A Moving Pseudo-Boundary MFS for Three-Dimensional Void Detection (Advances in Applied Mathematics and Mechanics, 2021)
We propose a new moving pseudo-boundary method offundamental solutions (MFS) for the determination of the boundary ofa three-dimensional void (rigid inclusion or cavity) within a conductinghomogeneous host medium from overdetermined Cauchy data on the accessible exterior boundary.The algorithm for imaging the interior of the medium also makes use of radial spherical parametrizationof the unknown star-shaped void and its centre in three dimensions. We also include the contraction anddilation factors in selecting the fictitious surfaces where the MFS sources are to be positioned in the set ofunknowns in the resulting regularized nonlinear least-squares minimization.The feasibility of this new method is illustrated in several numerical examples.