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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\u2010in\u2010time for elasticity have experienced difficulties, for example, the beating phenomenon. As a result, practical parallel\u2010in\u2010time 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\u2010relaxation) and, more importantly, a different formulation of the problem that is more amenable to parallel\u2010in\u2010time 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. The paper ends with supporting numerical results showing a practical algorithm enjoying speedup benefits over the sequential algorithm.<\/jats:p>","DOI":"10.1002\/nla.2155","type":"journal-article","created":{"date-parts":[[2018,2,14]],"date-time":"2018-02-14T09:42:53Z","timestamp":1518601373000},"source":"Crossref","is-referenced-by-count":22,"title":["Convergence of the multigrid reduction in time algorithm for the linear elasticity equations"],"prefix":"10.1002","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2681-5315","authenticated-orcid":false,"given":"A.","family":"Hessenthaler","sequence":"first","affiliation":[{"name":"Institute of Applied Mechanics (CE) University of Stuttgart  Pfaffenwaldring 7 Stuttgart 70569 Germany"}]},{"given":"D.","family":"Nordsletten","sequence":"additional","affiliation":[{"name":"Division of Imaging Sciences and Biomedical Engineering King's College London  4th Floor, Lambeth Wing, St.\u00a0Thomas Hospital, London SE1 7EH UK"}]},{"given":"O.","family":"R\u00f6hrle","sequence":"additional","affiliation":[{"name":"Institute of Applied Mechanics (CE) University of Stuttgart  Pfaffenwaldring 7 Stuttgart 70569 Germany"}]},{"given":"J. B.","family":"Schroder","sequence":"additional","affiliation":[{"name":"Center for Applied Scientific Computing Lawrence Livermore National Laboratory  P.O. Box 808, L-561 Livermore CA 94551 USA"}]},{"given":"R. D.","family":"Falgout","sequence":"additional","affiliation":[{"name":"Center for Applied Scientific Computing Lawrence Livermore National Laboratory  P.O. 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