Fast approximate computation of a time-harmonic scattered field using the on-surface radiation condition method

The numerical study of the on-surface radiation condition method applied to two- and three-dimensional time-harmonic scattering problems is examined. This approach allows us to quickly compute an approximate solution to the i nitial exact boundary-value problem. A general background for the numerical treatment of arbitrary convex-shaped objects is stated. New efficient on-s urface radiation conditions leading in a natural way to a symmetrical bound ary variational formulation are introduced. The approximation is based upon boundary finite-element methods. Moreover, this study requires a specific numerical treatment of the curvature operator. To this end, a numerical pro cedure using some results about the theory of local approximation of surfac es is described. Finally, the effectiveness and generality of the approach is numerically tested for several scatterers.