An extended stochastic pseudo‐spectral Galerkin finite element method (XS‐PS‐GFEM) for elliptic equations with hybrid uncertainties
Summary Nouy and Clement introduced the stochastic extended finite element method to solve linear elasticity problem defined on random domain. The material properties and boundary conditions were assumed to be deterministic. In this work, we extend this framework to account for multiple independent...
Gespeichert in:
| Veröffentlicht in: | International journal for numerical methods in engineering 2020-10, Vol.121 (19), p.4329-4346 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 4346 |
|---|---|
| container_issue | 19 |
| container_start_page | 4329 |
| container_title | International journal for numerical methods in engineering |
| container_volume | 121 |
| creator | Varghese Mathew, Tittu Rebbagondla, Jayamanideep Natarajan, Sundararajan |
| description | Summary
Nouy and Clement introduced the stochastic extended finite element method to solve linear elasticity problem defined on random domain. The material properties and boundary conditions were assumed to be deterministic. In this work, we extend this framework to account for multiple independent input uncertainties, namely, material, geometry, and external force uncertainties. The stochastic field is represented using the polynomial chaos expansion. The challenge in numerical integration over multidimensional probabilistic space is addressed using the pseudo‐spectral Galerkin method. Thereafter, a sensitivity analysis based on Sobol indices using the derived stochastic extended Finite Element Method solution is presented. The efficiency and accuracy of the proposed novel framework against conventional Monte Carlo methods is elucidated in detail for a few one and two dimensional problems. |
| doi_str_mv | 10.1002/nme.6433 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2441159120</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2441159120</sourcerecordid><originalsourceid>FETCH-LOGICAL-c2543-80061e97b705cbad9c01cb1db2b9b7c6b8c78d03027d2ce7f2db734a15c5a0703</originalsourceid><addsrcrecordid>eNp10MtKxDAUBuAgCo4X8BECbnRRPUnbyXQpMjMK3kAFdyWXUybaSWuSorNz685n9ElsHbduzlmcj__AT8gBgxMGwE_dEk_GWZpukBGDQiTAQWySUX8qkryYsG2yE8IzAGM5pCPyeeYovkd0Bg0NsdELGaLVtA3Ymeb74yu0qKOXNZ3LGv2LdbSyzkakWOMSXaRLjIvG0KOn-17fDWM-m14f06rxvaltO8ThayejbVygbzYu6GKlvDW0cxp9lNZFi2GPbFWyDrj_t3fJ42z6cH6RXN3OL8_PrhLN8yxNJgBjhoVQAnKtpCk0MK2YUVwVSuixmmgxMZACF4ZrFBU3SqSZZLnOJQhId8nhOrf1zWuHIZbPTedd_7LkWdbXUjA-qKO10r4JwWNVtt4upV-VDMqh6LIvuhyK7mmypm-2xtW_rry5nv76H-RPg6Y</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2441159120</pqid></control><display><type>article</type><title>An extended stochastic pseudo‐spectral Galerkin finite element method (XS‐PS‐GFEM) for elliptic equations with hybrid uncertainties</title><source>Wiley Journals</source><creator>Varghese Mathew, Tittu ; Rebbagondla, Jayamanideep ; Natarajan, Sundararajan</creator><creatorcontrib>Varghese Mathew, Tittu ; Rebbagondla, Jayamanideep ; Natarajan, Sundararajan</creatorcontrib><description>Summary
Nouy and Clement introduced the stochastic extended finite element method to solve linear elasticity problem defined on random domain. The material properties and boundary conditions were assumed to be deterministic. In this work, we extend this framework to account for multiple independent input uncertainties, namely, material, geometry, and external force uncertainties. The stochastic field is represented using the polynomial chaos expansion. The challenge in numerical integration over multidimensional probabilistic space is addressed using the pseudo‐spectral Galerkin method. Thereafter, a sensitivity analysis based on Sobol indices using the derived stochastic extended Finite Element Method solution is presented. The efficiency and accuracy of the proposed novel framework against conventional Monte Carlo methods is elucidated in detail for a few one and two dimensional problems.