A new robust multigrid method for 2D convection-diffusion problems

Abstract

Citation for published version (APA): Reusken, A. A. (1994). A new robust multigrid method for 2D convection-diffusion problems. (RANA : reports on applied and numerical analysis; Vol. 9404). Eindhoven: Eindhoven University of Technology. Document status and date:Published: 01/01/1994 Document Version:Publisher's PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication:• A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publicationGeneral rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal.If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement: www.tue.nl/taverne Take down policyIf you believe that this document breaches copyright please contact us at:openaccess@tue.nl providing details and we will investigate your claim. SummaryIn this paper we introduce a new multigrid approach for solving 2D convection-diffusion problems. As in the hierarchical basis multigrid method we use a transformed matrix with a relatively low generalized condition number. The transformation we use is not based on the nesting of the coarse and fine grid only, but uses more information from the matrix. After transforming back to the original matrix this results in a robust multigrid algorithm with matrix-dependent prolongations and restrictions.

A Multigrid Method Based on Incomplete Gaussian Elimination

“…A convection-diffusion equation is another example in which we have interesting problem parameters (convection/diffusion ratio, flow direction). In some recent work ( [10], [11], [12]) we studied multigrid methods based on Schur complement approximation. An important property of these methods is a strong robustness w.r.t.…”

Fourier analysis of a robust multigrid method for convection-diffusion equations

“…The Schur complement preconditioning is combined with a block Jacobi solver on the fine grid points which are not in the coarse grid. The resulting two-grid method, that is very similar to the methods discussed in [14,15], can be classified as a multiplicative Schwarz type of method. Let M be the iteration matrix of the two-grid method for the system Ax = b (discretization of (1.1)), SA the Schur complement of A and S the approximation of SAl we use.…”