Parallel domain decomposition schemes based on finite volume element discretization for nonsteady-state diffusion equations on distorted meshes
In this paper, several domain decomposition algorithms are considered to solve parallelly non-steady diffusion equations. The contributions of this work are threefold. The first one is that we present effective parallel domain decomposition schemes underlying the classical and monotone finite volume...
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Veröffentlicht in: | Computers & mathematics with applications (1987) 2022-04, Vol.112, p.97-115 |
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description | In this paper, several domain decomposition algorithms are considered to solve parallelly non-steady diffusion equations. The contributions of this work are threefold. The first one is that we present effective parallel domain decomposition schemes underlying the classical and monotone finite volume element discretization. These schemes adopt a three-stage technique, which is also used in the difference method and the finite volume method. Positivity of the parallel scheme based on monotone finite volume element method is proved. The second one is that we propose a new domain decomposition computational strategy to improve the correction step in prediction-correction frame such that the whole parallel process is simplified. The third one is that we consider a parallel algorithm build on quadratic finite volume element method, which preserves local conservation and has higher convergence rates. These parallel schemes are of intrinsic parallelism since we apply the prediction-correction technique to the interface of subdomains coming from an artificial division of computational domain or multi-medium physical domain. The proposed parallel schemes need only local communication among neighboring processors. Numerical results are presented to illuminate the accuracy, stability and parallelism of the parallel schemes. |
doi_str_mv | 10.1016/j.camwa.2022.02.021 |
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The contributions of this work are threefold. The first one is that we present effective parallel domain decomposition schemes underlying the classical and monotone finite volume element discretization. These schemes adopt a three-stage technique, which is also used in the difference method and the finite volume method. Positivity of the parallel scheme based on monotone finite volume element method is proved. The second one is that we propose a new domain decomposition computational strategy to improve the correction step in prediction-correction frame such that the whole parallel process is simplified. The third one is that we consider a parallel algorithm build on quadratic finite volume element method, which preserves local conservation and has higher convergence rates. These parallel schemes are of intrinsic parallelism since we apply the prediction-correction technique to the interface of subdomains coming from an artificial division of computational domain or multi-medium physical domain. The proposed parallel schemes need only local communication among neighboring processors. Numerical results are presented to illuminate the accuracy, stability and parallelism of the parallel schemes.</description><identifier>ISSN: 0898-1221</identifier><identifier>EISSN: 1873-7668</identifier><identifier>DOI: 10.1016/j.camwa.2022.02.021</identifier><language>eng</language><publisher>Oxford: Elsevier Ltd</publisher><subject>Algorithms ; Decomposition ; Discretization ; Domain decomposition method ; Domain decomposition methods ; Finite volume element method ; Finite volume method ; Mathematical analysis ; Monotone scheme ; Parallel processing</subject><ispartof>Computers & mathematics with applications (1987), 2022-04, Vol.112, p.97-115</ispartof><rights>2022 Elsevier Ltd</rights><rights>Copyright Elsevier BV Apr 15, 2022</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c331t-59610d968d6bcbb8c292d2a5c1a326cf63d1cb8c542a87586e44f177bf25deca3</citedby><cites>FETCH-LOGICAL-c331t-59610d968d6bcbb8c292d2a5c1a326cf63d1cb8c542a87586e44f177bf25deca3</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.2022.02.021$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3548,27922,27923,45993</link.rule.ids></links><search><creatorcontrib>Wu, Dan</creatorcontrib><creatorcontrib>Lv, Junliang</creatorcontrib><creatorcontrib>Qian, Hao</creatorcontrib><title>Parallel domain decomposition schemes based on finite volume element discretization for nonsteady-state diffusion equations on distorted meshes</title><title>Computers & mathematics with applications (1987)</title><description>In this paper, several domain decomposition algorithms are considered to solve parallelly non-steady diffusion equations. The contributions of this work are threefold. The first one is that we present effective parallel domain decomposition schemes underlying the classical and monotone finite