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We propose a novel on-surface radiation condition to approximate the outgoingsolution to the Helmholtz equation in the exterior of several impenetrableconvex obstacles. Based on a local approximation of the Dirichlet-to-Neumannoperator and a local formula for wave propagation, this new methodsimultaneously accounts for the outgoing behavior of the solution as well asthe reflections arising from the multiple obstacles. The method involvestangential derivatives only, avoiding the use of integration over the surfacesof the obstacles. As a consequence, the method leads to sparse matrices andO(N) complexity. Numerical results are presented to illustrate the performanceof the proposed method. Possible improvements and extensions are alsodiscussed.

Local on-surface radiation condition for multiple scattering of waves from convex obstacles