  Surface water waves are considered propagating over highly variable
non-smooth topographies. For this three dimensional problem a
Dirichlet-to-Neumann (DtN) operator is constructed reducing the numerical
modeling and evolution to the two dimensional free surface. The corresponding
Fourier-type operator is defined through a matrix decomposition. The
topographic component of the decomposition requires special care and a Galerkin
method is provided accordingly. One dimensional numerical simulations, along
the free surface, validate the DtN formulation in the presence of a large
amplitude, rapidly varying topography. An alternative, conformal mapping based,
method is used for benchmarking. A two dimensional simulation in the presence
of a Luneburg lens (a particular submerged mound) illustrates the accurate
performance of the three dimensional DtN operator.
