Multigrid Methods on Parallel Computers: A Survey on Recent Developments

Abstract

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Multiple semi-coarsened multigrid method with application to large eddy simulation

“…One way to reduce these large storage and workunit-per-cycle (operator complexity) requirements is to increase the semi-coarsening factor. For an arbitrary semi-coarsening factor f, the total storage requirement M for 3D MSG multigrid is bounded as follows: (8) where N is the size of the ÿne grid problem. For f = 2, the result is 8N as mentioned previously.…”

“…The ÿrst is the combination of standard isotropic coarsening and alternating plane smoothing (e.g. isotropic coarsening followed by plane smoothing sweeps in the xy, xz, and then yz-directions) [8]. The second is a combination of semi-coarsening in a ÿxed direction with plane-smoothing in the perpendicular direction (e.g.…”

Scalability and Performance of Data-Parallel Pressure-Based Multigrid Methods for Viscous Flows

“…There have also been efforts to devise novel multilevel algorithms with more parallelism for SIMD computation [18,19,20]. These efforts and others have recently been reviewed [11, 35,58]. Most of these algorithms are still untested in the context of the incompressible Navier-Stokes equations.…”

“…The convergence rate characteristics of the presmethods and parallel computing, there has been much sure-correction multigrid method are investigated in a Re ϭ 5000 lid-driven cavity flow and a Re ϭ 300 symmetric backward-facing interest in developing and testing parallel multigrid prostep flow, using either a defect-correction scheme or a second-order grams, as summarized in Refs. [31,35,58]. A key issue, upwind scheme.…”

Portable Anwendungssoftware für Parallelrechner/ Portable Applications Software for Parallel Computers

“…Die hier und in [4,9,11,13,14,18] beschriebene Gitterzerlegung ist -trotz ähnlicher Prinzipienvon der Methode der Gebietsdekomposition (domain decomposition) [10,16] zu unterscheiden. Anders als bei jenem Lösungsverfahren wird bei der Gitterzerlegung der ursprüngliche sequentielle Algorithmus reproduziert.…”