Compact Schemes for Acoustics in the Frequency Domain

Seongjai Kim

This article is concerned with the fourth-order compact scheme for an
accurate simulation of acoustic waves in the frequency domain.
The compact schemes are known for a long time; however, they have shown
difficulties, in particular, in dealing with general boundary conditions.
This article introduces a new formulation for the compact scheme for the
Helmholtz equation and an effective strategy of incorporating
absorbing boundary conditions.
It has been numerically verified that the resulting compact scheme is
fourth-order in general heterogeneous media and improves the accuracy
of the numerical solution dramatically, by more than two-digits, over
the standard second-order scheme.