We consider a new way of looking at quantum mechanical scattering, motivated by the need for a framework that would allow calculations within complex waveguide geometries and for small scale systems. The two dimensional scattering problem is considered as a variational problem. This allows the use of the finite element method, which discretizes the region of interest so that numerical results may be obtained. We introduce stealth finite elements at the ends of a waveguide which serve to attenuate the wave. We demonstrate the numerical power of this framework by considering complicated scattering centers within waveguides. A modal analysis is performed on the resulting scattered waves.
Worcester Polytechnic Institute
Major Qualifying Project
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