Diagonalization Based Parallel-in-Time Method for a Class of Fourth Order Time Dependent PDEs
In this paper, we design, analyze and implement efficient time parallel method for a class of fourth order time-dependent partial differential equations (PDEs), namely biharmonic heat equation, linearized Cahn-Hilliard (CH) equation and the nonlinear CH equation. We use diagonalization technique on...
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| creator | Garai, Gobinda Mandal, Bankim C |
| description | In this paper, we design, analyze and implement efficient time parallel
method for a class of fourth order time-dependent partial differential
equations (PDEs), namely biharmonic heat equation, linearized Cahn-Hilliard
(CH) equation and the nonlinear CH equation. We use diagonalization technique
on all-at-once system to develop efficient iterative time parallel methods for
investigating the solution behaviour of said equations. We present the
convergence analysis of Parallel-in-Time (PinT) algorithms. We verify our
findings by presenting numerical results. |
| doi_str_mv | 10.48550/arxiv.2304.14021 |
| format | Article |
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method for a class of fourth order time-dependent partial differential
equations (PDEs), namely biharmonic heat equation, linearized Cahn-Hilliard
(CH) equation and the nonlinear CH equation. We use diagonalization technique
on all-at-once system to develop efficient iterative time parallel methods for
investigating the solution behaviour of said equations. We present the
convergence analysis of Parallel-in-Time (PinT) algorithms. We verify our
findings by presenting numerical results.</description><identifier>DOI: 10.48550/arxiv.2304.14021</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/2304.14021$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2304.14021$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Garai, Gobinda</creatorcontrib><creatorcontrib>Mandal, Bankim C</creatorcontrib><title>Diagonalization Based Parallel-in-Time Method for a Class of Fourth Order Time Dependent PDEs</title><description>In this paper, we design, analyze and implement efficient time parallel
method for a class of fourth order time-dependent partial differential
equations (PDEs), namely biharmonic heat equation, linearized Cahn-Hilliard
(CH) equation and the nonlinear CH equation. We use diagonalization technique
on all-at-once system to develop efficient iterative time parallel methods for
investigating the solution behaviour of said equations. We present the
convergence analysis of Parallel-in-Time (PinT) algorithms. We verify our
findings by presenting numerical results.</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>eNotz8FOwzAQBFBfOKDCB3DCP5Bgx07iHEvSAlJRK9ErijbZdWvJjSsnIODrgcBpLqPRPMZupEi1yXNxB_HDvaeZEjqVWmTykr02Dg5hAO--YHJh4PcwEvIdRPCefOKGZO9OxJ9pOgbkNkQOvPYwjjxYvg5vcTrybUSKfO41dKYBaZj4rlmNV-zCgh_p-j8X7GW92tePyWb78FQvNwkUpUxs1lWdMT-3hIXKoJUIpLPSmKqQBrFUWKFFRUWvFPadEpDJ3pAEXem8UAt2-7c689pzdCeIn-0vs52Z6hu5zEzx</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>Diagonalization Based Parallel-in-Time Method for a Class of Fourth Order Time Dependent PDEs</title><author>Garai, Gobinda ; Mandal, Bankim C</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a671-f2b9b882300fa98df1dae427889618dd73d9dfd3e6c33dcb30a21c8e1a494563</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>Diagonalization Based Parallel-in-Time Method for a Class of Fourth Order Time Dependent PDEs</atitle><date>2023-04-27</date><risdate>2023</risdate><abstract>In this paper, we design, analyze and implement efficient time parallel
method for a class of fourth order time-dependent partial differential
equations (PDEs), namely biharmonic heat equation, linearized Cahn-Hilliard
(CH) equation and the nonlinear CH equation. We use diagonalization technique
on all-at-once system to develop efficient iterative time parallel methods for
investigating the solution behaviour of said equations. We present the
convergence analysis of Parallel-in-Time (PinT) algorithms. We verify our
findings by presenting numerical results.</abstract><doi>10.48550/arxiv.2304.14021</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Numerical Analysis Mathematics - Numerical Analysis |
| title | Diagonalization Based Parallel-in-Time Method for a Class of Fourth Order Time Dependent PDEs |
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