NONREFLECTING LOCAL BOUNDARY CONDITIONS FOR ELLIPTICAL-SHAPED EXTERIOR BOUNDARIES

A new class of nonreflecting boundary conditions is proposed for solving exterior Helmholtz problems. These boundary conditions are applicable to exterior elliptical-shaped boundaries that are more suitable in terms of cost-effectiveness for surrounding elongated scatterers and radiators. This class of conditions distinguishes itself from similar absorbing boundary conditions by (a) the. new conditions are exact for the first radiating modes, (b) they are easy to implement and to parallelize, and (c) they are compatible with the local structure of the computational finite element scheme. The analysis of the performance of these conditions shows that, in the low frequency regime, the now second order condition retains a good level of accuracy regardless of the slenderness of the artificial boundary.