volume element discretization. These schemes adopt a three-stage technique, which is also used in the difference method and the finite volume method. Positivity of the parallel scheme based on monotone finite volume element method is proved. The second one is that we propose a new domain decomposition computational strategy to improve the correction step in prediction-correction frame such that the whole parallel process is simplified. The third one is that we consider a parallel algorithm build on quadratic finite volume element method, which preserves local conservation and has higher convergence rates. These parallel schemes are of intrinsic parallelism since we apply the prediction-correction technique to the interface of subdomains coming from an artificial division of computational domain or multi-medium physical domain. The proposed parallel schemes need only local communication among neighboring processors. Numerical results are presented to illuminate the accuracy, stability and parallelism of the parallel schemes.</description><subject>Algorithms</subject><subject>Decomposition</subject><subject>Discretization</subject><subject>Domain decomposition method</subject><subject>Domain decomposition methods</subject><subject>Finite volume element method</subject><subject>Finite volume method</subject><subject>Mathematical analysis</subject><subject>Monotone scheme</subject><subject>Parallel processing</subject><issn>0898-1221</issn><issn>1873-7668</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp9kM1q3TAQhUVIITc_T5CNoGvf6seW7UUWJbRpIZAskrWQpRHRxbZuNHJK-hJ95cj3dh0YGJg53xnmEHLN2ZYzrr7tttZMf8xWMCG2bC1-Qja8a2XVKtWdkg3r-q7iQvAzco64Y4zVUrAN-fdokhlHGKmLkwkzdWDjtI8YcogzRfsCEyAdDIKjZeDDHDLQtzguE1AYy3bO1AW0CXL4aw6Uj4nOccYMxr1XmE0hXPB-wXULr8tBhqtfIXNMuZiXMy-Al-SLNyPC1f9-QZ5__ni6_VXdP9z9vv1-X1kpea6aXnHmetU5Ndhh6KzohROmsdxIoaxX0nFbxk0tTNc2nYK69rxtBy-a8qGRF-Tr0Xef4usCmPUuLmkuJ7VQTS170beiqORRZVNETOD1PoXJpHfNmV6T1zt9SF6vyWu2Fi_UzZGC8sBbgKTRBpgtuJDAZu1i-JT_AF9kkeU</recordid><startdate>20220415</startdate><enddate>20220415</enddate><creator>Wu, Dan</creator><creator>Lv, Junliang</creator><creator>Qian, Hao</creator><general>Elsevier Ltd</general><general>Elsevier BV</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20220415</creationdate><title>Parallel domain decomposition schemes based on finite volume element discretization for nonsteady-state diffusion equations on distorted meshes</title><author>Wu, Dan ; Lv, Junliang ; Qian, Hao</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c331t-59610d968d6bcbb8c292d2a5c1a326cf63d1cb8c542a87586e44f177bf25deca3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Algorithms</topic><topic>Decomposition</topic><topic>Discretization</topic><topic>Domain decomposition method</topic><topic>Domain decomposition methods</topic><topic>Finite volume element method</topic><topic>Finite volume method</topic><topic>Mathematical analysis</topic><topic>Monotone scheme</topic><topic>Parallel processing</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wu, Dan</creatorcontrib><creatorcontrib>Lv, Junliang</creatorcontrib><creatorcontrib>Qian, Hao</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Computers & mathematics with applications (1987)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Wu, Dan</au><au>Lv, Junliang</au><au>Qian, Hao</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Parallel domain decomposition schemes based on finite volume element discretization for nonsteady-state diffusion equations on distorted meshes</atitle><jtitle>Computers & mathematics with applications (1987)</jtitle><date>2022-04-15</date><risdate>2022</risdate><volume>112</volume><spage>97</spage><epage>115</epage><pages>97-115</pages><issn>0898-1221</issn><eissn>1873-7668</eissn><abstract>In this paper, several domain decomposition algorithms are considered to solve parallelly non-steady diffusion equations. 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These parallel schemes are of intrinsic parallelism since we apply the prediction-correction technique to the interface of subdomains coming from an artificial division of computational domain or multi-medium physical domain. The proposed parallel schemes need only local communication among neighboring processors. Numerical results are presented to illuminate the accuracy, stability and parallelism of the parallel schemes.</abstract><cop>Oxford</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.camwa.2022.02.021</doi><tpages>19</tpages></addata></record> |
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subjects | Algorithms Decomposition Discretization Domain decomposition method Domain decomposition methods Finite volume element method Finite volume method Mathematical analysis Monotone scheme Parallel processing |
title | Parallel domain decomposition schemes based on finite volume element discretization for nonsteady-state diffusion equations on distorted meshes |
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