The linear sampling method for cracks

We consider the inverse scattering problem of determining the shape of an infinite cylinder having an open arc as cross section from a knowledge of the TM-polarized scattered electromagnetic field corresponding to time-harmonic incident plane waves propagating from arbitrary directions. We assume that the arc is a (possibly) partially coated perfect conductor and develop the linear sampling method, which was originally developed for solving the inverse scattering problem for obstacles with nonempty interior, to include the above case of obstacles with empty interior.

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