  This paper introduces the first attempt to employ a localized meshless method
to analyze time-harmonic acoustic wave propagation on curved surfaces with
periodic holes/inclusions. In particular, the generalized finite difference
method is used as a localized meshless technique to discretize the surface
gradient and Laplace-Beltrami operators defined extrinsically in the governing
equations. An absorbing boundary condition is introduced to reduce reflections
from boundaries and accurately simulate wave propagation on unclosed surfaces
with periodic inclusions. Several benchmark examples demonstrate the efficiency
and accuracy of the proposed method in simulating acoustic wave propagation on
surfaces with diverse geometries, including complex shapes and periodic holes
or inclusions.
