Towards Textbook Efficiency for Parallel Multigrid. Issue 1 (3rd March 2015)

• Record Type: Journal Article
• Authors: Gmeiner, Björn; Rüde, Ulrich; Stengel, Holger; Waluga, Christian; Wohlmuth, Barbara
• Is Part Of: Numerical mathematics. Volume 8:Issue 1(2015)
• Page Start: 22
• Page End: 46
• Publication Date: 2015-03-03
• Subjects: 65N55, -- 68W10; Multigrid, -- parallel computing, -- textbook efficiency, -- finite element method; Numerical analysis -- Periodicals; Numerical analysis; Periodicals; 518.05
• DOI: 10.4208/nmtma.2015.w10si
• Languages: English
• ISSNs: 1004-8979

Abstract

Abstract : In this work, we extend Achi Brandt's notion of textbook multigrid efficiency (TME) to massively parallel algorithms. Using a finite element based geometric multigrid implementation, we recall the classical view on TME with experiments for scalar linear equations with constant and varying coefficients as well as linear systems with saddle-point structure. To extend the idea of TME to the parallel setting, we give a new characterization of a work unit (WU) in an architecture-aware fashion by taking into account performance modeling techniques. We illustrate our newly introduced parallel TME measure by large-scale computations, solving problems with up to 200 billion unknowns on a TOP-10 supercomputer.