Parallel-in-time multigrid for space–time finite element approximations of two-dimensional space-fractional diffusion equations
The paper investigates a non-intrusive parallel time integration with multigrid for space-fractional diffusion equations in two spatial dimensions, which is discretized by the space–time finite element method to propagate solutions. We develop a multigrid-reduction-in-time (MGRIT) algorithm with tim...
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| Veröffentlicht in: | Computers & mathematics with applications (1987) 2019-12, Vol.78 (11), p.3471-3484 |
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| container_issue | 11 |
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| container_title | Computers & mathematics with applications (1987) |
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| creator | Yue, Xiaoqiang Shu, Shi Xu, Xiaowen Bu, Weiping Pan, Kejia |
| description | The paper investigates a non-intrusive parallel time integration with multigrid for space-fractional diffusion equations in two spatial dimensions, which is discretized by the space–time finite element method to propagate solutions. We develop a multigrid-reduction-in-time (MGRIT) algorithm with time-dependent time-grid propagators and provide its two-level convergence theory under the assumptions of the stability and simultaneous diagonalizability on time-grid propagators. Numerical results show that the proposed method possesses the saturation error order, theoretical results of the two-level variant deliver good predictions for our model problems, and significant speedups of the MGRIT can be achieved when compared to the two-level variant with F-relaxation (an equivalent version of the parareal algorithm) and the sequential time-stepping approach. |
| doi_str_mv | 10.1016/j.camwa.2019.05.017 |
| format | Article |
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We develop a multigrid-reduction-in-time (MGRIT) algorithm with time-dependent time-grid propagators and provide its two-level convergence theory under the assumptions of the stability and simultaneous diagonalizability on time-grid propagators. Numerical results show that the proposed method possesses the saturation error order, theoretical results of the two-level variant deliver good predictions for our model problems, and significant speedups of the MGRIT can be achieved when compared to the two-level variant with F-relaxation (an equivalent version of the parareal algorithm) and the sequential time-stepping approach.</description><identifier>ISSN: 0898-1221</identifier><identifier>EISSN: 1873-7668</identifier><identifier>DOI: 10.1016/j.camwa.2019.05.017</identifier><language>eng</language><publisher>Oxford: Elsevier Ltd</publisher><subject>Algorithms ; Finite element method ; Parallel-in-time ; Parareal ; Reduction-based multigrid ; Space-fractional diffusion equations ; Space–time finite element ; Time dependence ; Time integration</subject><ispartof>Computers & mathematics with applications (1987), 2019-12, Vol.78 (11), p.3471-3484</ispartof><rights>2019 Elsevier Ltd</rights><rights>Copyright Elsevier BV Dec 1, 2019</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c376t-e88d5272d128b680b29232e244e451158daf1873154bdc93380cd3d2565a0b643</citedby><cites>FETCH-LOGICAL-c376t-e88d5272d128b680b29232e244e451158daf1873154bdc93380cd3d2565a0b643</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.camwa.2019.05.017$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995</link.rule.ids></links><search><creatorcontrib>Yue, Xiaoqiang</creatorcontrib><creatorcontrib>Shu, Shi</creatorcontrib><creatorcontrib>Xu, Xiaowen</creatorcontrib><creatorcontrib>Bu, Weiping</creatorcontrib><creatorcontrib>Pan, Kejia</creatorcontrib><title>Parallel-in-time multigrid for space–time finite element approximations of two-dimensional space-fractional diffusion equations</title><title>Computers & mathematics with applications (1987)</title><description>The paper investigates a non-intrusive parallel time integration with multigrid for space-fractional diffusion equations in two spatial dimensions, which is discretized by the space–time finite element method to propagate solutions. 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| ispartof | Computers & mathematics with applications (1987), 2019-12, Vol.78 (11), p.3471-3484 |
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| language | eng |
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| source | Elsevier ScienceDirect Journals Complete; EZB-FREE-00999 freely available EZB journals |
| subjects | Algorithms Finite element method Parallel-in-time Parareal Reduction-based multigrid Space-fractional diffusion equations Space–time finite element Time dependence Time integration |
| title | Parallel-in-time multigrid for space–time finite element approximations of two-dimensional space-fractional diffusion equations |
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