The dimension splitting reproducing kernel particle method for three‐dimensional potential problems
Summary In this paper, the dimension splitting reproducing kernel particle method (DSRKPM) for three‐dimensional (3D) potential problems is presented. In the DSRKPM, a 3D potential problem can be transformed into a series of two‐dimensional (2D) ones in the dimension splitting direction. The reprodu...
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| Veröffentlicht in: | International journal for numerical methods in engineering 2020-01, Vol.121 (1), p.146-164 |
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| container_title | International journal for numerical methods in engineering |
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| creator | Peng, P.P. Wu, Q. Cheng, Y.M. |
| description | Summary
In this paper, the dimension splitting reproducing kernel particle method (DSRKPM) for three‐dimensional (3D) potential problems is presented. In the DSRKPM, a 3D potential problem can be transformed into a series of two‐dimensional (2D) ones in the dimension splitting direction. The reproducing kernel particle method (RKPM) is used to solve each 2D problem, the essential boundary conditions are imposed by penalty method, and the discretized equation is obtained from Galerkin weak form of potential problems. Finite difference method is used in the dimension splitting direction. Then, by combining a series of the equations of the RKPM for solving 2D problems, the final equation of the DSRKPM for 3D potential problems is obtained. Five example problems on regular or irregular domains are selected to show that the DSRKPM has higher computational efficiency than the RKPM and the improved element‐free Galerkin method for 3D potential problems. |
| doi_str_mv | 10.1002/nme.6203 |
| format | Article |
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In this paper, the dimension splitting reproducing kernel particle method (DSRKPM) for three‐dimensional (3D) potential problems is presented. In the DSRKPM, a 3D potential problem can be transformed into a series of two‐dimensional (2D) ones in the dimension splitting direction. The reproducing kernel particle method (RKPM) is used to solve each 2D problem, the essential boundary conditions are imposed by penalty method, and the discretized equation is obtained from Galerkin weak form of potential problems. Finite difference method is used in the dimension splitting direction. Then, by combining a series of the equations of the RKPM for solving 2D problems, the final equation of the DSRKPM for 3D potential problems is obtained. Five example problems on regular or irregular domains are selected to show that the DSRKPM has higher computational efficiency than the RKPM and the improved element‐free Galerkin method for 3D potential problems.</description><identifier>ISSN: 0029-5981</identifier><identifier>EISSN: 1097-0207</identifier><identifier>DOI: 10.1002/nme.6203</identifier><language>eng</language><publisher>Bognor Regis: Wiley Subscription Services, Inc</publisher><subject>Boundary conditions ; dimension splitting method ; dimension splitting reproducing kernel particle method ; Domains ; Finite difference method ; Galerkin method ; Kernels ; potential problem ; reproducing kernel particle method ; Splitting</subject><ispartof>International journal for numerical methods in engineering, 2020-01, Vol.121 (1), p.146-164</ispartof><rights>2019 John Wiley & Sons, Ltd.</rights><rights>2020 John Wiley & Sons, Ltd.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c2933-1ff16b1fe6e850ad88741c439e527edac380f485bcb6a9c1625486d654ef66573</citedby><cites>FETCH-LOGICAL-c2933-1ff16b1fe6e850ad88741c439e527edac380f485bcb6a9c1625486d654ef66573</cites><orcidid>0000-0002-0967-4111</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fnme.6203$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fnme.6203$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,780,784,1417,27923,27924,45573,45574</link.rule.ids></links><search><creatorcontrib>Peng, P.P.</creatorcontrib><creatorcontrib>Wu, Q.</creatorcontrib><creatorcontrib>Cheng, Y.M.</creatorcontrib><title>The dimension splitting reproducing kernel particle method for three‐dimensional potential problems</title><title>International journal for numerical methods in engineering</title><description>Summary
