An Improved Finite Element Meshing Strategy for Dynamic Optimization Problems
The finite element orthogonal collocation method is widely used in the discretization of differential algebraic equations (DAEs), while the discrete strategy significantly affects the accuracy and efficiency of the results. In this work, a finite element meshing method with error estimation on nonco...
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| Veröffentlicht in: | Mathematical problems in engineering 2017-01, Vol.2017 (2017), p.1-10 |
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| creator | Hu, Junjie Wang, Haokun Zhang, Quannan Jiang, Aipeng Gong, Minliang Lin, Yinghui |
| description | The finite element orthogonal collocation method is widely used in the discretization of differential algebraic equations (DAEs), while the discrete strategy significantly affects the accuracy and efficiency of the results. In this work, a finite element meshing method with error estimation on noncollocation point is proposed and several cases were studied. Firstly, the simultaneous strategy based on the finite element is used to transform the differential and algebraic optimization problems (DAOPs) into large scale nonlinear programming problems. Then, the state variables of the reaction process are obtained by simulating with fixed control variables. The noncollocation points are introduced to compute the error estimates of the state variables at noncollocation points. Finally, in order to improve the computational accuracy with less finite element, moving finite element strategy was used for dynamically adjusting the length of finite element appropriately to satisfy the set margin of error. The proposed strategy is applied to two classical control problems and a large scale reverse osmosis seawater desalination process. Computing result shows that the proposed strategy can effectively reduce the computing effort with satisfied accuracy for dynamic optimization problems. |
| doi_str_mv | 10.1155/2017/4829195 |
| format | Article |
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In this work, a finite element meshing method with error estimation on noncollocation point is proposed and several cases were studied. Firstly, the simultaneous strategy based on the finite element is used to transform the differential and algebraic optimization problems (DAOPs) into large scale nonlinear programming problems. Then, the state variables of the reaction process are obtained by simulating with fixed control variables. The noncollocation points are introduced to compute the error estimates of the state variables at noncollocation points. Finally, in order to improve the computational accuracy with less finite element, moving finite element strategy was used for dynamically adjusting the length of finite element appropriately to satisfy the set margin of error. The proposed strategy is applied to two classical control problems and a large scale reverse osmosis seawater desalination process. Computing result shows that the proposed strategy can effectively reduce the computing effort with satisfied accuracy for dynamic optimization problems.</description><identifier>ISSN: 1024-123X</identifier><identifier>EISSN: 1563-5147</identifier><identifier>DOI: 10.1155/2017/4829195</identifier><language>eng</language><publisher>Cairo, Egypt: Hindawi Publishing Corporation</publisher><subject>Accuracy ; Algebra ; Algorithms ; Chemical engineering ; Chemical reactions ; Collocation ; Computation ; Computer simulation ; Desalination ; Differential equations ; Dynamic programming ; Economic models ; Finite element method ; Meshing ; Methods ; Nonlinear programming ; Optimization ; Reverse osmosis ; Seawater ; Strategy ; Variables</subject><ispartof>Mathematical problems in engineering, 2017-01, Vol.2017 (2017), p.1-10</ispartof><rights>Copyright © 2017 Minliang Gong et al.</rights><rights>Copyright © 2017 Minliang Gong et al.; This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c360t-a9241c405b4d06764c5c1788a1b6ab8d00ee565bd4972afd7425eaee929316583</citedby><cites>FETCH-LOGICAL-c360t-a9241c405b4d06764c5c1788a1b6ab8d00ee565bd4972afd7425eaee929316583</cites><orcidid>0000-0002-0152-5963</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><contributor>Ellahi, Rahmat</contributor><creatorcontrib>Hu, Junjie</creatorcontrib><creatorcontrib>Wang, Haokun</creatorcontrib><creatorcontrib>Zhang, Quannan</creatorcontrib><creatorcontrib>Jiang, Aipeng</creatorcontrib><creatorcontrib>Gong, Minliang</creatorcontrib><creatorcontrib>Lin, Yinghui</creatorcontrib><title>An Improved Finite Element Meshing Strategy for Dynamic Optimization Problems</title><title>Mathematical problems in engineering</title><description>The finite element orthogonal collocation method is widely used in the discretization of differential algebraic equations (DAEs), while the discrete strategy significantly affects the accuracy and efficiency of the results. In this work, a finite element meshing method with error estimation on noncollocation point is proposed and several cases were studied. Firstly, the simultaneous strategy based on the finite element is used to transform the differential and algebraic optimization problems (DAOPs) into large scale nonlinear programming problems. Then, the state variables of the reaction process are obtained by simulating with fixed control variables. The noncollocation points are introduced to compute the error estimates of the state variables at noncollocation points. Finally, in order to improve the computational accuracy with less finite element, moving finite element strategy was used for dynamically adjusting the length of finite element appropriately to satisfy the set margin of error. The proposed strategy is applied to two classical control problems and a large scale reverse osmosis seawater desalination process. Computing result shows that the proposed strategy can effectively reduce the computing effort with satisfied accuracy for dynamic optimization problems.