018.03947

    Abstract This paper aims to apply a virtual boundary element method (VBEM) to solve the inverse problems of three-dimensional heat conduction in orthotropic media. This method avoids the singular integrations in the conventional boundary element method, and can be treated as a potential approach for solving the inverse problems of the heat conduction owing to the boundary-only discretization and semi-analytical algorithm. When the VBEM is applied to the inverse problems, the numerical instability may occur if a virtual boundary is not properly chosen. The method encounters a highly ill-conditioned matrix for the larger distance between the physical boundary and the virtual… More >

  • Open Access


    Inverse Analysis of Origin-Destination matrix for Microscopic Traffic Simulator

    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 >

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