Linear and Nonlinear Parareal Methods for the Cahn-Hilliard Equation
In this paper, we propose, analyze and implement efficient time parallel methods for the Cahn-Hilliard (CH) equation. It is of great importance to develop efficient numerical methods for the CH equation, given the range of applicability of the CH equation has. The CH equation generally needs to be s...
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| creator | Garai, Gobinda Mandal, Bankim C |
| description | In this paper, we propose, analyze and implement efficient time parallel
methods for the Cahn-Hilliard (CH) equation. It is of great importance to
develop efficient numerical methods for the CH equation, given the range of
applicability of the CH equation has. The CH equation generally needs to be
simulated for a very long time to get the solution of phase coarsening stage.
Therefore it is desirable to accelerate the computation using parallel method
in time. We present linear and nonlinear Parareal methods for the CH equation
depending on the choice of fine approximation. We illustrate our results by
numerical experiments. |
| doi_str_mv | 10.48550/arxiv.2304.14074 |
| format | Article |
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methods for the Cahn-Hilliard (CH) equation. It is of great importance to
develop efficient numerical methods for the CH equation, given the range of
applicability of the CH equation has. The CH equation generally needs to be
simulated for a very long time to get the solution of phase coarsening stage.
Therefore it is desirable to accelerate the computation using parallel method
in time. We present linear and nonlinear Parareal methods for the CH equation
depending on the choice of fine approximation. We illustrate our results by
numerical experiments.</description><identifier>DOI: 10.48550/arxiv.2304.14074</identifier><language>eng</language><subject>Computer Science - Numerical Analysis ; Mathematics - Numerical Analysis</subject><creationdate>2023-04</creationdate><rights>http://creativecommons.org/licenses/by/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2304.14074$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2304.14074$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Garai, Gobinda</creatorcontrib><creatorcontrib>Mandal, Bankim C</creatorcontrib><title>Linear and Nonlinear Parareal Methods for the Cahn-Hilliard Equation</title><description>In this paper, we propose, analyze and implement efficient time parallel
methods for the Cahn-Hilliard (CH) equation. It is of great importance to
develop efficient numerical methods for the CH equation, given the range of
applicability of the CH equation has. The CH equation generally needs to be
simulated for a very long time to get the solution of phase coarsening stage.
Therefore it is desirable to accelerate the computation using parallel method
in time. We present linear and nonlinear Parareal methods for the CH equation
depending on the choice of fine approximation. We illustrate our results by
numerical experiments.</description><subject>Computer Science - Numerical Analysis</subject><subject>Mathematics - Numerical Analysis</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotz81OwzAQBGBfOKDCA_SEXyDBP-s6HFEotFL4OfQebeNdxZJxwA0I3h5oOY1GI430CbHUqobGOXWN5St-1sYqqDUoD-firouZsEjMQT5NOZ3aCxYshEk-0jxO4SB5KnIeSbY45moTU4pYgly_f-Acp3whzhjTgS7_cyF29-tdu6m654dte9tVuPJQsWO8IUOo94zWAGpwqJvGuAGBB7_S4XdVgdCQZtgHRQ68ZR7AkPXBLsTV6fbI6N9KfMXy3f9x-iPH_gA-QUXJ</recordid><startdate>20230427</startdate><enddate>20230427</enddate><creator>Garai, Gobinda</creator><creator>Mandal, Bankim C</creator><scope>AKY</scope><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20230427</creationdate><title>Linear and Nonlinear Parareal Methods for the Cahn-Hilliard Equation</title><author>Garai, Gobinda ; Mandal, Bankim C</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a674-f5fa9e2ea1bfa324a145a18825ca4fc761de2e0dea2e1f4bd0e5473ffc42e37d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Computer Science - Numerical Analysis</topic><topic>Mathematics - Numerical Analysis</topic><toplevel>online_resources</toplevel><creatorcontrib>Garai, Gobinda</creatorcontrib><creatorcontrib>Mandal, Bankim C</creatorcontrib><collection>arXiv Computer Science</collection><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Garai, Gobinda</au><au>Mandal, Bankim C</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Linear and Nonlinear Parareal Methods for the Cahn-Hilliard Equation</atitle><date>2023-04-27</date><risdate>2023</risdate><abstract>In this paper, we propose, analyze and implement efficient time parallel
methods for the Cahn-Hilliard (CH) equation. It is of great importance to
develop efficient numerical methods for the CH equation, given the range of
applicability of the CH equation has. The CH equation generally needs to be
simulated for a very long time to get the solution of phase coarsening stage.
Therefore it is desirable to accelerate the computation using parallel method
in time. We present linear and nonlinear Parareal methods for the CH equation
depending on the choice of fine approximation. We illustrate our results by
numerical experiments.</abstract><doi>10.48550/arxiv.2304.14074</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Numerical Analysis Mathematics - Numerical Analysis |
| title | Linear and Nonlinear Parareal Methods for the Cahn-Hilliard Equation |
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