</description><subject>Accuracy</subject><subject>Algebra</subject><subject>Algorithms</subject><subject>Chemical engineering</subject><subject>Chemical reactions</subject><subject>Collocation</subject><subject>Computation</subject><subject>Computer simulation</subject><subject>Desalination</subject><subject>Differential equations</subject><subject>Dynamic programming</subject><subject>Economic models</subject><subject>Finite element method</subject><subject>Meshing</subject><subject>Methods</subject><subject>Nonlinear programming</subject><subject>Optimization</subject><subject>Reverse osmosis</subject><subject>Seawater</subject><subject>Strategy</subject><subject>Variables</subject><issn>1024-123X</issn><issn>1563-5147</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><sourceid>RHX</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNqF0EtLAzEUBeAgCtbqzrUEXOpobh7zWJbaaqGlggruhszMnZrSmalJqtRfb0oLLl3dLL6c3BxCLoHdASh1zxkk9zLlGWTqiPRAxSJSIJPjcGZcRsDF-yk5c27JGAcFaY_MBi2dNGvbfWFFx6Y1HulohQ22ns7QfZh2QV-81R4XW1p3lj5sW92Yks7X3jTmR3vTtfTZdkW45M7JSa1XDi8Os0_exqPX4VM0nT9OhoNpVIqY-UhnXEIpmSpkxeIklqUqIUlTDUWsi7RiDFHFqqhklnBdV4nkCjVixjMBsUpFn1zvc8Pinxt0Pl92G9uGJ3MI2WkMQqigbveqtJ1zFut8bU2j7TYHlu8Ky3eF5YfCAr_Z8_DpSn-b__TVXmMwWOs_DRlTwMQvNW9zbQ</recordid><startdate>20170101</startdate><enddate>20170101</enddate><creator>Hu, Junjie</creator><creator>Wang, Haokun</creator><creator>Zhang, Quannan</creator><creator>Jiang, Aipeng</creator><creator>Gong, Minliang</creator><creator>Lin, Yinghui</creator><general>Hindawi Publishing Corporation</general><general>Hindawi</general><general>Hindawi Limited</general><scope>ADJCN</scope><scope>AHFXO</scope><scope>RHU</scope><scope>RHW</scope><scope>RHX</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>CWDGH</scope><scope>DWQXO</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>KR7</scope><scope>L6V</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><orcidid>https://orcid.org/0000-0002-0152-5963</orcidid></search><sort><creationdate>20170101</creationdate><title>An Improved Finite Element Meshing Strategy for Dynamic Optimization Problems</title><author>Hu, Junjie ; Wang, Haokun ; Zhang, Quannan ; Jiang, Aipeng ; Gong, Minliang ; Lin, Yinghui</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c360t-a9241c405b4d06764c5c1788a1b6ab8d00ee565bd4972afd7425eaee929316583</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Accuracy</topic><topic>Algebra</topic><topic>Algorithms</topic><topic>Chemical engineering</topic><topic>Chemical reactions</topic><topic>Collocation</topic><topic>Computation</topic><topic>Computer simulation</topic><topic>Desalination</topic><topic>Differential equations</topic><topic>Dynamic programming</topic><topic>Economic models</topic><topic>Finite element method</topic><topic>Meshing</topic><topic>Methods</topic><topic>Nonlinear programming</topic><topic>Optimization</topic><topic>Reverse osmosis</topic><topic>Seawater</topic><topic>Strategy</topic><topic>Variables</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hu, Junjie</creatorcontrib><creatorcontrib>Wang, Haokun</creatorcontrib><creatorcontrib>Zhang, Quannan</creatorcontrib><creatorcontrib>Jiang, Aipeng</creatorcontrib><creatorcontrib>Gong, Minliang</creatorcontrib><creatorcontrib>Lin, Yinghui</creatorcontrib><collection>الدوريات العلمية والإحصائية - e-Marefa Academic and Statistical Periodicals</collection><collection>معرفة - المحتوى العربي الأكاديمي المتكامل - e-Marefa Academic Complete</collection><collection>Hindawi Publishing Complete</collection><collection>Hindawi Publishing Subscription Journals</collection><collection>Hindawi Publishing Open Access</collection><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>Middle East & Africa Database</collection><collection>ProQuest Central Korea</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><jtitle>Mathematical problems in engineering</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hu, Junjie</au><au>Wang, Haokun</au><au>Zhang, Quannan</au><au>Jiang, Aipeng</au><au>Gong, Minliang</au><au>Lin, Yinghui</au><au>Ellahi, Rahmat</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An Improved Finite Element Meshing Strategy for Dynamic Optimization Problems</atitle><jtitle>Mathematical problems in engineering</jtitle><date>2017-01-01</date><risdate>2017</risdate><volume>2017</volume><issue>2017</issue><spage>1</spage><epage>10</epage><pages>1-10</pages><issn>1024-123X</issn><eissn>1563-5147</eissn><abstract>The finite element orthogonal collocation method is widely used in the discretization of differential algebraic equations (DAEs), while the discrete strategy significantly affects the accuracy and efficiency of the results. In this work, a finite element meshing method with error estimation on noncollocation point is proposed and several cases were studied. Firstly, the simultaneous strategy based on the finite element is used to transform the differential and algebraic optimization problems (DAOPs) into large scale nonlinear programming problems. Then, the state variables of the reaction process are obtained by simulating with fixed control variables. The noncollocation points are introduced to compute the error estimates of the state variables at noncollocation points. Finally, in order to improve the computational accuracy with less finite element, moving finite element strategy was used for dynamically adjusting the length of finite element appropriately to satisfy the set margin of error. The proposed strategy is applied to two classical control problems and a large scale reverse osmosis seawater desalination process. Computing result shows that the proposed strategy can effectively reduce the computing effort with satisfied accuracy for dynamic optimization problems.</abstract><cop>Cairo, Egypt</cop><pub>Hindawi Publishing Corporation</pub><doi>10.1155/2017/4829195</doi><tpages>10</tpages><orcidid>https://orcid.org/0000-0002-0152-5963</orcidid><oa>free_for_read</oa></addata></record> |
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| subjects | Accuracy Algebra Algorithms Chemical engineering Chemical reactions Collocation Computation Computer simulation Desalination Differential equations Dynamic programming Economic models Finite element method Meshing Methods Nonlinear programming Optimization Reverse osmosis Seawater Strategy Variables |
| title | An Improved Finite Element Meshing Strategy for Dynamic Optimization Problems |
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