A Robust Optimal Finite Difference Scheme for the Three-Dimensional Helmholtz Equation

Table 2

Numerical dispersion of the new scheme versus that of a standard second-order scheme.

Scheme		(0°, 45°)	(30°, 60°)	(45°, 75°)	(75°, 30°)	(45°, 90°)
7-point	(1.0,1.0)	0.0506	0.0418	0.0474	0.0870	0.0506
27-point	(1.0,1.0)	0.0002	0.0006	0.0001	0.0016	0.0009
7-point	(2.0,1.0)	0.1191	0.1261	0.1074	0.0871	0.1191
27-point	(2.0,1.0)	0.0123	0.0277	0.0009	0.0014	0.0146
7-point	(1.0,2.0)	0.0506	0.0601	0.1156	0.3140	0.1191
27-point	(1.0,2.0)	0.0118	0.0116	0.0016	0.0355	0.0061
7-point	(2.0,2.0)	0.1191	0.1462	0.1806	0.3142	0.1924
27-point	(2.0,2.0)	0.0121	0.0364	0.0035	0.0358	0.0637