An efficient moving pseudo-boundary MFS for void detection

We consider the method of fundamental solutions (MFS) for the determination of the boundary of a void. In the proposed formulation the location of the pseudo-boundary is not fixed. The MFS discretization of the corresponding inverse geometric boundary value problem yields a system of nonlinear equations in which the coefficients in the MFS approximation, the discrete radii in the polar parametrization, the coordinates of the centre of the void and the expansion and dilation coefficients of the pseudo-boundaries are unknown. For the minimization of the resulting functional we employ the nonlinear least squares minimization routine lsqnonlin from the MATLAB® optimization toolbox . In contrast to previous studies, we exploit the option which enables the user to provide the analytical expression for the Jacobian of the system, and show that, although tedious, this leads to spectacular savings in computational time. The case of multiple voids is also addressed.