A field expansions method for scattering by periodic multilayered media

The interaction of acoustic and electromagnetic waves with periodic structures plays an important role in a wide range of problems of scientific and technological interest. This contribution focuses upon the robust and high-order numerical simulation of a model for the interaction of pressure waves generated within the earth incident upon layers of sediment near the surface. Herein described is a boundary perturbation method for the numerical simulation of scattering returns from irregularly shaped periodic layered media. The method requires only the discretization of the layer interfaces (so that the number of unknowns is an order of magnitude smaller than finite difference and finite element simulations), while it avoids not only the need for specialized quadrature rules but also the dense linear systems characteristic of boundary integral/element methods. The approach is a generalization to multiple layers of Bruno and Reitich's "Method of Field Expansions" for dielectric structures with two layers. By simply considering the entire structure simultaneously, rather than solving in individual layers separately, the full field can be recovered in time proportional to the number of interfaces. As with the original field expansions method, this approach is extremely efficient and spectrally accurate.