Dispersion

Since the digital waveguide mesh is lossless by construction (when modeling lossless membranes and volumes), and since it is also linear and time-invariant by construction, being made of ordinary digital filtering computations, there is only one type of error exhibited by the mesh: dispersion. Dispersion can be quantified as an error in propagation speed as a function of frequency and direction along the mesh. The mesh geometry (rectilinear, triangular, hexagonal, tetrahedral, etc.) strongly influences the dispersion properties. Many cases are analyzed in [50] using von Neumann analysis (see also Appendix L).

The triangular waveguide mesh [136] turns out to be the simplest mesh geometry in 2D having the least dispersion variation as a function of direction of propagation on the mesh. In other terms, the triangular mesh is closer to isotropic than all other known elementary geometries. The interpolated waveguide mesh [369] can also be configured to optimize isotropy, but at a somewhat higher compuational cost.