  The multiple-Dirichlet-to-Neumann (multiple-DtN) non-reflecting boundary
condition is adapted to acoustic scattering from obstacles embedded in the
half-plane. The multiple-DtN map is coupled with the method of images as an
alternative model for multiple acoustic scattering in the presence of
acoustically soft and hard plane boundaries. As opposed to the current practice
of enclosing all obstacles with a large semicircular artificial boundary that
contains portion of the plane boundary, the proposed technique uses small
artificial circular boundaries that only enclose the immediate vicinity of each
obstacle in the half-plane. The adapted multiple-DtN condition is
simultaneously imposed in each of the artificial circular boundaries. As a
result the computational effort is significantly reduced. A computationally
advantageous boundary value problem is numerically solved with a finite
difference method supported on boundary-fitted grids. Approximate solutions to
problems involving two scatterers of arbitrary geometry are presented. The
proposed numerical method is validated by comparing the approximate and exact
far-field patterns for the scattering from a single and from two circular
obstacles in the half-plane.
