OPTIMAL LOCAL NONREFLECTING BOUNDARY-CONDITIONS

A class of numerical methods to solve problems in unbounded domains is based on truncating the infinite domain via an artificial boundary a and applying some boundary condition on B, which is called a Non-Refle cting Boundary Condition (NRBC). In this paper a systematic way to der ive optimal local NRBCs of given order is developed in various configu rations. The optimality is in the sense that the local NRBC best appro ximates the exact nonlocal Dirichlet-to-Neumann (DtN) boundary conditi on for C-infinity functions in the L-2 norm. The optimal NRBC may be o f low order but still represent high-order modes in the solution. It i s shown that the previously derived localized DtN conditions are speci al cases of the new optimal conditions. The performance of the first-o rder optimal NRBC is demonstrated via numerical examples, in conjuncti on with the finite element method. (C) 1998 Elsevier Science B.V. and IMACS. All rights reserved.