The MFS for the Cauchy problem in two-dimensional steady-state linear thermoelasticity

We study the reconstruction of the missing thermal and mechanical fields on an inaccessible part of the boundary for two-dimensional linear isotropic thermoelastic materials from over-prescribed noisy (Cauchy) data on the remaining accessible boundary. This problem is solved with the method of fundamental solutions (MFS) together with the method of particular solutions (MPS) via the MFS-based particular solution for two-dimensional problems in uncoupled thermoelasticity developed in Marin and Karageorghis, 2012a and Marin and Karageorghis, 2013. The stabilisation/regularization of this inverse problem is achieved by using the Tikhonov regularization method (Tikhonov and Arsenin, 1986), whilst the optimal value of the regularization parameter is selected by employing Hansen’s L-curve method (Hansen, 1998).