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Higher Order Time Filters for Evolution Equations

Guzel, Ahmet (2018) Higher Order Time Filters for Evolution Equations. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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Time filter is a non-intrusive technique that post-processes the previously computed values of given numerical methods. The purpose of this study is to construct new time filters, which will increase the accuracy and stability of existing legacy codes. We focus on time filters for the leapfrog method and the backward Euler method.

The leapfrog scheme is a second-order, symplectic, explicit method, which is widely used in the numerical models of weather and climate, currently in conjunction with the Robert- Asselin (RA) and Robert-Asselin-Williams (RAW) time filters.
• We propose and analyze a novel filter, which combines the higher-order Robert-Asselin (hoRA) filter with a Williams’ step (LF-hoRAW). This filter better addresses the issue of time-splitting instability of the leapfrog scheme and increases the stability of hoRA, reduces the magnitude of the truncation error, improves the accuracy of amplitude compared to the hoRA, and conserves the three-time-level mean.
• We perform linear error analysis for general high-order Robert-Asselin (ghoRA) time filter applied to the leapfrog scheme, and derive the phase and amplitude errors for a pre-determined order of accuracy using the modified equation.

The fully implicit (backward) Euler method is one of the first method commonly implemented when extending a code for the steady state problem, and often the method of last resort for complex applications.
• We construct a time filter for the backward Euler method, which reduces the discrete curvature of the solution, increases accuracy from first to second-order, gives an immediate error estimator and induces an equivalent two-step, A-stable, linear multistep method.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Guzel, Ahmetahg13@pitt.eduahg13
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairTrenchea, Catalintrenchea@pitt.edutrenchea
Committee MemberLayton, Williamwjl@pitt.eduwjl
Committee MemberNeilan, Michaelneilan@pitt.eduneilan
Committee MemberSmolinski, Patrickpatsmol@pitt.edupatsmol
Date: 28 June 2018
Date Type: Publication
Defense Date: 20 March 2018
Approval Date: 28 June 2018
Submission Date: 9 February 2018
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Number of Pages: 76
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: A-stability, Backward Euler method, Leapfrog method, Modified equation, Robert-Asselin-Williams, Time filters.
Date Deposited: 28 Jun 2018 12:56
Last Modified: 28 Jun 2018 12:56

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