DISCRETE DIRICHLET-TO-NEUMANN MAPS FOR UNBOUNDED-DOMAINS

It is shown how to construct a discrete counterpart of the Dirichlet-t o-Neumann (DtN) map for use on an artificial boundary B introduced in exterior boundary value problems, following the idea of Deakin and Dry den. This discrete map provides an approximate non-reflecting or absor bing boundary condition for use in formulating a problem in the finite computational domain Omega bounded by B. Different discrete maps are constructed for use with finite difference and finite element methods in Omega The solution of some simple problems shows that use of the di screte Dirichlet-to-Neumann (DDtN) map yields nearly the same accuracy as that of using the continuous DtN map. (C) 1998 Elsevier Science S. A. All rights reserved.