Shape Optimization for Inverse Electromagnetic Scattering Problems

Maria Schütte^*, Stephan Schmidt and Andrea Walther

This work is motivated by a real-world application arising from gas turbines. Our focus is set on the detection of radial gaps. This identification is very challenging, since common strategies like light-based methods fail in operation mode. Therefore radar measurements leading to an inverse scattering problem are used as possible alternative. While common strategies like FDTD-methods have serious problems in dealing with complex geometries, a discontinuous Galerkin method is applied here. For combining all local elementwise solutions into a global solution, an upwind flux is used. One of the main aspects of this talk is the optimization of the topology. Therefore one needs to consider and solve the adjoint equations. Another important part of the optimization is the shape gradient, which has to be derived from the Maxwell's equations. For the computation of the numerical results, FEniCS, a tool for the solution of pdes, is used. Theoretical and numerical results will be presented and discussed.

Mathematics Subject Classification: 35R30 49Q12

Keywords: inverse scattering problems: discontinuous Galerkin methods; adjoint equations; shape optimization

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