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Numerical boundary conditions for ODE
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis. (ANLA)
2000 (English)Report (Other academic)
Place, publisher, year, edition, pages
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2000-026
National Category
Computational Mathematics
URN: urn:nbn:se:uu:diva-78982OAI: oai:DiVA.org:uu-78982DiVA: diva2:106895
Available from: 2007-02-15 Created: 2007-02-15 Last updated: 2011-11-17Bibliographically approved
In thesis
1. Convergence Acceleration for Flow Problems
Open this publication in new window or tab >>Convergence Acceleration for Flow Problems
2001 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Convergence acceleration techniques for the iterative solution of system of equations arising in the discretisations of compressible flow problems governed by the steady state Euler or Navier-Stokes equations is considered. The system of PDE is discretised using a finite difference or finite volume method yielding a large sparse system of equations. A solution is computed by integrating the corresponding time dependent problem in time until steady state is reached.

A convergence acceleration technique based on semicirculant approximations is applied. For scalar model problems, it is proved that the preconditioned coefficient matrix has a bounded spectrum well separated from the origin. A very simple time marching scheme such as the forward Euler method can be used, and the time step is not limited by a CFL-type criterion. Instead, the time step can asymptotically be chosen as a constant, independent of the number of grid points and the Reynolds number. Numerical experiments show that grid and parameter independent convergence is achieved also in more complicated problem settings. A comparison with a multigrid method shows that the semicirculant convergence acceleration technique is more efficient in terms of arithmetic complexity.

Another convergence acceleration technique based on fundamental solutions is proposed. An algorithm based on Fourier technique is provided for the fast application. Scalar model problems are considered and a theory, where the preconditioner is represented as an integral operator is derived. Theory and numerical experiments show that for first order partial differential equations, grid independent convergence is achieved.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2001. 22 p.
Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1104-232X ; 598
Computational fluid dynamics, convergence acceleration, semicirculant preconditioning, fundamental solutions
National Category
Computational Mathematics
Research subject
Numerical Analysis
urn:nbn:se:uu:diva-576 (URN)91-554-4914-X (ISBN)
Public defence
2001-02-09, Room 2347, Polacksbacken, Uppsala University, Uppsala, 13:15 (English)
Available from: 2001-01-19 Created: 2001-01-19 Last updated: 2011-10-26Bibliographically approved

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Brandén, Henrik
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