  We propose a novel on-surface radiation condition to approximate the outgoing
solution to the Helmholtz equation in the exterior of several impenetrable
convex obstacles. Based on a local approximation of the Dirichlet-to-Neumann
operator and a local formula for wave propagation, this new method
simultaneously accounts for the outgoing behavior of the solution as well as
the reflections arising from the multiple obstacles. The method involves
tangential derivatives only, avoiding the use of integration over the surfaces
of the obstacles. As a consequence, the method leads to sparse matrices and
O(N) complexity. Numerical results are presented to illustrate the performance
of the proposed method. Possible improvements and extensions are also
discussed.
