Regularized MFS solution of inverse boundary value problems in three-dimensional steady-state linear thermoelasticity

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• 作者：Liviu Marin ; ^a ; ^b ; ^{marin.liviu@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; ^{liviu.marin@fmi.unibuc.ro" class="auth_mail" title="E-mail the corresponding author} ; Andreas Karageorghis^c ; ^{andreask@ucy.ac.cy" class="auth_mail" title="E-mail the corresponding author} ; Daniel Lesnic^d ; ^{amt5ld@maths.leeds.ac.uk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Inverse boundary value problem ; Three-dimensional linear thermoelasticity ; Method of fundamental solutions (MFS) ; Singular value decomposition (SVD) ; Regularization
• 刊名：International Journal of Solids and Structures
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：91
• 期：Complete
• 页码：127-142
• 全文大小：5242 K

文摘

We investigate the numerical reconstruction of the missing thermal and mechanical boundary conditions on an inaccessible part of the boundary in the case of three-dimensional linear isotropic thermoelastic materials from the knowledge of over-prescribed noisy data on the remaining accessible boundary. We employ the method of fundamental solutions (MFS) and several singular value decomposition (SVD)-based regularization methods, e.g. the Tikhonov regularization method (Tikhonov and Arsenin, 1986), the damped SVD and the truncated SVD (Hansen, 1998), whilst the regularization parameter is selected according to the discrepancy principle (Morozov, 1966),generalized cross-validation criterion (Golub et al., 1979) and Hansen’s L-curve method (Hansen and O’Leary, 1993).