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Title: Components of nonlinear oscillation and optimal averaging for stiff PDEs
Author: Peddle, Adam
ISNI:       0000 0004 7226 1947
Awarding Body: University of Exeter
Current Institution: University of Exeter
Date of Award: 2018
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A novel solver which uses finite wave averaging to mitigate oscillatory stiffness is proposed and analysed. We have found that triad resonances contribute to the oscillatory stiffness of the problem and that they provide a natural way of understanding stability limits and the role averaging has on reducing stiffness. In particular, an explicit formulation of the nonlinearity gives rise to a stiffness regulator function which allows for analysis of the wave averaging. A practical application of such a solver is also presented. As this method provides large timesteps at comparable computational cost but with some additional error when compared to a full solution, it is a natural choice for the coarse solver in a Parareal-style parallel-in-time method.
Supervisor: Wingate, Beth ; Ashwin, Peter Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available