3D multigrid on partially ordered sets of grids

P.W. Hemker, B. Koren, J. Noordmans

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureConferentiebijdrageAcademicpeer review

Samenvatting

In this paper we discuss different possibilities of using partially ordered sets of grids in multigrid algorithms. Because, for a classical sequence of regular grids the number of degrees of freedom grows much faster with the refinement level for 3D than for 2D, it is more difficult to find sufficiently effective relaxation procedures. Therefore, we study the possibility of using different families of (regular rectangular) grids. Semi-coarsening is one technique in which a partially ordered set of grids is used. In this case still a unique discrete fine-grid problem is solved. On the other hand, sparse grid techniques are more efficient if we compare the accuracy obtained with the number of degrees of freedom used. However, in the latter case it is not always straightforward to identify an appropriate discrete equation that should be solved. The different approaches are compared. The relation between the different approaches is described by looking at hierarchical bases and by considering fulI approximation (FAS). We show that, by lack of a semi-orthogonality property, the 3D situation is essentially more difficult than the 2D case. We also describe different multigrid strategies. Numerical results are given for a transonic Euler-flow over the ONERA M6-wing.
Originele taal-2Engels
TitelMultigrid Methods V (Proceedings of the Fifth European Multigrid Conference, Stuttgart, Germany, October 1-4, 1996)
RedacteurenW. Hackbusch, G. Wittum
Plaats van productieBerlin
UitgeverijSpringer
Pagina's107-124
StatusGepubliceerd - 1998

Publicatie series

NaamLecture Notes in Computational Science and Engineering
Volume3
ISSN van geprinte versie1439-7358

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  • Citeer dit

    Hemker, P. W., Koren, B., & Noordmans, J. (1998). 3D multigrid on partially ordered sets of grids. In W. Hackbusch, & G. Wittum (editors), Multigrid Methods V (Proceedings of the Fifth European Multigrid Conference, Stuttgart, Germany, October 1-4, 1996) (blz. 107-124). (Lecture Notes in Computational Science and Engineering; Vol. 3). Springer.