The MFS For The Detection Of Inner Boundaries
In Linear Elasticity
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
Related Book
Other papers in this volume
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