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Reconstruction of a two-dimensional binary obstacle by controlled evolution of a level-set. (English) Zbl 0912.35158
The authors study the inverse problem under homogeneous transmission boundary conditions. This is the problem to determine the shape of the scattering obstacle from measurements of the scattered field outside the object. The authors suggest a level-set approach where the level-sets depend on a continuous parameter t. The evolution of the level-set is controlled by a Hamilton-Jacobi-type equation where the velocity explicitly depends on the total field and its adjoint. Numerical examples show that this approach is able to detect scatterers which consist of several components.

MSC:
35R30Inverse problems for PDE
35J05Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
35P25Scattering theory (PDE)