A numerical study of the SVDMFS solution of inverse boundary value problems in two-dimensional steady-state linear thermoelasticity

We study the reconstruction of the missing thermal and mechanical data on an inaccessible part of the boundary in the case of two-dimensional linear isotropic thermoelastic materials from overprescribed noisy measurements taken on the remaining accessible boundary part. This inverse problem is solved by using the method of fundamental solutions together with the method of particular solutions. The stabilization of this inverse problem is achieved using several singular value decomposition (SVD)-based regularization methods, such as the Tikhonov regularization method (Tikhonov and Arsenin, Methods for solving ill-posed problems, Nauka, Moscow, 1986), the damped SVD and the truncated SVD (Hansen, Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion, SIAM, Philadelphia, 1998), whilst the optimal regularization parameter is selected according to the discrepancy principle (Morozov, Sov Math Doklady 7 (1966), 414-417), generalized cross-validation criterion (Golub et al. Technometrics 22 (1979), 1-35) and Hansen's L-curve method (Hansen and O'Leary, SIAM J Sci Comput 14 (1993), 1487-503).