Convergence of the multigrid reduction in time algorithm for the linear elasticity equations

Hessenthaler, A.; Nordsletten, D.; Röhrle, O.; Schroder, J. B.; Falgout, R. D.

doi:10.1002/nla.2155

Convergence of the multigrid reduction in time algorithm for the linear elasticity equations

Journal Article · Tue Feb 13 23:00:00 EST 2018 · Numerical Linear Algebra with Applications

DOI:https://doi.org/10.1002/nla.2155· OSTI ID:1734614

^[1]; Nordsletten, D. ^[2]; Röhrle, O. ^[1]; Schroder, J. B. ^[3]; Falgout, R. D. ^[3]

Univ. of Stuttgart (Germany)
King's College London (United Kingdom)
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing

This paper presents some recent advances for parallel-in-time methods applied to linear elasticity. With recent computer architecture changes leading to stagnant clock speeds, but ever increasing numbers of cores, future speedups will be available through increased concurrency. Thus, sequential algorithms, such as time stepping, will suffer a bottleneck. This paper explores multigrid reduction in time (MGRIT) for an important application area, linear elasticity. Previously, efforts at parallel-in-time for elasticity have experienced difficulties, for example, the beating phenomenon. As a result, practical parallel-in-time algorithms for this application area currently do not exist. This paper proposes some solutions made possible by MGRIT (e.g., slow temporal coarsening and FCF-relaxation) and, more importantly, a different formulation of the problem that is more amenable to parallel-in-time methods. Using a recently developed convergence theory for MGRIT and Parareal, we show that the changed formulation of the problem avoids the instability issues and allows the reduction of the error using two temporal grids. We then extend our approach to the multilevel case, where we demonstrate how slow temporal coarsening improves convergence. Finally, the paper ends with supporting numerical results showing a practical algorithm enjoying speedup benefits over the sequential algorithm.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); European Research Council (ERC); Engineering and Physical Sciences Research Council

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1734614

Report Number(s):: LLNL-JRNL--731168; 882287

Journal Information:: Numerical Linear Algebra with Applications, Journal Name: Numerical Linear Algebra with Applications Journal Issue: 3 Vol. 25; ISSN 1070-5325

Publisher:: WileyCopyright Statement

Country of Publication:: United States

Language:: English

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97 MATHEMATICS AND COMPUTING
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Convergence of the multigrid reduction in time algorithm for the linear elasticity equations

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