On a robust multilevel method applied for solving large-scale linear elasticity problems
The paper discusses an iterative scheme for solving large‐scale three‐dimensional linear elasticity problems, discretized on a tensor product of two‐dimensional and one‐dimensional meshes. A framework is chosen of the additive AMLI method to develop a preconditioner of a ‘black‐box’ type which is ro...
Gespeichert in:
| Veröffentlicht in: | Communications in numerical methods in engineering 1999-03, Vol.15 (3), p.153-165 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 165 |
|---|---|
| container_issue | 3 |
| container_start_page | 153 |
| container_title | Communications in numerical methods in engineering |
| container_volume | 15 |
| creator | Padiy, Alexander |
| description | The paper discusses an iterative scheme for solving large‐scale three‐dimensional linear elasticity problems, discretized on a tensor product of two‐dimensional and one‐dimensional meshes. A framework is chosen of the additive AMLI method to develop a preconditioner of a ‘black‐box’ type which is robust with respect to discontinuities of the problem coefficients and imposes only weak (and acceptable in practice) restrictions on the choice of the meshing procedure. The preconditioner works on a hierarchical sequence of nested finite element spaces to solve the problem with arithmetic cost, nearly proportional to the number of degrees of freedom on the finest mesh. It is particularly well suited for the case when the solution is known to be strongly varying in certain subregions of the domain and the mesh is locally prerefined there to reduce the discretization error. Copyright © 1999 John Wiley & Sons, Ltd. |
| doi_str_mv | 10.1002/(SICI)1099-0887(199903)15:3<153::AID-CNM231>3.0.CO;2-L |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_27011295</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>27011295</sourcerecordid><originalsourceid>FETCH-LOGICAL-c4891-ac08b02b62a7b2ffc68f25b8b05ee9bead03b2c9d11c58fcabd2d38b69a998753</originalsourceid><addsrcrecordid>eNqFkF1v0zAUhiPEJMbgP_gCoe3C3bFNErugSVNgo1JpJT53d-Q4zjA4SWen2_rvlyjVuACJG9s6ev28R0-SnDGYMQB-evxlUSxOGChFQcr8mCmlQJywdC7esVTM5-eL97RYfeKCnYkZzIr1W06XT5LDxy9Px3emqORKPUuex_gLABRIOEyu1i3RJHTlNvak2freeXtrPWls_7OriN5svLMVqbtAYudvXXtNvA7XlkajvSXetVYHYr2OvTOu35HNwPK2iS-Sg1r7aF_u76Pk28WHr8VHulxfLorzJTVvpGJUG5Al8DLjOi95XZtM1jwth1lqrSqtrkCU3KiKMZPK2uiy4pWQZaa0UjJPxVHyeuIOxTdbG3tsXDTWe93abhuR58AYV2Pw-xQ0oYsx2Bo3wTU67JABjqIRR9E4WsPRGk6ikaU4HgJxEI2T6GECWKyR43IAv9pvoEcpddCtcfEPPWcZh2yIXU2xu0Hx7q_y_3T_s3o_GdB0QrvY2_tHtA6_MctFnuKP1SVmbLWSecHws3gAQrOufA</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>27011295</pqid></control><display><type>article</type><title>On a robust multilevel method applied for solving large-scale linear elasticity problems</title><source>Wiley Online Library Journals Frontfile Complete</source><creator>Padiy, Alexander</creator><creatorcontrib>Padiy, Alexander</creatorcontrib><description>The paper discusses an iterative scheme for solving large‐scale three‐dimensional linear elasticity problems, discretized on a tensor product of two‐dimensional and one‐dimensional meshes. A framework is chosen of the additive AMLI method to develop a preconditioner of a ‘black‐box’ type which is robust with respect to discontinuities of the problem coefficients and imposes only weak (and acceptable in practice) restrictions on the choice of the meshing procedure. The preconditioner works on a hierarchical sequence of nested finite element spaces to solve the problem with arithmetic cost, nearly proportional to the number of degrees of freedom on the finest mesh. It is particularly well suited for the case when the solution is known to be strongly varying in certain subregions of the domain and the mesh is locally prerefined there to reduce the discretization error. Copyright © 1999 John Wiley & Sons, Ltd.</description><identifier>ISSN: 1069-8299</identifier><identifier>EISSN: 1099-0887</identifier><identifier>DOI: 10.1002/(SICI)1099-0887(199903)15:3<153::AID-CNM231>3.0.CO;2-L</identifier><language>eng</language><publisher>Chichester, UK: John Wiley & Sons, Ltd</publisher><subject>Applied sciences ; Buildings. Public works ; Computational techniques ; Continuous cycle engines: steam and gas turbines, jet engines ; elasticity problems ; Engines and turbines ; Exact sciences and technology ; Finite-element and galerkin methods ; Fundamental areas of phenomenology (including applications) ; iterative methods ; Mathematical methods in physics ; Mechanical engineering. Machine design ; non-uniform discretization meshes ; Physics ; Solid mechanics ; Static elasticity ; Static elasticity (thermoelasticity...) ; Strength of materials (elasticity, plasticity, buckling, etc.) ; Structural analysis. Stresses ; Structural and continuum mechanics</subject><ispartof>Communications in numerical methods in engineering, 1999-03, Vol.15 (3), p.153-165</ispartof><rights>Copyright © 1999 John Wiley & Sons, Ltd.