On-surface radiation condition for multiple scattering of waves
For researchers in computational wave scattering, this offers a simpler alternative to boundary integral equations for multiple obstacles, though it is acknowledged as a crude approximation.
The paper extends the on-surface radiation condition (OSRC) to handle wave scattering from multiple obstacles, accounting for multiple reflections. The method yields smooth kernel integral equations that can be solved without singularity removal, and under weak scattering it provides a convergent iterative method that avoids solving single scattering problems per iteration.
The formulation of the on-surface radiation condition (OSRC) is extended to handle wave scattering problems in the presence of multiple obstacles. The new multiple-OSRC simultaneously accounts for the outgoing behavior of the wave fields, as well as, the multiple wave reflections between the obstacles. Like boundary integral equations (BIE), this method leads to a reduction in dimensionality (from volume to surface) of the discretization region. However, as opposed to BIE, the proposed technique leads to boundary integral equations with smooth kernels. Hence, these Fredholm integral equations can be handled accurately and robustly with standard numerical approaches without the need to remove singularities. Moreover, under weak scattering conditions, this approach renders a convergent iterative method which bypasses the need to solve single scattering problems at each iteration. Inherited from the original OSRC, the proposed multiple-OSRC is generally a crude approximate method. If accuracy is not satisfactory, this approach may serve as a good initial guess or as an inexpensive pre-conditioner for Krylov iterative solutions of BIE.