SC 98-32 Frank Schmidt: An Alternative Derivation of the Exact DtN-Map on a Circle
Abstract: The paper supplies an alternative derivation of the
exact boundary conditions needed for the solution of time-harmonic
acoustic scattering problems modeled by the Helmholtz equation. The main
idea is to consider the exterior domain problem as an initial value
problem with initial data given on the boundary of a disc or sphere. The
solution of the exterior domain problem is obtained via Laplace
transformation techniques, where the asymptotic Sommerfeld radiation
condition is reformulated accordingly.
(only electronic version available)
Keywords: Helmholtz equation,
Dirichlet-to-Neumann map,
Sommerfeld radiation condition
MSC: 65C20, 65N99