Adaptive linear second-order energy stable schemes for time-fractional Allen-Cahn equation with volume constraint
•A volume-preserving time-fractional Allen-Cahn model is developed.•Adaptive linear second-order energy stable schemes are developed.•The proposed adaptive time-stepping algorithms are appropriate for accurately resolv- ing the initial singularity of solution and for efficiently capturing the fast d...
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Veröffentlicht in: | Communications in nonlinear science & numerical simulation 2020-11, Vol.90, p.105366, Article 105366 |
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container_title | Communications in nonlinear science & numerical simulation |
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creator | Ji, Bingquan Liao, Hong-lin Gong, Yuezheng Zhang, Luming |
description | •A volume-preserving time-fractional Allen-Cahn model is developed.•Adaptive linear second-order energy stable schemes are developed.•The proposed adaptive time-stepping algorithms are appropriate for accurately resolv- ing the initial singularity of solution and for efficiently capturing the fast dynamics away initial time.
A time-fractional Allen-Cahn equation with volume constraint is first proposed by introducing a nonlocal time-dependent Lagrange multiplier. Adaptive linear second-order energy stable schemes are developed for the proposed model by combining invariant energy quadratization and scalar auxiliary variable approaches with the recent L1+ formula. The new developed methods are proved to be volume-preserving and unconditionally energy stable on arbitrary nonuniform time meshes. The accelerated algorithm and adaptive time strategy are employed in numerical implementation. Numerical results show that the proposed algorithms are computationally efficient in multi-scale simulations, and appropriate for accurately resolving the intrinsically initial singularity of solution and for efficiently capturing the fast dynamics away initial time. |
doi_str_mv | 10.1016/j.cnsns.2020.105366 |
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A time-fractional Allen-Cahn equation with volume constraint is first proposed by introducing a nonlocal time-dependent Lagrange multiplier. Adaptive linear second-order energy stable schemes are developed for the proposed model by combining invariant energy quadratization and scalar auxiliary variable approaches with the recent L1+ formula. The new developed methods are proved to be volume-preserving and unconditionally energy stable on arbitrary nonuniform time meshes. The accelerated algorithm and adaptive time strategy are employed in numerical implementation. Numerical results show that the proposed algorithms are computationally efficient in multi-scale simulations, and appropriate for accurately resolving the intrinsically initial singularity of solution and for efficiently capturing the fast dynamics away initial time.</description><identifier>ISSN: 1007-5704</identifier><identifier>EISSN: 1878-7274</identifier><identifier>DOI: 10.1016/j.cnsns.2020.105366</identifier><language>eng</language><publisher>Amsterdam: Elsevier B.V</publisher><subject>Adaptive algorithms ; Algorithms ; Invariant energy quadratization ; L1[formula omitted] Formula ; Lagrange multiplier ; Nonlinear equations ; Numerical analysis ; Scalar auxiliary variable ; Schrodinger equation ; Simulation ; Time dependence ; Time-fractional Aallen-Cahn equation with volume constraint ; Unconditional energy stable</subject><ispartof>Communications in nonlinear science & numerical simulation, 2020-11, Vol.90, p.105366, Article 105366</ispartof><rights>2020</rights><rights>Copyright Elsevier Science Ltd. Nov 2020</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c331t-7422aa88082fba458ae2e1386c30ce596c0cfb7be392e4b5bcb73e5463e6fb013</citedby><cites>FETCH-LOGICAL-c331t-7422aa88082fba458ae2e1386c30ce596c0cfb7be392e4b5bcb73e5463e6fb013</cites><orcidid>0000-0001-5626-8784 ; 0000-0003-0777-6832</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.cnsns.2020.105366$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995</link.rule.ids></links><search><creatorcontrib>Ji, Bingquan</creatorcontrib><creatorcontrib>Liao, Hong-lin</creatorcontrib><creatorcontrib>Gong, Yuezheng</creatorcontrib><creatorcontrib>Zhang, Luming</creatorcontrib><title>Adaptive linear second-order energy stable schemes for time-fractional Allen-Cahn equation with volume constraint</title><title>Communications in nonlinear science & numerical simulation</title><description>•A volume-preserving time-fractional Allen-Cahn model is developed.•Adaptive linear second-order energy stable schemes are developed.•The proposed adaptive time-stepping algorithms are appropriate for accurately resolv- ing the initial singularity of solution and for efficiently capturing the fast dynamics away initial time.
