High-order nonreflecting boundary conditions without high-order derivatives

A wave problem in an unbounded domain is often treated numerically by trunc ating the infinite domain via an artificial boundary a, imposing a so-calle d nonreflecting boundary condition (NRBC) on B, and then solving the proble m numerically in the finite domain bounded by B. A general approach is devi sed here to construct high-order local NRBCs with a symmetric structure and with only low (first- or second-) order spatial and/or temporal derivative s. This enables the practical use of NRBCs of arbitrarily high order. In th e case of time-harmonic waves with finite element discretization. the appro ach yields a symmetric C-0 finite element formulation in which standard ele ments can be employed. The general methodology is presented for both the ti me-harmonic case (Helmholtz equation) and the time-dependent case (the wave equation) and is demonstrated numerically in the former case. (C) 2001 Aca demic Press.