An alternative collocation boundary element method for static and dynamic problems
A collocation boundary element formulation is presented which is based on a mixed approximation formulation similar to the Galerkin boundary element method presented by Steinbach (SIAM J Numer Anal 38:401–413, 2000) for the solution of Laplace’s equation. The method is also applicable to vector prob...
Gespeichert in:
| Veröffentlicht in: | Computational mechanics 2009-07, Vol.44 (2), p.247-261 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 261 |
|---|---|
| container_issue | 2 |
| container_start_page | 247 |
| container_title | Computational mechanics |
| container_volume | 44 |
| creator | Rüberg, Thomas Schanz, Martin |
| description | A collocation boundary element formulation is presented which is based on a mixed approximation formulation similar to the Galerkin boundary element method presented by Steinbach (SIAM J Numer Anal 38:401–413, 2000) for the solution of Laplace’s equation. The method is also applicable to vector problems such as elasticity. Moreover, dynamic problems of acoustics and elastodynamics are included. The resulting system matrices have an ordered structure and small condition numbers in comparison to the standard collocation approach. Moreover, the employment of Robin boundary conditions is easily included in this formulation. Details on the numerical integration of the occurring regular and singular integrals and on the solution of the arising systems of equations are given. Numerical experiments have been carried out for different reference problems. In these experiments, the presented approach is compared to the common nodal collocation method with respect to accuracy, condition numbers, and stability in the dynamic case. |
| doi_str_mv | 10.1007/s00466-009-0369-4 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_35006668</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>35006668</sourcerecordid><originalsourceid>FETCH-LOGICAL-c347t-fbe7c2e1eb4328bd1d0b85474d8bbf5ec077003ed046c139bcef790930464a1e3</originalsourceid><addsrcrecordid>eNp1kE9LxDAQxYMouK5-AG8BwVt00qRNe1wW_8GCIHoOTTLVXdpkTbrCfnuzVBAETzMDvzcz7xFyyeGGA6jbBCCrigE0DETVMHlEZlyKgkFTyGMyA65qpipVnpKzlDYAvKxFOSMvC0_bfsTo23H9hdSGvg8298FTE3betXFPsccB_UgHHD-Co12INI2ZsbT1jrq9b4fcb2MwGUzn5KRr-4QXP3VO3u7vXpePbPX88LRcrJgVUo2sM6hsgRxNfrM2jjswdSmVdLUxXYkWlAIQ6LIxy0VjLHaqgUbkWbYcxZxcT3vz4c8dplEP62Sx71uPYZe0KAGqqqozePUH3IRdNtwnXRQVF5xLJTLFJ8rGkFLETm_jesj2NQd9yFhPGeucsT5krGXWFJMmZda_Y_zd_L_oG9WSf0M</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2261311473</pqid></control><display><type>article</type><title>An alternative collocation boundary element method for static and dynamic problems</title><source>Springer Nature - Complete Springer Journals</source><creator>Rüberg, Thomas ; Schanz, Martin</creator><creatorcontrib>Rüberg, Thomas ; Schanz, Martin</creatorcontrib><description>A collocation boundary element formulation is presented which is based on a mixed approximation formulation similar to the Galerkin boundary element method presented by Steinbach (SIAM J Numer Anal 38:401–413, 2000) for the solution of Laplace’s equation. The method is also applicable to vector problems such as elasticity. Moreover, dynamic problems of acoustics and elastodynamics are included. The resulting system matrices have an ordered structure and small condition numbers in comparison to the standard collocation approach. Moreover, the employment of Robin boundary conditions is easily included in this formulation. Details on the numerical integration of the occurring regular and singular integrals and on the solution of the arising systems of equations are given. Numerical experiments have been carried out for different reference problems. In these experiments, the presented approach is compared to the common nodal collocation method with respect to accuracy, condition numbers, and stability in the dynamic case.</description><identifier>ISSN: 0178-7675</identifier><identifier>EISSN: 1432-0924</identifier><identifier>DOI: 10.1007/s00466-009-0369-4</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer-Verlag</publisher><subject>Acoustics ; Boundary conditions ; Boundary element method ; Classical and Continuum Physics ; Collocation methods ; Computational Science and Engineering ; Dynamic stability ; Elasticity ; Elastodynamics ; Engineering ; Galerkin method ; Mathematical analysis ; Nonlinear programming ; Numerical integration ; Original Paper ; Theoretical and Applied Mechanics</subject><ispartof>Computational mechanics, 2009-07, Vol.44 (2), p.247-261</ispartof><rights>Springer-Verlag 2009</rights><rights>Computational Mechanics is a copyright of Springer, (2009). All Rights Reserved.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c347t-fbe7c2e1eb4328bd1d0b85474d8bbf5ec077003ed046c139bcef790930464a1e3</citedby><cites>FETCH-LOGICAL-c347t-fbe7c2e1eb4328bd1d0b85474d8bbf5ec077003ed046c139bcef790930464a1e3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00466-009-0369-4$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00466-009-0369-4$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>Rüberg, Thomas</creatorcontrib><creatorcontrib>Schanz, Martin</creatorcontrib><title>An alternative collocation boundary element method for static and dynamic problems</title><title>Computational mechanics</title><addtitle>Comput Mech</addtitle><description>A collocation boundary element formulation is presented which is based on a mixed approximation formulation similar to the Galerkin boundary element method presented by Steinbach (SIAM J Numer Anal 38:401–413, 2000) for the solution of Laplace’s equation. The method is also applicable to vector problems such as elasticity. Moreover, dynamic problems of acoustics and elastodynamics are included. The resulting system matrices have an ordered structure and small condition numbers in comparison to the standard collocation approach. Moreover, the employment of Robin boundary conditions is easily included in this formulation. Details on the numerical integration of the occurring regular and singular integrals and on the solution of the arising systems of equations are given. Numerical experiments have been carried out for different reference problems. In these experiments, the presented approach is compared to the common nodal collocation method with respect to accuracy, condition numbers, and stability in the dynamic case.