Compact h4 finite-difference approximations to operators of Navier-Stokes type
Journal of Computational Physics
Comparison of second- and fourth-order discretizations for multigrid Poisson solvers
Journal of Computational Physics
Multigrid Simulation for High-Frequency Solutions of the Helmholtz Problem in Heterogeneous Media
SIAM Journal on Scientific Computing
The use of compact boundary value method for the solution of two-dimensional Schrödinger equation
Journal of Computational and Applied Mathematics
Compact optimal quadratic spline collocation methods for the Helmholtz equation
Journal of Computational Physics
Mathematical and Computer Modelling: An International Journal
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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.