Compact schemes for acoustics in the frequency domain

This article is concerned with the fourth-order compact scheme for an accurate simulation of acoustic waves in the frequency domain. The compact schemes have been known for a long time; however, they have exhibited 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.