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

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