A time-fractional Allen-Cahn equation with volume constraint is first proposed by introducing a nonlocal time-dependent Lagrange multiplier. Adaptive linear second-order energy stable schemes are developed for the proposed model by combining invariant energy quadratization and scalar auxiliary variable approaches with the recent L1+ formula. The new developed methods are proved to be volume-preserving and unconditionally energy stable on arbitrary nonuniform time meshes. The accelerated algorithm and adaptive time strategy are employed in numerical implementation. Numerical results show that the proposed algorithms are computationally efficient in multi-scale simulations, and appropriate for accurately resolving the intrinsically initial singularity of solution and for efficiently capturing the fast dynamics away initial time.</description><subject>Adaptive algorithms</subject><subject>Algorithms</subject><subject>Invariant energy quadratization</subject><subject>L1[formula omitted] Formula</subject><subject>Lagrange multiplier</subject><subject>Nonlinear equations</subject><subject>Numerical analysis</subject><subject>Scalar auxiliary variable</subject><subject>Schrodinger equation</subject><subject>Simulation</subject><subject>Time dependence</subject><subject>Time-fractional Aallen-Cahn equation with volume constraint</subject><subject>Unconditional energy stable</subject><issn>1007-5704</issn><issn>1878-7274</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9kEtPwzAQhCMEEuXxC7hY4pziV-L0wKGqeEmVuMDZsp0NdZTYre0U9d-TEM6cdjWaGe1-WXZH8JJgUj60S-Oii0uK6aQUrCzPsgWpRJULKvj5uGMs8kJgfpldxdjiMbUq-CI7rGu1T_YIqLMOVEARjHd17kMNAYGD8HVCMSndAYpmBz1E1PiAku0hb4IyyXqnOrTuOnD5Ru0cgsOgJhV927RDR98NPaCxNKagrEs32UWjugi3f_M6-3x--ti85tv3l7fNepsbxkjKBadUqarCFW204kWlgAJhVWkYNlCsSoNNo4UGtqLAdaGNFgwKXjIoG40Ju87u59598IcBYpKtH8J4a5SUF0yMcMjkYrPLBB9jgEbug-1VOEmC5cRWtvKXrZzYypntmHqcUzA-cLQQZDQWnIHaBjBJ1t7-m_8BXgeFgQ</recordid><startdate>202011</startdate><enddate>202011</enddate><creator>Ji, Bingquan</creator><creator>Liao, Hong-lin</creator><creator>Gong, Yuezheng</creator><creator>Zhang, Luming</creator><general>Elsevier B.V</general><general>Elsevier Science Ltd</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0001-5626-8784</orcidid><orcidid>https://orcid.org/0000-0003-0777-6832</orcidid></search><sort><creationdate>202011</creationdate><title>Adaptive linear second-order energy stable schemes for time-fractional Allen-Cahn equation with volume constraint</title><author>Ji, Bingquan ; Liao, Hong-lin ; Gong, Yuezheng ; Zhang, Luming</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c331t-7422aa88082fba458ae2e1386c30ce596c0cfb7be392e4b5bcb73e5463e6fb013</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Adaptive algorithms</topic><topic>Algorithms</topic><topic>Invariant energy quadratization</topic><topic>L1[formula omitted] Formula</topic><topic>Lagrange multiplier</topic><topic>Nonlinear equations</topic><topic>Numerical analysis</topic><topic>Scalar auxiliary variable</topic><topic>Schrodinger equation</topic><topic>Simulation</topic><topic>Time dependence</topic><topic>Time-fractional Aallen-Cahn equation with volume constraint</topic><topic>Unconditional energy stable</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ji, Bingquan</creatorcontrib><creatorcontrib>Liao, Hong-lin</creatorcontrib><creatorcontrib>Gong, Yuezheng</creatorcontrib><creatorcontrib>Zhang, Luming</creatorcontrib><collection>CrossRef</collection><jtitle>Communications in nonlinear science & numerical simulation</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ji, Bingquan</au><au>Liao, Hong-lin</au><au>Gong, Yuezheng</au><au>Zhang, Luming</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Adaptive linear second-order energy stable schemes for time-fractional Allen-Cahn equation with volume constraint</atitle><jtitle>Communications in nonlinear science & numerical simulation</jtitle><date>2020-11</date><risdate>2020</risdate><volume>90</volume><spage>105366</spage><pages>105366-</pages><artnum>105366</artnum><issn>1007-5704</issn><eissn>1878-7274</eissn><abstract>•A volume-preserving time-fractional Allen-Cahn model is developed.•Adaptive linear second-order energy stable schemes are developed.•The proposed adaptive time-stepping algorithms are appropriate for accurately resolv- ing the initial singularity of solution and for efficiently capturing the fast dynamics away initial time.
A time-fractional Allen-Cahn equation with volume constraint is first proposed by introducing a nonlocal time-dependent Lagrange multiplier. Adaptive linear second-order energy stable schemes are developed for the proposed model by combining invariant energy quadratization and scalar auxiliary variable approaches with the recent L1+ formula. The new developed methods are proved to be volume-preserving and unconditionally energy stable on arbitrary nonuniform time meshes. The accelerated algorithm and adaptive time strategy are employed in numerical implementation. Numerical results show that the proposed algorithms are computationally efficient in multi-scale simulations, and appropriate for accurately resolving the intrinsically initial singularity of solution and for efficiently capturing the fast dynamics away initial time.</abstract><cop>Amsterdam</cop><pub>Elsevier B.V</pub><doi>10.1016/j.cnsns.2020.105366</doi><orcidid>https://orcid.org/0000-0001-5626-8784</orcidid><orcidid>https://orcid.org/0000-0003-0777-6832</orcidid></addata></record> |
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subjects | Adaptive algorithms Algorithms Invariant energy quadratization L1[formula omitted] Formula Lagrange multiplier Nonlinear equations Numerical analysis Scalar auxiliary variable Schrodinger equation Simulation Time dependence Time-fractional Aallen-Cahn equation with volume constraint Unconditional energy stable |
title | Adaptive linear second-order energy stable schemes for time-fractional Allen-Cahn equation with volume constraint |
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