Discrete Dirichlet-to-Neumann maps for unbounded domains Original Research Article

It is shown how to construct a discrete counterpart of the Dirichlet-to-Neumann (DtN) map for use on an artificial boundary B introduced in exterior boundary value problems, following the idea of Deakin and Dryden. This discrete map provides an approximate non-reflecting or absorbing boundary condition for use in formulating a problem in the finite computational domain Ω bounded by B. Different discrete maps are constructed for use with finite difference and finite element methods in Ω. The solution of some simple problems shows that use of the discrete Dirichlet-to-Neumann (DDtN) map yields nearly the same accuracy as that of using the continuous DtN map.