  This work is concerned with a unique combination of high order local
absorbing boundary conditions (ABC) with a general curvilinear Finite Element
Method (FEM) and its implementation in Isogeometric Analysis (IGA) for
time-harmonic acoustic waves. The ABC employed were recently devised by
Villamizar, Acosta and Dastrup [J. Comput. Phys. 333 (2017) 331] . They are
derived from exact Farfield Expansions representations of the outgoing waves in
the exterior of the regions enclosed by the artificial boundary. As a
consequence, the error due to the ABC on the artificial boundary can be reduced
conveniently such that the dominant error comes from the volume discretization
method used in the interior of the computational domain. Reciprocally, the
error in the interior can be made as small as the error at the artificial
boundary by appropriate implementation of {\it p-} and {\it h}- refinement. We
apply this novel method to cylindrical, spherical and arbitrary shape
scatterers including a prototype submarine. Our numerical results exhibits
spectral-like approximation and high order convergence rate. Additionally, they
show that the proposed method can reduce both the pollution and artificial
boundary errors to negligible levels even in very low- and high- frequency
regimes with rather coarse discretization densities in the IGA. As a result, we
have developed a highly accurate computational platform to numerically solve
time-harmonic acoustic wave scattering in two- and three-dimensions.
