Title: High order local absorbing boundary conditions for acoustic waves in terms of farfield expansions,
Abstract: We devise a new high order local absorbing boundary condition (ABC) for
radiating problems and scattering of time-harmonic acoustic waves from
obstacles of arbitrary shape. By introducing an artificial boundary $S$
enclosing the scatterer, the original unbounded domain $\Omega$ is decomposed
into a bounded computational domain $\Omega^{-}$ and an exterior unbounded
domain $\Omega^{+}$. Then, we define interface conditions at the artificial
boundary $S$, from truncated versions of the well-known Wilcox and Karp
farfield expansion representations of the exact solution in the exterior region
$\Omega^{+}$. As a result, we obtain a new local absorbing boundary condition
(ABC) for a bounded problem on $\Omega^{-}$, which effectively accounts for the
outgoing behavior of the scattered field. Contrary to the low order absorbing
conditions previously defined, the order of the error induced by this ABC can
easily match the order of the numerical method in $\Omega^{-}$. We accomplish
this by simply adding as many terms as needed to the truncated farfield
expansions of Wilcox or Karp. The convergence of these expansions guarantees
that the order of approximation of the new ABC can be increased arbitrarily
without having to enlarge the radius of the artificial boundary. We include
numerical results in two and three dimensions which demonstrate the improved
accuracy and simplicity of this new formulation when compared to other
absorbing boundary conditions.