A BOUNDARY INTEGRAL-EQUATION METHOD FOR AN INVERSE PROBLEM RELATED TO CRACK DETECTION

This paper discusses an application of a boundary integral equation method (BIEM) to an inverse problem of determining the shape and the location of cracks by boundary measurements. Suppose that a given body contains an interior crack, the shape and the location of which are unknown. On the exterior boundary of this body one carries out measurements which are interpreted mathematically as prescribing Dirichlet data and measuring the corresponding Neumann data, or vice versa, for a field governed by Laplace's equation. The inverse problem considered here attempts to determine the geometry of the crack from these experimental data, We propose to solve this problem by minimizing the error of a certain boundary integral equation (BIE). The process of this minimization, however, is shown to require solutions of certain hypersingular integral equations. Hence regularization methods suitable for solving these integral equations are proposed. Several 2D and 3D numerical examples are given in order to test the performance of the present method.