</rights><rights>1999 INIST-CNRS</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c4891-ac08b02b62a7b2ffc68f25b8b05ee9bead03b2c9d11c58fcabd2d38b69a998753</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2F%28SICI%291099-0887%28199903%2915%3A3%3C153%3A%3AAID-CNM231%3E3.0.CO%3B2-L$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2F%28SICI%291099-0887%28199903%2915%3A3%3C153%3A%3AAID-CNM231%3E3.0.CO%3B2-L$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,778,782,1414,27907,27908,45557,45558</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=1716206$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Padiy, Alexander</creatorcontrib><title>On a robust multilevel method applied for solving large-scale linear elasticity problems</title><title>Communications in numerical methods in engineering</title><addtitle>Commun. Numer. Meth. Engng</addtitle><description>The paper discusses an iterative scheme for solving large‐scale three‐dimensional linear elasticity problems, discretized on a tensor product of two‐dimensional and one‐dimensional meshes. A framework is chosen of the additive AMLI method to develop a preconditioner of a ‘black‐box’ type which is robust with respect to discontinuities of the problem coefficients and imposes only weak (and acceptable in practice) restrictions on the choice of the meshing procedure. The preconditioner works on a hierarchical sequence of nested finite element spaces to solve the problem with arithmetic cost, nearly proportional to the number of degrees of freedom on the finest mesh. It is particularly well suited for the case when the solution is known to be strongly varying in certain subregions of the domain and the mesh is locally prerefined there to reduce the discretization error. Copyright © 1999 John Wiley & Sons, Ltd.</description><subject>Applied sciences</subject><subject>Buildings. Public works</subject><subject>Computational techniques</subject><subject>Continuous cycle engines: steam and gas turbines, jet engines</subject><subject>elasticity problems</subject><subject>Engines and turbines</subject><subject>Exact sciences and technology</subject><subject>Finite-element and galerkin methods</subject><subject>Fundamental areas of phenomenology (including applications)</subject><subject>iterative methods</subject><subject>Mathematical methods in physics</subject><subject>Mechanical engineering. Machine design</subject><subject>non-uniform discretization meshes</subject><subject>Physics</subject><subject>Solid mechanics</subject><subject>Static elasticity</subject><subject>Static elasticity (thermoelasticity...)</subject><subject>Strength of materials (elasticity, plasticity, buckling, etc.)</subject><subject>Structural analysis. Stresses</subject><subject>Structural and continuum mechanics</subject><issn>1069-8299</issn><issn>1099-0887</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1999</creationdate><recordtype>article</recordtype><recordid>eNqFkF1v0zAUhiPEJMbgP_gCoe3C3bFNErugSVNgo1JpJT53d-Q4zjA4SWen2_rvlyjVuACJG9s6ev28R0-SnDGYMQB-evxlUSxOGChFQcr8mCmlQJywdC7esVTM5-eL97RYfeKCnYkZzIr1W06XT5LDxy9Px3emqORKPUuex_gLABRIOEyu1i3RJHTlNvak2freeXtrPWls_7OriN5svLMVqbtAYudvXXtNvA7XlkajvSXetVYHYr2OvTOu35HNwPK2iS-Sg1r7aF_u76Pk28WHr8VHulxfLorzJTVvpGJUG5Al8DLjOi95XZtM1jwth1lqrSqtrkCU3KiKMZPK2uiy4pWQZaa0UjJPxVHyeuIOxTdbG3tsXDTWe93abhuR58AYV2Pw-xQ0oYsx2Bo3wTU67JABjqIRR9E4WsPRGk6ikaU4HgJxEI2T6GECWKyR43IAv9pvoEcpddCtcfEPPWcZh2yIXU2xu0Hx7q_y_3T_s3o_GdB0QrvY2_tHtA6_MctFnuKP1SVmbLWSecHws3gAQrOufA</recordid><startdate>199903</startdate><enddate>199903</enddate><creator>Padiy, Alexander</creator><general>John Wiley & Sons, Ltd</general><general>Wiley</general><scope>BSCLL</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope></search><sort><creationdate>199903</creationdate><title>On a robust multilevel method applied for solving large-scale linear elasticity problems</title><author>Padiy, Alexander</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c4891-ac08b02b62a7b2ffc68f25b8b05ee9bead03b2c9d11c58fcabd2d38b69a998753</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1999</creationdate><topic>Applied