FDTD and DW Equivalence

In [67,70], it is shown that the FDS and DW recursions for the ideal vibrating string are equivalent. That is, a one-to-one linear transformation exists which translates the state space of one to the other, and the time updates perform the same state-space transition in each case. As a result, the methods only differ in low-level computational details such as numerical sensitivity, cost efficiency, and the implementations of excitations and boundary conditions. In one dimension, the DW method is much more efficient in most applications. In higher dimensions, however, in which membranes and acoustic spaces are modeled using a grid of intersecting digital waveguides--the so-called digital waveguide mesh--the FDS approach is generally more efficient than the DW method. (See [3] for quantitative comparisons).