Performance and Scalability of Hierarchical Hybrid Multigrid Solvers for Stokes Systems

Gmeiner B, Rüde U, Stengel H, Waluga C, Wohlmuth BI (2015)

Publication Language: English

Publication Type: Journal article, Original article

Publication year: 2015

Journal

SIAM Journal on Scientific Computing Society for Industrial and Applied Mathematics

Publisher: Society for Industrial and Applied Mathematics

Book Volume: 37

Pages Range: C143 - C 168

Journal Issue: 2

URI: http://epubs.siam.org/doi/pdf/10.1137/130941353

DOI: 10.1137/130941353

Open Access Link: http://epubs.siam.org/doi/pdf/10.1137/130941353

Abstract

In many applications involving incompressible fluid flow, the Stokes system plays an important role. Complex flow problems may require extremely fine resolutions, easily resulting in saddle-point problems with more than a trillion (1012) unknowns. Even on the most advanced supercomputers, the fast solution of such systems of equations is a highly nontrivial and challenging task. In this work we consider a realization of an iterative saddle-point solver which is based mathematically on the Schur-complement formulation of the pressure and algorithmically on the abstract concept of hierarchical hybrid grids. The design of our fast multigrid solver is guided by an innovative performance analysis for the computational kernels in combination with a quantification of the communication overhead. Excellent node performance and good scalability to almost a million parallel threads are demonstrated on different characteristic types of modern supercomputers.

Authors with CRIS profile

Björn Gmeiner Lehrstuhl für Informatik 10 (Systemsimulation) (LSS) Ulrich Rüde Lehrstuhl für Informatik 10 (Systemsimulation) (LSS)

Related research project(s)

TERRA-NEO - Integrated Co-Design of an Exascale Earth Mantle Modeling Framework (TERRA-NEO) SPP 1648: Software for Exascale Computing Oct. 12, 2005 - Sept. 30, 2019

Involved external institutions

Technische Universität München (TUM) DE Germany (DE)

How to cite

APA:

Gmeiner, B., Rüde, U., Stengel, H., Waluga, C., & Wohlmuth, B.I. (2015). Performance and Scalability of Hierarchical Hybrid Multigrid Solvers for Stokes Systems. SIAM Journal on Scientific Computing, 37(2), C143 - C 168. https://doi.org/10.1137/130941353

MLA:

Gmeiner, Björn, et al. "Performance and Scalability of Hierarchical Hybrid Multigrid Solvers for Stokes Systems." SIAM Journal on Scientific Computing 37.2 (2015): C143 - C 168.

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