Mathematics Colloquia and Seminars

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In this talk, I will give an overview of time-harmonic acoustic scattering (the Helmholtz equation) in a waveguide and its corresponding inverse problem in which the shape of the scatterer is the unknown. Mathematical relations between the direct problem and its inverse problem will be presented through the proof of a uniqueness theorem of an inverse problem. An inversion scheme with its numerical results, which does not use nonlinear optimization methods and is relatively independent of the geometry and physical properties of the scatterer, will also be given in this talk. If time permits, I will sketch the proof of a uniqueness theorem of the direct obstacle scattering in a multi-layer waveguide.