On the evaluation of Poisson equation with dual interpolation boundary face method
This paper presents a new implementation of the dual reciprocity method (DRM) in connection with the dual interpolation boundary face method (DiBFM) for the Poisson equation. In DiBFM, the nodes of an element are categorized into two groups: (i) source nodes (ii) virtual nodes. First layer interpola...
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Veröffentlicht in: | European journal of mechanics, A, Solids A, Solids, 2021-07, Vol.88, p.104248, Article 104248 |
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creator | Khan, Suliman He, Rui Khan, Feroz Khan, M. Riaz Arshad, Muhammad Shah, Hasrat Hussain |
description | This paper presents a new implementation of the dual reciprocity method (DRM) in connection with the dual interpolation boundary face method (DiBFM) for the Poisson equation. In DiBFM, the nodes of an element are categorized into two groups: (i) source nodes (ii) virtual nodes. First layer interpolation is used to interpolate the physical variables, while boundary integrals are evaluated on the source nodes only. Moreover, moving least squares (MLS) interpolation is used and provides additional constraints equations to establish the relationship between source and virtual nodes. Additionally, augmented thin plate spline (ATPS) is used to better interpolate the non-homogeneous term. Finally, it is claimed that the proposed method is much superior to the DRM for Poisson type equation with different geometries, especially for complex geometry. Numerical examples are evaluated and compared with the DRM to ensure the superiority of the proposed method.
•A novel implementation of DRM for Poisson equation with dual interpolation boundary face method.•The integrand quantities are calculated from curves rather than from elements, which eliminate the geometric error.•Augmented thin plate spline is used to better interpolate the non-homogeneous term.•The proposed method is more accurate and efficient than the DRM, especially for problems with complex geometries. |
doi_str_mv | 10.1016/j.euromechsol.2021.104248 |
format | Article |
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•A novel implementation of DRM for Poisson equation with dual interpolation boundary face method.•The integrand quantities are calculated from curves rather than from elements, which eliminate the geometric error.•Augmented thin plate spline is used to better interpolate the non-homogeneous term.•The proposed method is more accurate and efficient than the DRM, especially for problems with complex geometries.</description><identifier>ISSN: 0997-7538</identifier><identifier>EISSN: 1873-7285</identifier><identifier>DOI: 10.1016/j.euromechsol.2021.104248</identifier><language>eng</language><publisher>Berlin: Elsevier Masson SAS</publisher><subject>Augmented thin plate spline ; Complex geometry ; Dual interpolation boundary face method ; Dual reciprocity method ; Interpolation ; Moving least squares interpolation ; Nodes ; Poisson equation ; Reciprocity ; Thin plates</subject><ispartof>European journal of mechanics, A, Solids, 2021-07, Vol.88, p.104248, Article 104248</ispartof><rights>2021 Elsevier Masson SAS</rights><rights>Copyright Elsevier BV Jul/Aug 2021</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c349t-e92bf8fb467f835e5a78799df0fb9d5f13e010c227810f7be5fa64b6dd028d5b3</citedby><cites>FETCH-LOGICAL-c349t-e92bf8fb467f835e5a78799df0fb9d5f13e010c227810f7be5fa64b6dd028d5b3</cites><orcidid>0000-0002-2230-6882 ; 0000-0002-8351-9021</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.euromechsol.2021.104248$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995</link.rule.ids></links><search><creatorcontrib>Khan, Suliman</creatorcontrib><creatorcontrib>He, Rui</creatorcontrib><creatorcontrib>Khan, Feroz</creatorcontrib><creatorcontrib>Khan, M. Riaz</creatorcontrib><creatorcontrib>Arshad, Muhammad</creatorcontrib><creatorcontrib>Shah, Hasrat Hussain</creatorcontrib><title>On the evaluation of Poisson equation with dual interpolation boundary face method</title><title>European journal of mechanics, A, Solids</title><description>This paper presents a new implementation of the dual reciprocity method (DRM) in connection with the dual interpolation boundary face method (DiBFM) for the Poisson equation. In DiBFM, the nodes of an element are categorized into two groups: (i) source nodes (ii) virtual nodes. First layer interpolation is used to interpolate the physical variables, while boundary integrals are evaluated on the source nodes only. Moreover, moving least squares (MLS) interpolation is used and provides additional constraints equations to establish the relationship between source and virtual nodes. Additionally, augmented thin plate spline (ATPS) is used to better interpolate the non-homogeneous term. Finally, it is claimed that the proposed method is much superior to the DRM for Poisson type equation with different geometries, especially for complex geometry. Numerical examples are evaluated and compared with the DRM to ensure the superiority of the proposed method.
