Boundary reconstruction in two-dimensional steady state anisotropic heat conduction using a regularized meshless method |
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| Authors: | Liviu Marin Ligia Munteanu |
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| Affiliation: | 1. Henry Samueli School of Engineering and Applied Science, Mechanical and Aerospace Engineering, University of California Los Angeles, Los Angeles, CA 90095, United States;2. School of Mechanical, Materials and Energy Engineering, Indian Institute of Technology Ropar, Rupnagar, Punjab 140001, India;1. Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung, Taiwan;2. Department of Systems Engineering and Naval Architecture, National Taiwan Ocean University, Keelung, Taiwan;3. Department of Civil Engineering, National Taiwan University, Taipei, Taiwan;1. Mechanical Engineering Department, Shiraz Branch, Islamic Azad University, P.O. Box 71955-845, Shiraz, Iran;2. Department of Bioresource Engineering, McGill University, 21111 Lakeshore Road, Ste. Anne de Bellevue, QC, Canada H9X 3V9;1. School of Science, Chang’an University, Xi’an 710064, PR China;2. School of Science, Anhui Agricultural University, Hefei 230036, PR China |
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| Abstract: | We study the stable numerical identification of an unknown portion of the boundary on which either a Dirichlet or a Robin boundary condition is provided, while additional Cauchy data are given on the remaining known part of the boundary of a two-dimensional domain, in the case of steady state anisotropic heat conduction problems. This inverse geometric problem is solved using the method of fundamental solutions (MFS) in conjunction with the Tikhonov regularization method 53]. The optimal value for the regularization parameter is chosen according to Hansen’s L-curve criterion 17]. The stability, convergence, accuracy and efficiency of the proposed method are investigated by considering several examples in both smooth and piecewise smooth geometries. |
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