A meshless method for solving the cauchy problem in three-dimensional elastostatics

The application of the method of fundamental solutions to the Cauchy problem in three-dimensional isotropic linear elasticity is investigated. The resulting system of linear algebraic equations is ill-conditioned and therefore, its solution is regularized by employing the first-order Tikhonov functional, while the choice of the regularization parameter is based on the L-curve method. Numerical results are presented for both under- and equally-determined Cauchy problems in a piece-wise smooth geometry. The convergence, accuracy, and stability of the method with respect to increasing the number of source points and the distance between the source points and the boundary of the solution domain, and decreasing the amount of noise added into the input data, respectively, are analysed.