2D and 3D simulations need not be limited to rectilinear grid patterns. A variety of alternative topologies have been proposed and explored for improved dispersion characteristics, as well as better efficiency.
A two-dimensional, three-port hexagonal grid pattern is shown in Fig. 5.
A two-dimensional 3-port hexagonal mesh pattern.
A two-dimensional, six-port triangular grid pattern is shown in Fig. 6.
A two-dimensional 6-port triangular mesh pattern.
The dispersion error for the triangular waveguide mesh is shown in Fig. 7.
A contour plot of wave dispersion in the 6-port triangular mesh pattern.
When the rectilinear, hexagonal, and triangular meshes are compared with respect to a given space aliasing error, the triangular waveguide mesh uses the least number of junctions per unit area (the hexagonal mesh requires the most junctions per unit area) (Fontana and Rocchesso, 1998).
When the rectilinear, hexagonal, and triangular meshes are compared with respect to a minimum necessary sample rate, the triangular waveguide mesh again does the best job (and again, the hexagonal mesh requires the highest sample rate) (Fontana and Rocchesso, 1998).
Van Duyne and Smith (1996) proposed a 4-port tetrahedral grid pattern for modeling 3D objects. The resulting dispersion error pattern appears significantly more complex than those of either the triangular or hexagonal meshes. Memory and sample rate comparisons for this structure are not currently available.