Time Dependent Phase Space Filters by Avy Soffer & Chris Stucchio & Minh-Binh Tran

Author:Avy Soffer & Chris Stucchio & Minh-Binh Tran
Language: eng
Format: epub
ISBN: 9789811968181
Publisher: Springer Nature Singapore

Step 6: To minimize the error of the filtering, we need to take k inf > 3∕σ. (in this case the error from removing a Gaussian with minimum velocity, will be of the order , A is the amplitude of the removed gaussian. If you double the size of σ, the error will be . From here, one could see that that removing a gaussian with small velocity is producing big error. But the program can store/leave/notify when such gaussian shows up.

Step 7: The expansion for a function in the filter domain, is done by taking the usual scalar product of the function with the dual frame functions. The width of the filter is determined by the max velocity, mainly. It should be wide enough so that its length w, should be at least 3D T. D T is the time interval after which we apply the filtering. It should be chosen as long as possible, to reduce the number of filtering steps. But of course, too long, will make w too big. w should also be much bigger than the main support of the mother frame. When a Gaussian is too slow mover, and higher accuracy is needed, one can remove such Gaussians and upload on a new computational domain, with size twice as large as the original one, but with the same number of lattice point as the old one. In the linear case all such Gaussians can be propagated under the original flow independently of the rest of the solution.

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