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Mathematics of Computation

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Stochastic subspace correction methods and fault tolerance


Authors: Michael Griebel and Peter Oswald
Journal: Math. Comp.
MSC (2010): Primary 65F10, 65N22, 65N55, 65Y05, 68W20
DOI: https://doi.org/10.1090/mcom/3459
Published electronically: August 5, 2019
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Abstract: We present convergence results in expectation for stochastic subspace correction schemes and their accelerated versions to solve symmetric positive-definite variational problems, and discuss their potential for achieving fault tolerance in an unreliable compute network. We employ an overlapping domain decomposition algorithm for PDE discretizations to discuss the latter aspect.


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Additional Information

Michael Griebel
Affiliation: Institute for Numerical Simulation, Universität Bonn, Endenicher Allee 19b, 53115 Bonn, Germany; and Fraunhofer Institute for Algorithms and Scientific Computing (SCAI), Schloss Birlinghoven, 53754 Sankt Augustin, Germany, Corresponding author, tel.: +49-228-73-69829, fax: +49-228-73-69847
Email: griebel@ins.uni-bonn.de

Peter Oswald
Affiliation: Institute for Numerical Simulation, Universität Bonn, Endenicher Allee 19b, 53115 Bonn, Germany
Email: agp.oswald@gmail.com

DOI: https://doi.org/10.1090/mcom/3459
Keywords: Subspace correction, Schwarz iterative methods, randomization, convergence rates, fault tolerance
Received by editor(s): July 16, 2018
Received by editor(s) in revised form: March 8, 2019
Published electronically: August 5, 2019
Additional Notes: The first author acknowledges the support from the DFG priority program 1648 “Software for Exascale Computing” within the project “EXAHD - An Exa-Scalable Two-Level Sparse Grid Approach for Higher-Dimensional Problems in Plasma Physics and Beyond”.
The main results of this paper were obtained during a yearlong stay of the second author at the Institute for Numerical Simulation (INS) sponsored by the Hausdorff Center for Mathematics of the University of Bonn and funded by the Deutsche Forschungsgemeinschaft. He is grateful for this support.
Article copyright: © Copyright 2019 American Mathematical Society