In this paper, the dimension splitting reproducing kernel particle method (DSRKPM) for three‐dimensional (3D) potential problems is presented. In the DSRKPM, a 3D potential problem can be transformed into a series of two‐dimensional (2D) ones in the dimension splitting direction. The reproducing kernel particle method (RKPM) is used to solve each 2D problem, the essential boundary conditions are imposed by penalty method, and the discretized equation is obtained from Galerkin weak form of potential problems. Finite difference method is used in the dimension splitting direction. Then, by combining a series of the equations of the RKPM for solving 2D problems, the final equation of the DSRKPM for 3D potential problems is obtained. Five example problems on regular or irregular domains are selected to show that the DSRKPM has higher computational efficiency than the RKPM and the improved element‐free Galerkin method for 3D potential problems.</description><subject>Boundary conditions</subject><subject>dimension splitting method</subject><subject>dimension splitting reproducing kernel particle method</subject><subject>Domains</subject><subject>Finite difference method</subject><subject>Galerkin method</subject><subject>Kernels</subject><subject>potential problem</subject><subject>reproducing kernel particle method</subject><subject>Splitting</subject><issn>0029-5981</issn><issn>1097-0207</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp1kMtOwzAQRS0EEqUg8QmR2LBJ8SN2nCWqykMqsClrK3HG1CWJg-0Kdccn8I18CQlF7FjNlebozuggdE7wjGBMr7oWZoJidoAmBBd5iinOD9FkWBUpLyQ5RichbDAmhGM2QbBaQ1LbFrpgXZeEvrEx2u4l8dB7V2_1mF_Bd9Akfemj1Q0kLcS1qxPjfBLXHuDr4_Ovohw4F6GLdkzeVQ204RQdmbIJcPY7p-j5ZrGa36XLp9v7-fUy1bRgLCXGEFERAwIkx2UtZZ4RnbECOM2hLjWT2GSSV7oSZaGJoDyTohY8AyMEz9kUXex7h8NvWwhRbdzWDz8FRRmlXBJO-UBd7intXQgejOq9bUu_UwSrUaIaJKpR4oCme_TdNrD7l1OPD4sf_hvpBXV0</recordid><startdate>20200115</startdate><enddate>20200115</enddate><creator>Peng, P.P.</creator><creator>Wu, Q.</creator><creator>Cheng, Y.M.</creator><general>Wiley Subscription Services, Inc</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><orcidid>https://orcid.org/0000-0002-0967-4111</orcidid></search><sort><creationdate>20200115</creationdate><title>The dimension splitting reproducing kernel particle method for three‐dimensional potential problems</title><author>Peng, P.P. ; Wu, Q. ; Cheng, Y.M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2933-1ff16b1fe6e850ad88741c439e527edac380f485bcb6a9c1625486d654ef66573</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Boundary conditions</topic><topic>dimension splitting method</topic><topic>dimension splitting reproducing kernel particle method</topic><topic>Domains</topic><topic>Finite difference method</topic><topic>Galerkin method</topic><topic>Kernels</topic><topic>potential problem</topic><topic>reproducing kernel particle method</topic><topic>Splitting</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Peng, P.P.</creatorcontrib><creatorcontrib>Wu, Q.</creatorcontrib><creatorcontrib>Cheng, Y.M.</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>International journal for numerical methods in engineering</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Peng, P.P.</au><au>Wu, Q.</au><au>Cheng, Y.M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The dimension splitting reproducing kernel particle method for three‐dimensional potential problems</atitle><jtitle>International journal for numerical methods in engineering</jtitle><date>2020-01-15</date><risdate>2020</risdate><volume>121</volume><issue>1</issue><spage>146</spage><epage>164</epage><pages>146-164</pages><issn>0029-5981</issn><eissn>1097-0207</eissn><abstract>Summary
In this paper, the dimension splitting reproducing kernel particle method (DSRKPM) for three‐dimensional (3D) potential problems is presented. In the DSRKPM, a 3D potential problem can be transformed into a series of two‐dimensional (2D) ones in the dimension splitting direction. The reproducing kernel particle method (RKPM) is used to solve each 2D problem, the essential boundary conditions are imposed by penalty method, and the discretized equation is obtained from Galerkin weak form of potential problems. Finite difference method is used in the dimension splitting direction. Then, by combining a series of the equations of the RKPM for solving 2D problems, the final equation of the DSRKPM for 3D potential problems is obtained. Five example problems on regular or irregular domains are selected to show that the DSRKPM has higher computational efficiency than the RKPM and the improved element‐free Galerkin method for 3D potential problems.</abstract><cop>Bognor Regis</cop><pub>Wiley Subscription Services, Inc</pub><doi>10.1002/nme.6203</doi><tpages>19</tpages><orcidid>https://orcid.org/0000-0002-0967-4111</orcidid></addata></record> |
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| subjects | Boundary conditions dimension splitting method dimension splitting reproducing kernel particle method Domains Finite difference method Galerkin method Kernels potential problem reproducing kernel particle method Splitting |
| title | The dimension splitting reproducing kernel particle method for three‐dimensional potential problems |
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