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An algebraic multigrid method for high order time-discretizations of the div-grad and the curl-curl equations

Boonen, Tim; Van lent, Jan; Vandewalle, Stefan

An algebraic multigrid method for high order time-discretizations of the div-grad and the curl-curl equations Thumbnail


Authors

Tim Boonen

Stefan Vandewalle



Abstract

We present an algebraic multigrid algorithm for fully coupled implicit Runge-Kutta and Boundary Value Method time-discretizations of the div-grad and curl-curl equations. The algorithm uses a blocksmoother and a multigrid hierarchy derived from the hierarchy built by any algebraic multigrid algorithm for the stationary version of the problem. By a theoretical analysis and numerical experiments, we show that the convergence is similar to or better than the convergence of the scalar algebraic multigrid algorithm on which it is based. The algorithm benefits from several possibilities for implementation optimization. This results in a computational complexity which, for a modest number of stages, scales almost linearly as a function of the number of variables. © 2008 IMACS.

Journal Article Type Article
Publication Date Mar 1, 2009
Deposit Date Dec 7, 2010
Publicly Available Date Nov 15, 2016
Journal Applied Numerical Mathematics
Print ISSN 0168-9274
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 59
Issue 3-4
Pages 507-521
DOI https://doi.org/10.1016/j.apnum.2008.03.004
Keywords algebraic multigrid, high order time-discretization
Public URL https://uwe-repository.worktribe.com/output/1014210
Publisher URL http://dx.doi.org/10.1016/j.apnum.2008.03.004
Additional Information Additional Information : Selected Papers from NUMDIFF-11
Contract Date Nov 15, 2016

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