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 initial exact boundary-value problem. A general background for the numerical treatment of arbitrary convex-shaped objects is stated. New efficient on-surface radiation conditions leading in a natural way to a symmetrical boundary 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 procedure using some results about the theory of local approximation of surfaces is described. Finally, the effectiveness and generality of the approach is numerically tested for several scatterers.