Computational Complexity

The DW model is more efficient in one dimension because it can make use of delay lines to obtain an ${\cal O}(1)$ computation per time sample [414], whereas the FDTD scheme is ${\cal O}(M)$ per sample ($M$ being the number of spatial samples along the string). There is apparently no known way to achieve ${\cal O}(1)$ complexity for the FDTD scheme. In higher dimensions, i.e., when simulating membranes and volumes, the delay-line advantage disappears, and the FDTD scheme has the lower operation count (and memory storage requirements).