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Multigrid software for industrial applications - From MG00 to SAMG

: Trottenberg, U.; Clees, T.


Hirschel, E.H.:
100 Volumes of 'Notes on numerical fluid mechanics' : 40 years of numerical fluid mechanics and aerodynamics in retrospect
Berlin: Springer, 2009 (Notes on numerical fluid mechanics and multidisciplinary design (NNFM) 100)
ISBN: 978-3-540-70804-9
ISBN: 978-3-540-70805-6
ISSN: 0179-9614
Aufsatz in Buch
Fraunhofer SCAI ()

In this article, we review the development of multigrid methods for partial differential equations over the last 30 years, illuminating, in particular, the software question. With respect to industrial software development, we will distinguish "optimal" multigrid, multigrid "acceleration" and "robust" multigrid. Surprisingly, not geometric multigrid but algebraic multigrid (AMG) finally brought the breakthrough. With the software package SAMG, which is based on block-type AMG, systems of partial differential equations can be treated efficiently also. Finally, we outline how SAMG is used for industrial applications.