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Step-size control and corrector methods in numerical continuation of ocean circulation and fill-reducing orderings in multilevel ILU methods

Niet, A. de (2002) Step-size control and corrector methods in numerical continuation of ocean circulation and fill-reducing orderings in multilevel ILU methods. Master's Thesis / Essay, Mathematics.

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Abstract

The equations of the thermohaline ocean circulation model are complex and contain a large number of physical constants and parameters. For stability analysis of the equations a numerical continuation program is used, that is based on the predictor-corrector method. We examine several possible improvements of the continuation code. The standard corrector is the Newton method. However the Newton iterations are expensive due to the solution of a large linear system. We test the performance of several alternative correctors. The adaptive Shamanskii method, a combination of the Newton and Newton-chord method, appears to be the fastest corrector. We also develop a method in order to adapt the step size along the branch automatically. The implementation of adaptive Shamanskii and step size control in the continuation code causes a considerable speed up of about a factor 4. In the corrector iterations large sparse linear systems of saddle point type are to be solved. The solver in the present code is MRILU. We present some alternative solvers from literature for the saddle point equation and do some convergence analysis on them. Finally we examine the possibility of incorporation of fill-reducing ordering ideas in multilevel ILU methods. We are able to construct a useful ILU factorization based on a nested-dissection ordening. The preconditioner is compared with MRILU for the Poisson and Stokes equation.

Item Type: Thesis (Master's Thesis / Essay)
Degree programme: Mathematics
Thesis type: Master's Thesis / Essay
Language: English
Date Deposited: 15 Feb 2018 07:28
Last Modified: 15 Feb 2018 07:28
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/8441

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