Resilience for Massively Parallel Multigrid Solvers

Huber M, Gmeiner B, Rüde U, Wohlmuth BI (2016)

Publication Language: English

Publication Type: Journal article, Original article

Publication year: 2016

Journal

SIAM Journal on Scientific Computing Society for Industrial and Applied Mathematics

Publisher: Society for Industrial and Applied Mathematics

Book Volume: 38

Pages Range: 217-239

Journal Issue: 5

URI: http://epubs.siam.org/doi/pdf/10.1137/15M1026122

DOI: 10.1137/15M1026122

Open Access Link: http://epubs.siam.org/doi/pdf/10.1137/15M1026122

Abstract

Fault tolerant massively parallel multigrid methods for elliptic partial differential equations are a step towards resilient solvers. Here, we combine domain partitioning with geometric multigrid methods to obtain fast and fault-robust solvers for three-dimensional problems. The recovery strategy is based on the redundant storage of ghost values, as they are commonly used in distributed memory parallel programs. In the case of a fault, the redundant interface values can be easily recovered, while the lost inner unknowns are recomputed approximately with recovery algorithms using multigrid cycles for solving a local Dirichlet problem. Different strategies are compared and evaluated with respect to performance, computational cost, and speedup. Especially effective are asynchronous strategies combining global solves with accelerated local recovery. By this, multiple faults can be fully compensated with respect to both the number of iterations and run-time. For illustration, we use a state-of-the-art petascale supercomputer to study failure scenarios when solving systems with up to 6 · 1011 (0.6 trillion) unknowns.

Authors with CRIS profile

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

Involved external institutions

Technische Universität München (TUM) DE Germany (DE)

How to cite

APA:

Huber, M., Gmeiner, B., Rüde, U., & Wohlmuth, B.I. (2016). Resilience for Massively Parallel Multigrid Solvers. SIAM Journal on Scientific Computing, 38(5), 217-239. https://doi.org/10.1137/15M1026122

MLA:

Huber, Markus, et al. "Resilience for Massively Parallel Multigrid Solvers." SIAM Journal on Scientific Computing 38.5 (2016): 217-239.

BibTeX: Download