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An iterative method for parameter identification and shape reconstruction. (English) Zbl 1182.65166

Summary: An iterative strategy for the reconstruction of objects buried in a medium and the identification of their material parameters is analysed. The algorithm alternates guesses of the domains using topological derivatives with corrections of the parameters obtained by descent techniques. Numerical experiments in geometries with multiple scatterers show that our scheme predicts the number, location and shape of objects, together with their physical parameters, with reasonable accuracy in a few steps.

MSC:

65N21 Numerical methods for inverse problems for boundary value problems involving PDEs
35R30 Inverse problems for PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65N38 Boundary element methods for boundary value problems involving PDEs
78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory
78M15 Boundary element methods applied to problems in optics and electromagnetic theory
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