Multigrid with Matrix-dependent Transfer Operators for Convection-diffusion Problems

Reusken, Arnold

doi:10.1007/978-3-0348-8524-9_20

Cited by 22 publications

(20 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For convection diffusion equations discretized by the upwind type schemes, some forms of algebraic multigrid approaches have been shown to be efficient [4,17,20]. An ILU preconditioning technique has also been used to solve the sparse linear systems arising from discretized convection diffusion equations with the central difference, upwind difference, and the fourth-order compact schemes [35].…”

Section: Multigrid Methodsmentioning

confidence: 99%

High Accuracy Iterative Solution of Convection Diffusion Equation with Boundary Layers on Nonuniform Grids

Ge¹,

Jun²

2001

Journal of Computational Physics

View full text Add to dashboard Cite

Section: Multigrid Methodsmentioning

confidence: 99%

High Accuracy Iterative Solution of Convection Diffusion Equation with Boundary Layers on Nonuniform Grids

Ge¹,

Jun²

2001

Journal of Computational Physics

View full text Add to dashboard Cite

“…So if A is stable then A is stable too. A precise statement concerning this stability is given in [10]. From the results in Lemma 3.1 we then conclude that SA is a stable 9-point operator on the coarse grid 11H.…”

Section: A Two-grid Approach Based On Approximate Lu-factorizationmentioning

confidence: 70%

“…To avoid fill-in we replace All A 12 in SR by a suitable approximation All A 12 • This approximation is made using a so called lumping approach (also used in [10]). In this lumping method we use information about the underlying differential equation.…”

Section: A Two-grid Approach Based On Approximate Lu-factorizationmentioning

confidence: 99%

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

Reusken

1995

Notes on Numerical Fluid Mechanics (NNFM)

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…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.…”

Section: Introductionmentioning

confidence: 99%

“…Because A is a "discretization" of A it will be of the same type as A and its Schur complement SA will also be of the same type. One can prove (d. [14]) that if A is an M-matrix, then A and SA are M-matrices, too. So stability is preserved.…”

mentioning

confidence: 99%

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

Reusken

1995

Numerische Mathematik

Self Cite

View full text Add to dashboard Cite

Summary. We consider a two-grid method for solving 2D convection-diffusion problems. The coarse grid correction is based on approximation of the Schur complement. As a preconditioner of the Schur complement we use the exact Schur complement of modified fine grid equations. We assume constant coefficients and periodic boundary conditions and apply Fourier analysis. We prove an upper bound for the spectral radius of the two-grid iteration matrix that is smaller than one and independent of the mesh size, the convection/diffusion ratio and the flow direction; i.e. we have a (strong) robustness result. Numerical results illustrating the robustness of the corresponding multigrid W-cycle are given.Mathematics Subject Classification: 65N20, 65N30, 65N55.

show abstract

Multigrid with Matrix-dependent Transfer Operators for Convection-diffusion Problems

Cited by 22 publications

References 12 publications

High Accuracy Iterative Solution of Convection Diffusion Equation with Boundary Layers on Nonuniform Grids

High Accuracy Iterative Solution of Convection Diffusion Equation with Boundary Layers on Nonuniform Grids

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

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

Contact Info

Product

Resources

About