sciences</topic><topic>Buildings. Public works</topic><topic>Computational techniques</topic><topic>Continuous cycle engines: steam and gas turbines, jet engines</topic><topic>elasticity problems</topic><topic>Engines and turbines</topic><topic>Exact sciences and technology</topic><topic>Finite-element and galerkin methods</topic><topic>Fundamental areas of phenomenology (including applications)</topic><topic>iterative methods</topic><topic>Mathematical methods in physics</topic><topic>Mechanical engineering. Machine design</topic><topic>non-uniform discretization meshes</topic><topic>Physics</topic><topic>Solid mechanics</topic><topic>Static elasticity</topic><topic>Static elasticity (thermoelasticity...)</topic><topic>Strength of materials (elasticity, plasticity, buckling, etc.)</topic><topic>Structural analysis. Stresses</topic><topic>Structural and continuum mechanics</topic><toplevel>online_resources</toplevel><creatorcontrib>Padiy, Alexander</creatorcontrib><collection>Istex</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Communications in numerical methods in engineering</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Padiy, Alexander</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On a robust multilevel method applied for solving large-scale linear elasticity problems</atitle><jtitle>Communications in numerical methods in engineering</jtitle><addtitle>Commun. Numer. Meth. Engng</addtitle><date>1999-03</date><risdate>1999</risdate><volume>15</volume><issue>3</issue><spage>153</spage><epage>165</epage><pages>153-165</pages><issn>1069-8299</issn><eissn>1099-0887</eissn><abstract>The paper discusses an iterative scheme for solving large‐scale three‐dimensional linear elasticity problems, discretized on a tensor product of two‐dimensional and one‐dimensional meshes. A framework is chosen of the additive AMLI method to develop a preconditioner of a ‘black‐box’ type which is robust with respect to discontinuities of the problem coefficients and imposes only weak (and acceptable in practice) restrictions on the choice of the meshing procedure. The preconditioner works on a hierarchical sequence of nested finite element spaces to solve the problem with arithmetic cost, nearly proportional to the number of degrees of freedom on the finest mesh. It is particularly well suited for the case when the solution is known to be strongly varying in certain subregions of the domain and the mesh is locally prerefined there to reduce the discretization error. Copyright © 1999 John Wiley & Sons, Ltd.</abstract><cop>Chichester, UK</cop><pub>John Wiley & Sons, Ltd</pub><doi>10.1002/(SICI)1099-0887(199903)15:3<153::AID-CNM231>3.0.CO;2-L</doi><tpages>13</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1069-8299 |
| ispartof | Communications in numerical methods in engineering, 1999-03, Vol.15 (3), p.153-165 |
| issn | 1069-8299 1099-0887 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_27011295 |
| source | Wiley Online Library Journals Frontfile Complete |
| subjects | Applied sciences Buildings. Public works Computational techniques Continuous cycle engines: steam and gas turbines, jet engines elasticity problems Engines and turbines Exact sciences and technology Finite-element and galerkin methods Fundamental areas of phenomenology (including applications) iterative methods Mathematical methods in physics Mechanical engineering. Machine design non-uniform discretization meshes Physics Solid mechanics Static elasticity Static elasticity (thermoelasticity...) Strength of materials (elasticity, plasticity, buckling, etc.) Structural analysis. Stresses Structural and continuum mechanics |
| title | On a robust multilevel method applied for solving large-scale linear elasticity problems |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-16T11%3A23%3A02IST&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=On%20a%20robust%20multilevel%20method%20applied%20for%20solving%20large-scale%20linear%20elasticity%20problems&rft.jtitle=Communications%20in%20numerical%20methods%20in%20engineering&rft.au=Padiy,%20Alexander&rft.date=1999-03&rft.volume=15&rft.issue=3&rft.spage=153&rft.epage=165&rft.pages=153-165&rft.issn=1069-8299&rft.eissn=1099-0887&rft_id=info:doi/10.1002/(SICI)1099-0887(199903)15:3%3C153::AID-CNM231%3E3.0.CO;2-L&rft_dat=%3Cproquest_cross%3E27011295%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=27011295&rft_id=info:pmid/&rfr_iscdi=true |