TY - JOUR T1 - Towards Textbook Efficiency for Parallel Multigrid AU - Björn Gmeiner, Ulrich Rüde, Holger Stengel, Christian Waluga & Barbara Wohlmuth JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 22 EP - 46 PY - 2015 DA - 2015/08 SN - 8 DO - http://doi.org/10.4208/nmtma.2015.w10si UR - https://global-sci.org/intro/article_detail/nmtma/12398.html KW - AB -

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.