Solution of inverse problems by boundary integral equations without residual minimization

In this paper the solution of some inverse problems for potential ®elds is tackled. The aim is to compute the position and shape of an unknown ¯aw within a body, using some experimental measures as additional data. By the linearization of the di€erence between the Boundary Integral Equation for the actual con®guration and the same equation for an assumed con®guration, an integral equation for the variations is deduced. This integral equation is carried to the boundary by a limiting process and a solution procedure is devised to compute an approximation to the actual ¯aw. The solution method proceeds iteratively, solving a direct and an inverse problem in every step, but no minimization algorithm is involved. The performance of the method is shown in several numerical examples.