•A novel implementation of DRM for Poisson equation with dual interpolation boundary face method.•The integrand quantities are calculated from curves rather than from elements, which eliminate the geometric error.•Augmented thin plate spline is used to better interpolate the non-homogeneous term.•The proposed method is more accurate and efficient than the DRM, especially for problems with complex geometries.</description><subject>Augmented thin plate spline</subject><subject>Complex geometry</subject><subject>Dual interpolation boundary face method</subject><subject>Dual reciprocity method</subject><subject>Interpolation</subject><subject>Moving least squares interpolation</subject><subject>Nodes</subject><subject>Poisson equation</subject><subject>Reciprocity</subject><subject>Thin plates</subject><issn>0997-7538</issn><issn>1873-7285</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNqNkEtLxDAUhYMoOI7-h4jrjknaNMlSBl8gjIiuQ9vc0JROM5OkI_57O3QWLl3dy-Gc-_gQuqVkRQkt77sVjMFvoWmj71eMMDrpBSvkGVpQKfJMMMnP0YIoJTLBc3mJrmLsCCFH7wJ9bAacWsBwqPqxSs4P2Fv87l2MUwv7k_btUovNWPXYDQnCzvezXvtxMFX4wbZqAG8htd5cowtb9RFuTnWJvp4eP9cv2dvm-XX98JY1eaFSBorVVtq6KIWVOQdeCSmUMpbYWhluaQ6EkoYxISmxogZuq7KoS2MIk4bX-RLdzXN3we9HiEl3fgzDtFIznjOq5JSdXGp2NcHHGMDqXXDb6WRNiT4i1J3-g1AfsegZ4ZRdz1mY3jg4CDo2DoYGjAvQJG28-8eUX7-tgYA</recordid><startdate>202107</startdate><enddate>202107</enddate><creator>Khan, Suliman</creator><creator>He, Rui</creator><creator>Khan, Feroz</creator><creator>Khan, M. Riaz</creator><creator>Arshad, Muhammad</creator><creator>Shah, Hasrat Hussain</creator><general>Elsevier Masson SAS</general><general>Elsevier BV</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SR</scope><scope>7TB</scope><scope>8BQ</scope><scope>8FD</scope><scope>FR3</scope><scope>JG9</scope><scope>KR7</scope><orcidid>https://orcid.org/0000-0002-2230-6882</orcidid><orcidid>https://orcid.org/0000-0002-8351-9021</orcidid></search><sort><creationdate>202107</creationdate><title>On the evaluation of Poisson equation with dual interpolation boundary face method</title><author>Khan, Suliman ; He, Rui ; Khan, Feroz ; Khan, M. 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Riaz</creatorcontrib><creatorcontrib>Arshad, Muhammad</creatorcontrib><creatorcontrib>Shah, Hasrat Hussain</creatorcontrib><collection>CrossRef</collection><collection>Engineered Materials Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>METADEX</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Materials Research Database</collection><collection>Civil Engineering Abstracts</collection><jtitle>European journal of mechanics, A, Solids</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Khan, Suliman</au><au>He, Rui</au><au>Khan, Feroz</au><au>Khan, M. Riaz</au><au>Arshad, Muhammad</au><au>Shah, Hasrat Hussain</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the evaluation of Poisson equation with dual interpolation boundary face method</atitle><jtitle>European journal of mechanics, A, Solids</jtitle><date>2021-07</date><risdate>2021</risdate><volume>88</volume><spage>104248</spage><pages>104248-</pages><artnum>104248</artnum><issn>0997-7538</issn><eissn>1873-7285</eissn><abstract>This paper presents a new implementation of the dual reciprocity method (DRM) in connection with the dual interpolation boundary face method (DiBFM) for the Poisson equation. In DiBFM, the nodes of an element are categorized into two groups: (i) source nodes (ii) virtual nodes. First layer interpolation is used to interpolate the physical variables, while boundary integrals are evaluated on the source nodes only. Moreover, moving least squares (MLS) interpolation is used and provides additional constraints equations to establish the relationship between source and virtual nodes. Additionally, augmented thin plate spline (ATPS) is used to better interpolate the non-homogeneous term. Finally, it is claimed that the proposed method is much superior to the DRM for Poisson type equation with different geometries, especially for complex geometry. Numerical examples are evaluated and compared with the DRM to ensure the superiority of the proposed method.
•A novel implementation of DRM for Poisson equation with dual interpolation boundary face method.•The integrand quantities are calculated from curves rather than from elements, which eliminate the geometric error.•Augmented thin plate spline is used to better interpolate the non-homogeneous term.•The proposed method is more accurate and efficient than the DRM, especially for problems with complex geometries.</abstract><cop>Berlin</cop><pub>Elsevier Masson SAS</pub><doi>10.1016/j.euromechsol.2021.104248</doi><orcidid>https://orcid.org/0000-0002-2230-6882</orcidid><orcidid>https://orcid.org/0000-0002-8351-9021</orcidid></addata></record> |
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subjects | Augmented thin plate spline Complex geometry Dual interpolation boundary face method Dual reciprocity method Interpolation Moving least squares interpolation Nodes Poisson equation Reciprocity Thin plates |
title | On the evaluation of Poisson equation with dual interpolation boundary face method |
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