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Dissertation/Thesis Abstract

Analysis of Time Filters in Multistep Methods
by Hurl, Nicholas, Ph.D., University of Pittsburgh, 2017, 65; 10645835
Abstract (Summary)

Geophysical ow simulations have evolved sophisticated implicit-explicit time stepping methods (based on fast-slow wave splittings) followed by time filters to control any unstable models that result. Time filters are modular and parallel. Their effect on stability of the overall process has been tested in numerous simulations, but never analyzed. Stability is proven herein for the Crank-Nicolson Leapfrog (CNLF) method with the Robert-Asselin (RA) time filter and for the Crank-Nicolson Leapfrog method with the Robert-Asselin-Williams (RAW) time filter for systems by energy methods. We derive an equivalent multistep method for CNLF+RA and CNLF+RAW and stability regions are obtained. The time step restriction for energy stability of CNLF+RA is smaller than CNLF and CNLF+RAW time step restriction is even smaller. Numerical tests find that RA and RAW add numerical dissipation.

This thesis also shows that all modes of the Crank-Nicolson Leap Frog (CNLF) method are asymptotically stable under the standard timestep condition.

Indexing (document details)
Advisor: Layton, William
School: University of Pittsburgh
School Location: United States -- Pennsylvania
Source: DAI-B 79/01(E), Dissertation Abstracts International
Subjects: Mathematics
Publication Number: 10645835
ISBN: 978-0-355-19089-2
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