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  • Open Access


    On the solution of a coefficient inverse problem for the non-stationary kinetic equation

    Mustafa Yildiz1

    The International Conference on Computational & Experimental Engineering and Sciences, Vol.12, No.3, pp. 103-110, 2009, DOI:10.3970/icces.2009.012.103

    Abstract The solvability conditions of an inverse problem for the non-stationary kinetic equation is formulated and a new numerical method is developed to obtain the approximate solution of the problem. A comparison between the approximate solution and the exact solution of the problem is presented. More >

  • Open Access


    Application of Numerical Methods to Elasticity Imaging

    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 >

  • 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 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 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 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 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 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 can be gained 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 More >

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