Non-iterative regularized MFS solution of inverse boundary value problems in linear elasticity: A numerical study

• Numerical reconstruction of the missing boundary data in 2D and 3D linear elasticity.
• Noisy over-prescribed data are available on the remaining accessible boundary.
• The inverse problem is solved by a meshless method, i.e. the method of fundamental solutions (MFS).
• Stabilization is achieved via several SVD-based regularization methods.
• The regularization parameter is selected via the criteria used for inverse problems.

The numerical reconstruction of the missing Dirichlet and Neumann data on an inaccessible part of the boundary in the case of two- and three-dimensional linear isotropic elastic materials from the knowledge of over-prescribed noisy measurements taken on the remaining accessible boundary part is investigated. This inverse problem is solved using the method of fundamental solutions (MFS), whilst its stabilization is achieved through several singular value decomposition (SVD)-based regularization methods, such as the Tikhonov regularization method [48], the damped SVD and the truncated SVD [18]. The regularization parameter is selected according to the discrepancy principle [40], generalized cross-validation criterion [14] and Hansen’s L-curve method [20].