We would like to add that an interesting future direction of development of waveguide meshes might involve the use of fully unstructured grids--that is, grids whose points cannot be ordered according to some regular indexing system. An unstructured DWN is certainly conceivable (and has been used for artificial reverberation ), though it is difficult to design a structure which is locally consistent with the continuous parallel-plate problem (though it will be passive, regardless). Such a structure would, of course, be very useful for dealing with the irregular geometries which typically arise in almost all musical instrument bodies. On the other hand, FDTD has evolved in this direction, specifically by making use of the finite volume method [89,140], long known in the fluid dynamics community. The FVTD (finite volume time domain) method is the result--the general idea is that instead of using finite differences to approximate derivative terms, the integral forms of the governing equations (Maxwell's, for the FDTD people, but mechanical systems can be treated equally easily) are discretized over cells of finite size which may not have any particular ordering. For a look at some recent work in this area, we refer the reader to  and .