</description><subject>Acoustics</subject><subject>Boundary conditions</subject><subject>Boundary element method</subject><subject>Classical and Continuum Physics</subject><subject>Collocation methods</subject><subject>Computational Science and Engineering</subject><subject>Dynamic stability</subject><subject>Elasticity</subject><subject>Elastodynamics</subject><subject>Engineering</subject><subject>Galerkin method</subject><subject>Mathematical analysis</subject><subject>Nonlinear programming</subject><subject>Numerical integration</subject><subject>Original Paper</subject><subject>Theoretical and Applied Mechanics</subject><issn>0178-7675</issn><issn>1432-0924</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><sourceid>AFKRA</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNp1kE9LxDAQxYMouK5-AG8BwVt00qRNe1wW_8GCIHoOTTLVXdpkTbrCfnuzVBAETzMDvzcz7xFyyeGGA6jbBCCrigE0DETVMHlEZlyKgkFTyGMyA65qpipVnpKzlDYAvKxFOSMvC0_bfsTo23H9hdSGvg8298FTE3betXFPsccB_UgHHD-Co12INI2ZsbT1jrq9b4fcb2MwGUzn5KRr-4QXP3VO3u7vXpePbPX88LRcrJgVUo2sM6hsgRxNfrM2jjswdSmVdLUxXYkWlAIQ6LIxy0VjLHaqgUbkWbYcxZxcT3vz4c8dplEP62Sx71uPYZe0KAGqqqozePUH3IRdNtwnXRQVF5xLJTLFJ8rGkFLETm_jesj2NQd9yFhPGeucsT5krGXWFJMmZda_Y_zd_L_oG9WSf0M</recordid><startdate>20090701</startdate><enddate>20090701</enddate><creator>Rüberg, Thomas</creator><creator>Schanz, Martin</creator><general>Springer-Verlag</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>AFKRA</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>H8D</scope><scope>KR7</scope><scope>L7M</scope></search><sort><creationdate>20090701</creationdate><title>An alternative collocation boundary element method for static and dynamic problems</title><author>Rüberg, Thomas ; Schanz, Martin</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c347t-fbe7c2e1eb4328bd1d0b85474d8bbf5ec077003ed046c139bcef790930464a1e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2009</creationdate><topic>Acoustics</topic><topic>Boundary conditions</topic><topic>Boundary element method</topic><topic>Classical and Continuum Physics</topic><topic>Collocation methods</topic><topic>Computational Science and Engineering</topic><topic>Dynamic stability</topic><topic>Elasticity</topic><topic>Elastodynamics</topic><topic>Engineering</topic><topic>Galerkin method</topic><topic>Mathematical analysis</topic><topic>Nonlinear programming</topic><topic>Numerical integration</topic><topic>Original Paper</topic><topic>Theoretical and Applied Mechanics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Rüberg, Thomas</creatorcontrib><creatorcontrib>Schanz, Martin</creatorcontrib><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering 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><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Computational mechanics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Rüberg, Thomas</au><au>Schanz, Martin</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An alternative collocation boundary element method for static and dynamic problems</atitle><jtitle>Computational mechanics</jtitle><stitle>Comput Mech</stitle><date>2009-07-01</date><risdate>2009</risdate><volume>44</volume><issue>2</issue><spage>247</spage><epage>261</epage><pages>247-261</pages><issn>0178-7675</issn><eissn>1432-0924</eissn><abstract>A collocation boundary element formulation is presented which is based on a mixed approximation formulation similar to the Galerkin boundary element method presented by Steinbach (SIAM J Numer Anal 38:401–413, 2000) for the solution of Laplace’s equation. The method is also applicable to vector problems such as elasticity. Moreover, dynamic problems of acoustics and elastodynamics are included. The resulting system matrices have an ordered structure and small condition numbers in comparison to the standard collocation approach. Moreover, the employment of Robin boundary conditions is easily included in this formulation. Details on the numerical integration of the occurring regular and singular integrals and on the solution of the arising systems of equations are given. Numerical experiments have been carried out for different reference problems. In these experiments, the presented approach is compared to the common nodal collocation method with respect to accuracy, condition numbers, and stability in the dynamic case.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer-Verlag</pub><doi>10.1007/s00466-009-0369-4</doi><tpages>15</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0178-7675 |
| ispartof | Computational mechanics, 2009-07, Vol.44 (2), p.247-261 |
| issn | 0178-7675 1432-0924 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_35006668 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Acoustics Boundary conditions Boundary element method Classical and Continuum Physics Collocation methods Computational Science and Engineering Dynamic stability Elasticity Elastodynamics Engineering Galerkin method Mathematical analysis Nonlinear programming Numerical integration Original Paper Theoretical and Applied Mechanics |
| title | An alternative collocation boundary element method for static and dynamic problems |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-23T19%3A53%3A35IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=An%20alternative%20collocation%20boundary%20element%20method%20for%20static%20and%20dynamic%20problems&rft.jtitle=Computational%20mechanics&rft.au=R%C3%BCberg,%20Thomas&rft.date=2009-07-01&rft.volume=44&rft.issue=2&rft.spage=247&rft.epage=261&rft.pages=247-261&rft.issn=0178-7675&rft.eissn=1432-0924&rft_id=info:doi/10.1007/s00466-009-0369-4&rft_dat=%3Cproquest_cross%3E35006668%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2261311473&rft_id=info:pmid/&rfr_iscdi=true |