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 are known for a long time; however, they have shown diÆculties, in particular, in dealing with general boundary conditions. This article introduces a new formulation for the compact scheme for the Helmholtz equation and an e ective strategy of incorporating absorbing boundary conditions. It has been numerically veri ed 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.