An interesting approach to dispersion compensation is based on frequency-warping the signals going into the mesh . Frequency warping can be used to compensate frequency-dependent dispersion, but it does not address angle-dependent dispersion. Therefore, frequency-warping is used in conjunction with an isotropic mesh.
The 3D waveguide mesh [518,521,399] is seeing more use for efficient simulation of acoustic spaces [396,182]. It has also been applied to statistical modeling of violin body resonators in [203,202,422,428], in which the digital waveguide mesh was used to efficiently model only the ``reverberant'' aspects of a violin body's impulse response in statistically matched fashion (but close to perceptually equivalent). The ``instantaneous'' filtering by the violin body is therefore modeled using a separate equalizer capturing the important low-frequency body and air modes explicitly. A unified view of the digital waveguide mesh and wave digital filters (§F.1) as particular classes of energy invariant finite difference schemes (Appendix D) appears in . The problem of modeling diffusion at a mesh boundary was addressed in , and maximally diffusing boundaries, using quadratic residue sequences, was investigated in ; an introduction to this topic is given in §C.14.6 below.
2D Mesh and the Wave Equation