DIRICHLET-TO-NEUMANN MAPS FOR UNBOUNDED WAVE-GUIDES

Dirichlet-to-Neumann (DtN) boundary conditions for unbounded wave guid es in two and three dimensions are derived and analyzed, defining prob lems that are suitable for finite element analysis. In the most genera l cases considered wave numbers may vary in arbitrary cross sections. The full DtN operator, in the form of an infinite series, is exact. No nunique solutions may occur when this operator is truncated. Simple cr iteria for the number of terms in the truncated operator that guarante e unique solutions are presented. A simple modification of the truncat ed operator leads to uniqueness for any number of terms. Numerical res ults validate the performance of DtN formulations for wave guides and confirm the criteria for uniqueness. (C) 1998 Academic Press.