Anton Arnold

Transparent boundary conditions for quantum-waveguides and in underwater acoustics

The electron transport through a quantum-waveguide can be modeled in good approximation by a Schrödinger equation on an unbounded domain. For numerical simulations, however, it is necessary to restrict this problem to a finite domain. This is possible without changing the solution by introducing "transparent boundary conditions" (TBC). In this talk we shall discuss numerical discretizations of these artificial boundary conditions, the approximation of the involved discrete convolutions by exponential sums, and the stability of the resulting numerical scheme. A very similar question appears in wave propagation problems like underwater acoustics. If horizontal reflections within the water can be neglected, the acoustic field emanated from a time-harmonic source can be modeled by a pseudo-differential 1-way-wave equation of Schrödinger type.

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