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Efficient Computation of Periodic Orbits in Space-Time Discretised Nonlinear Dynamical Systems

Greidanus, J.W. (2010) Efficient Computation of Periodic Orbits in Space-Time Discretised Nonlinear Dynamical Systems. Master's Thesis / Essay, Mathematics.

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Abstract

In many dynamical systems one can find periodic solutions, for example in ocean flow dynamics, where the seasonal cycle of the atmosphere imposes a periodic forcing. We can formulate these problems as a four dimensional nonlinear system in which time is included, in other words time stepping can be omitted. In order to solve these systems Newton’s method is used. In the execution of the Newton method we have to solve sparse large linear systems, which is done by GMRES. For an efficient solve with GMRES the use of a preconditioner is essential. In this report such a preconditioning technique is presented, the advantage of this technique is that it allows for easy parallelisation. In this thesis this technique is tested for 1-D shallow-water equations and the THCM ocean model and the performance is compared with existing approaches.

Item Type: Thesis (Master's Thesis / Essay)
Degree programme: Mathematics
Thesis type: Master's Thesis / Essay
Language: English
Date Deposited: 15 Feb 2018 07:44
Last Modified: 15 Feb 2018 07:44
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/9380

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