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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 [441], 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).


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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4.
Copyright © 2014-06-11 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA