DETERMINATION OF CRACKS HAVING ARBITRARY SHAPES WITH THE BOUNDARY INTEGRAL-EQUATION METHOD

This paper discusses an application of the boundary integral equation method (BIEM) to an inverse problem of reconstructing a 2D curved crack from an experiment using a quantity governed by Laplace's equation. This problem is solved with the help of BIEM and a nonlinear programming technique. In this inverse problem we consider an infinite domain which contains one unknown crack in its interior. This cracked body is subjected to known far fields, and the resulting near fields are measured at several interior points. The most plausible crack is then determined as the minimiser of a fit-to-data cost function. This numerical process of minimisation, however, tends to become unstable as the degrees of freedom allowed for the unknown crack increase. However, a remedy of this ill-posedness based on Tikhonov's regularisation is shown to be effective. Some numerical examples are presented to confirm the applicability of the proposed method.