Numerical solution of the variation boundary integral equation for inverse problems

In this paper a procedure to solve the identi cation inverse problems for two-dimensional potential elds is presented. The procedure relies on a boundary integral equation (BIE) for the variations of the potential, ux, and geometry. This equation is a linearization of the regular BIE for small changes in the geometry. The aim in the identi cation inverse problems is to nd an unknown part of the boundary of the domain, usually an internal aw, using experimental measurements as additional information. In this paper this problem is solved without resorting to a minimization of a functional, but by an iterative algorithm which alternately solves the regular BIE and the variation BIE. The variation of the geometry of the aw is modelled by a virtual strain eld, which allows for greater exibility in the shape of the assumed aw. Several numerical examples demonstrate the e ectiveness and reliability of the proposed approach