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conclusion and future work

After conducting the aforementioned tests, I still cannot say why wavefield propagation by the proposed methodology does not function beyond a certain time step size. I can only conclude that for some reason the spectral factorization fails when the finite-difference weights, which I wish to factorize, are not dominated by the central finite-difference weight. Since the entire purpose of attempting to use the combination of implicit finite-difference and spectral factorization for propagation was to increase the time step size (thereby decreasing the total computation time, but also decreasing dominance of the central finite-difference weight), this failure makes the method unuseful. At the time step sizes for which this method does work, explicit methods will function better and faster.

There is one possible avenue in which to continue research of this method. The central weight of the finite-difference scheme which I used does decrease in dominance as the time step size is increased, but I am not bound to use this scheme only. It is possible that an alternate implicit finite-difference scheme will not have this attribute, and will thus be more amenable to factorization when the time step size is increased.

One source of such a scheme could be the pseudo-Laplacian discussed in Etgen and Bransdsberg-Dahl (2009).


next up previous [pdf]

Next: Bibliography Up: Barak: Implicit helical finite-difference Previous: Wilson-Burg vs. Kolmogoroff spectral

2010-11-26