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Desingularized meshless method for solving Laplace equation with over-specified boundary conditions using regularization techniques

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Abstract

The desingularized meshless method (DMM) has been successfully used to solve boundary-value problems with specified boundary conditions (a direct problem) numerically. In this paper, the DMM is applied to deal with the problems with over-specified boundary conditions. The accompanied ill-posed problem in the inverse problem is remedied by using the Tikhonov regularization method and the truncated singular value decomposition method. The numerical evidences are given to verify the accuracy of the solutions after comparing with the results of analytical solutions through several numerical examples. The comparisons of results using Tikhonov method and truncated singular value decomposition method are also discussed in the examples.

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Authors and Affiliations

  1. Department of Civil Engineering, National Ilan University, Ilan, 26047, Taiwan

    K. H. Chen

  2. Department of Hydraulic and Ocean Engineering, National Cheng Kung University, Tainan, 70101, Taiwan

    J. H. Kao

  3. Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung, 20224, Taiwan

    J. T. Chen

  4. Department of Civil Engineering, National Taiwan University, Taipei, 10617, Taiwan

    K. L. Wu

Authors
  1. K. H. Chen
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  2. J. H. Kao
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  3. J. T. Chen
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  4. K. L. Wu
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Correspondence to K. H. Chen.

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Chen, K.H., Kao, J.H., Chen, J.T. et al. Desingularized meshless method for solving Laplace equation with over-specified boundary conditions using regularization techniques. Comput Mech 43, 827–837 (2009). https://doi.org/10.1007/s00466-008-0348-1

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  • DOI: https://doi.org/10.1007/s00466-008-0348-1

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