Author(s)

A. Karageorghis, D. Lesnic & L.Marin

Abstract

We propose a nonlinear minimization method of fundamental solutions for the detection (shape, size and location) of unknown inner boundaries corresponding to either a rigid inclusion or a cavity inside a linear elastic body from nondestructive boundary measurements of displacement and traction. The stability of the numerical method is investigated by inverting measurements contaminated with noise. Keywords: Cauchy–Navier equations, method of fundamental solutions, regularization. 1 Introduction The method of fundamental solutions (MFS) [1, 2] is a meshless boundary collocation method [3] which may be used for the numerical solution of certain boundary value problems. The method has become increasingly popular over the last three decades primarily because of the ease with which it can be implemented. A comparison between the MFS and the boundary element method (BEM), as applied to direct problems, has been performed in [4]. In recent years, theMFS has been used extensively for the numerical solution of inverse problems primarily. An extensive survey of the applications of the MFS to inverse problems is provided in [5]. Themost difficult class of inverse problems are the so-called inverse geometric problems in which the location and shape of part of the boundary of the domain of the problem in question are unknown and need to be calculated as part of the solution. The MFS was used for the first time for the solution of inverse geometric

Keywords

Cauchy–Navier equations, method of fundamental solutions, regularization