


 Implementing implicit finitedifference in the timespace domain using spectral factorization and helical deconvolution  

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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 finitedifference weights, which I wish to factorize, are not dominated by the central finitedifference weight. Since the entire purpose of attempting to use the combination of implicit finitedifference 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 finitedifference 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 finitedifference 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 finitedifference 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 pseudoLaplacian discussed in Etgen and BransdsbergDahl (2009).



 Implementing implicit finitedifference in the timespace domain using spectral factorization and helical deconvolution  

Next: Bibliography
Up: Barak: Implicit helical finitedifference
Previous: WilsonBurg vs. Kolmogoroff spectral
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