Boundary Element Regularisation Methods for Solving the Cauchy Problem in Linear Elasticity

In this article several boundary element regularisation methods, such as iterative, conjugate gradient, Tikhonov regularisation and singular value decomposition methods, for solving the Cauchy problem in isotropic linear elasticity are developed and compared. Regularising stopping criteria are developed and the convergence, as well as the stability, of the numerical methods proposed are analysed. The Cauchy problem in isotropic linear elasticity can be regularised by various methods, such as the general regularisation methods presented in this article, but more accurate results are obtained by particular methods which take into account the particular structure of the problem, such as the alternating iterative algorithm originally proposed by [V.A. Kozlov, V.G. Maz'ya and A.F. Fomin, (1991). An iterative method for solving the Cauchy problem for elliptic equations. Comput. Maths. Math. Phys ., 31 , 45-52].