</description><identifier>ISSN: 0029-5981</identifier><identifier>EISSN: 1097-0207</identifier><identifier>DOI: 10.1002/nme.6433</identifier><language>eng</language><publisher>Hoboken, USA: John Wiley & Sons, Inc</publisher><subject>Boundary conditions ; Elliptic functions ; Finite element analysis ; Finite element method ; force uncertainty ; Galerkin method ; geometric uncertainty ; Material properties ; material uncertainty ; Mathematical analysis ; Monte Carlo simulation ; Numerical integration ; polynomial chaos ; Polynomials ; random level set ; Sensitivity analysis ; Sobol index ; stochastic Galerkin pseudo‐spectral method ; Uncertainty ; XFEM</subject><ispartof>International journal for numerical methods in engineering, 2020-10, Vol.121 (19), p.4329-4346</ispartof><rights>2020 John Wiley & Sons, Ltd.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c2543-80061e97b705cbad9c01cb1db2b9b7c6b8c78d03027d2ce7f2db734a15c5a0703</cites><orcidid>0000-0002-0409-0096</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.6433$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fnme.6433$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,780,784,1417,27924,27925,45574,45575</link.rule.ids></links><search><creatorcontrib>Varghese Mathew, Tittu</creatorcontrib><creatorcontrib>Rebbagondla, Jayamanideep</creatorcontrib><creatorcontrib>Natarajan, Sundararajan</creatorcontrib><title>An extended stochastic pseudo‐spectral Galerkin finite element method (XS‐PS‐GFEM) for elliptic equations with hybrid uncertainties</title><title>International journal for numerical methods in engineering</title><description>Summary
Nouy and Clement introduced the stochastic extended finite element method to solve linear elasticity problem defined on random domain. The material properties and boundary conditions were assumed to be deterministic. In this work, we extend this framework to account for multiple independent input uncertainties, namely, material, geometry, and external force uncertainties. The stochastic field is represented using the polynomial chaos expansion. The challenge in numerical integration over multidimensional probabilistic space is addressed using the pseudo‐spectral Galerkin method. Thereafter, a sensitivity analysis based on Sobol indices using the derived stochastic extended Finite Element Method solution is presented. The efficiency and accuracy of the proposed novel framework against conventional Monte Carlo methods is elucidated in detail for a few one and two dimensional problems.</description><subject>Boundary conditions</subject><subject>Elliptic functions</subject><subject>Finite element analysis</subject><subject>Finite element method</subject><subject>force uncertainty</subject><subject>Galerkin method</subject><subject>geometric uncertainty</subject><subject>Material properties</subject><subject>material uncertainty</subject><subject>Mathematical analysis</subject><subject>Monte Carlo simulation</subject><subject>Numerical integration</subject><subject>polynomial chaos</subject><subject>Polynomials</subject><subject>random level set</subject><subject>Sensitivity analysis</subject><subject>Sobol index</subject><subject>stochastic Galerkin pseudo‐spectral method</subject><subject>Uncertainty</subject><subject>XFEM</subject><issn>0029-5981</issn><issn>1097-0207</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp10MtKxDAUBuAgCo4X8BECbnRRPUnbyXQpMjMK3kAFdyWXUybaSWuSorNz685n9ElsHbduzlmcj__AT8gBgxMGwE_dEk_GWZpukBGDQiTAQWySUX8qkryYsG2yE8IzAGM5pCPyeeYovkd0Bg0NsdELGaLVtA3Ymeb74yu0qKOXNZ3LGv2LdbSyzkakWOMSXaRLjIvG0KOn-17fDWM-m14f06rxvaltO8ThayejbVygbzYu6GKlvDW0cxp9lNZFi2GPbFWyDrj_t3fJ42z6cH6RXN3OL8_PrhLN8yxNJgBjhoVQAnKtpCk0MK2YUVwVSuixmmgxMZACF4ZrFBU3SqSZZLnOJQhId8nhOrf1zWuHIZbPTedd_7LkWdbXUjA-qKO10r4JwWNVtt4upV-VDMqh6LIvuhyK7mmypm-2xtW_rry5nv76H-RPg6Y</recordid><startdate>20201015</startdate><enddate>20201015</enddate><creator>Varghese Mathew, Tittu</creator><creator>Rebbagondla, Jayamanideep</creator><creator>Natarajan, Sundararajan</creator><general>John Wiley & Sons, Inc</general><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/0000-0002-0409-0096</orcidid></search><sort><creationdate>20201015</creationdate><title>An extended stochastic pseudo‐spectral Galerkin finite element method (XS‐PS‐GFEM) for elliptic equations with hybrid uncertainties</title><author>Varghese Mathew, Tittu ; Rebbagondla, Jayamanideep ; Natarajan, Sundararajan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2543-80061e97b705cbad9c01cb1db2b9b7c6b8c78d03027d2ce7f2db734a15c5a0703</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Boundary conditions</topic><topic>Elliptic functions</topic><topic>Finite element analysis</topic><topic>Finite element method</topic><topic>force uncertainty</topic><topic>Galerkin method</topic><topic>geometric uncertainty</topic><topic>Material properties</topic><topic>material uncertainty</topic><topic>Mathematical analysis</topic><topic>Monte Carlo simulation</topic><topic>Numerical integration</topic><topic>polynomial chaos</topic><topic>Polynomials</topic><topic>random level set</topic><topic>Sensitivity analysis</topic><topic>Sobol index</topic><topic>stochastic Galerkin pseudo‐spectral method</topic><topic>Uncertainty</topic><topic>XFEM</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Varghese Mathew, Tittu</creatorcontrib><creatorcontrib>Rebbagondla, Jayamanideep</creatorcontrib><creatorcontrib>Natarajan, Sundararajan</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>Varghese Mathew, Tittu</au><au>Rebbagondla, Jayamanideep</au><au>Natarajan, Sundararajan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An extended stochastic pseudo‐spectral Galerkin finite element method (XS‐PS‐GFEM) for elliptic equations with hybrid uncertainties</atitle><jtitle>International journal for numerical methods in engineering</jtitle><date>2020-10-15</date><risdate>2020</risdate><volume>121</volume><issue>19</issue><spage>4329</spage><epage>4346</epage><pages>4329-4346</pages><issn>0029-5981</issn><eissn>1097-0207</eissn><abstract>Summary
Nouy and Clement introduced the stochastic extended finite element method to solve linear elasticity problem defined on random domain. The material properties and boundary conditions were assumed to be deterministic. In this work, we extend this framework to account for multiple independent input uncertainties, namely, material, geometry, and external force uncertainties. The stochastic field is represented using the polynomial chaos expansion. The challenge in numerical integration over multidimensional probabilistic space is addressed using the pseudo‐spectral Galerkin method. Thereafter, a sensitivity analysis based on Sobol indices using the derived stochastic extended Finite Element Method solution is presented. The efficiency and accuracy of the proposed novel framework against conventional Monte Carlo methods is elucidated in detail for a few one and two dimensional problems.</abstract><cop>Hoboken, USA</cop><pub>John Wiley & Sons, Inc</pub><doi>10.1002/nme.6433</doi><tpages>18</tpages><orcidid>https://orcid.org/0000-0002-0409-0096</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0029-5981 |
| ispartof | International journal for numerical methods in engineering, 2020-10, Vol.121 (19), p.4329-4346 |
| issn | 0029-5981 1097-0207 |
| language | eng |
| recordid | cdi_proquest_journals_2441159120 |
| source | Wiley Journals |
| subjects | Boundary conditions Elliptic functions Finite element analysis Finite element method force uncertainty Galerkin method geometric uncertainty Material properties material uncertainty Mathematical analysis Monte Carlo simulation Numerical integration polynomial chaos Polynomials random level set Sensitivity analysis Sobol index stochastic Galerkin pseudo‐spectral method Uncertainty XFEM |
| title | An extended stochastic pseudo‐spectral Galerkin finite element method (XS‐PS‐GFEM) for elliptic equations with hybrid uncertainties |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-05T00%3A33%3A04IST&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%20extended%20stochastic%20pseudo%E2%80%90spectral%20Galerkin%20finite%20element%20method%20(XS%E2%80%90PS%E2%80%90GFEM)%20for%20elliptic%20equations%20with%20hybrid%20uncertainties&rft.jtitle=International%20journal%20for%20numerical%20methods%20in%20engineering&rft.au=Varghese%20Mathew,%20Tittu&rft.date=2020-10-15&rft.volume=121&rft.issue=19&rft.spage=4329&rft.epage=4346&rft.pages=4329-4346&rft.issn=0029-5981&rft.eissn=1097-0207&rft_id=info:doi/10.1002/nme.6433&rft_dat=%3Cproquest_cross%3E2441159120%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=2441159120&rft_id=info:pmid/&rfr_iscdi=true |