Abstract
Exact computations of high-frequency scattering by targets or rough surfaces can be challenging because of the large number of unknowns. A compromise can be obtained, however, using approximate Dirichlet-to-Neumann surface operators that are known in pseudo-differential form and efficiently implemented using rational approximations. These operators can be used as preconditioners to obtain well-conditioned iterative algorithms to solve the Helmholtz integral equation. Using these algorithms, we compute scattering by two- and three-dimensional targets, and rough surfaces with smooth concave or convex parts with incident fields near grazing angles of interest. This case is particularly important for underwater acoustics, where sounds field graze the free surface or bottom in shallow water.
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