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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:
65N21Inverse problems (BVP of PDE, numerical methods)
35R30Inverse problems for PDE
35J05Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
65N38Boundary element methods (BVP of PDE)
78A46Inverse scattering problems
78M15Boundary element methods (optics)