Loading…
Use of singularity capturing functions in the solution of problems with discontinuous boundary conditions
A method is proposed to improve the accuracy of the numerical solution of elliptic problems with discontinuous boundary conditions using both global and local meshless collocation methods with multiquadrics as basis functions. It is based on the use of special functions which capture the singular be...
Saved in:
Published in: | Engineering analysis with boundary elements 2009-02, Vol.33 (2), p.200-208 |
---|---|
Main Authors: | , , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
cited_by | cdi_FETCH-LOGICAL-c384t-2340fd1287fb5f1ed5e7ea613be035f5c0a7ee5719b1c53521e7db03a37b6d953 |
---|---|
cites | cdi_FETCH-LOGICAL-c384t-2340fd1287fb5f1ed5e7ea613be035f5c0a7ee5719b1c53521e7db03a37b6d953 |
container_end_page | 208 |
container_issue | 2 |
container_start_page | 200 |
container_title | Engineering analysis with boundary elements |
container_volume | 33 |
creator | Bernal, F. Gutierrez, G. Kindelan, M. |
description | A method is proposed to improve the accuracy of the numerical solution of elliptic problems with discontinuous boundary conditions using both global and local meshless collocation methods with multiquadrics as basis functions. It is based on the use of special functions which capture the singular behavior near discontinuities in boundary conditions. In the case of global collocation, the method consists in enlarging the functional space spanned by the RBF basis functions, while in the case of local collocation, the method consists in modifying appropriately the problem in order to eliminate the singularities from the formulation. Numerical results for benchmark problems such as a stationary heat equation in a box (harmonic) and Stokes flow in a lid-driven square cavity, show significant improvements in accuracy and in compliance with the continuity equation. |
doi_str_mv | 10.1016/j.enganabound.2008.05.002 |
format | article |
fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_1082203939</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0955799708000702</els_id><sourcerecordid>1082203939</sourcerecordid><originalsourceid>FETCH-LOGICAL-c384t-2340fd1287fb5f1ed5e7ea613be035f5c0a7ee5719b1c53521e7db03a37b6d953</originalsourceid><addsrcrecordid>eNqNkEFrGzEQhUVpoa7b_6AeAr3sZrSKrNWxmDQpBHppoDehlUaJzFpyJG1K_31lO5QcyxwGhjdvvnmEfGbQM2Cby12P8cFEM6Ulun4AGHsQPcDwhqzYKHnHlPz1lqxACdFJpeR78qGUHQDjAJsVCfcFafK0hPiwzCaH-odac6hLbgPql2hrSLHQEGl9RFrSvBwHx5VDTtOM-0J_h_pIXSg2xRrikpZCTzgmN68UXThZfCTvvJkLfnrpa3L_7frn9ra7-3Hzffv1rrN8vKrdwK_AOzaM0k_CM3QCJZoN4xMCF15YMBJRSKYmZgUXA0PpJuCGy2njlOBr8uXs2_ieFixV7xsazrOJ2NA0g3EYgKtWa6LOUptTKRm9PuSwb9hNpI_x6p1-Fa8-xqtB6BZv2714OWOKNbPPJtpQ_hkMoEYQDXtNtmcdtp-fA2ZdbMBo0YWMtmqXwn9c-wt_zZms</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1082203939</pqid></control><display><type>article</type><title>Use of singularity capturing functions in the solution of problems with discontinuous boundary conditions</title><source>ScienceDirect Freedom Collection 2022-2024</source><creator>Bernal, F. ; Gutierrez, G. ; Kindelan, M.</creator><creatorcontrib>Bernal, F. ; Gutierrez, G. ; Kindelan, M.</creatorcontrib><description>A method is proposed to improve the accuracy of the numerical solution of elliptic problems with discontinuous boundary conditions using both global and local meshless collocation methods with multiquadrics as basis functions. It is based on the use of special functions which capture the singular behavior near discontinuities in boundary conditions. In the case of global collocation, the method consists in enlarging the functional space spanned by the RBF basis functions, while in the case of local collocation, the method consists in modifying appropriately the problem in order to eliminate the singularities from the formulation. Numerical results for benchmark problems such as a stationary heat equation in a box (harmonic) and Stokes flow in a lid-driven square cavity, show significant improvements in accuracy and in compliance with the continuity equation.</description><identifier>ISSN: 0955-7997</identifier><identifier>EISSN: 1873-197X</identifier><identifier>DOI: 10.1016/j.enganabound.2008.05.002</identifier><language>eng</language><publisher>Kidlington: Elsevier Ltd</publisher><subject>Accuracy ; Analytical and numerical techniques ; Basis functions ; Boundary conditions ; Boundary-integral methods ; Collocation ; Computational techniques ; Discontinuous boundary conditions ; Exact sciences and technology ; Fluid dynamics ; Fundamental areas of phenomenology (including applications) ; General theory ; Heat transfer ; Laminar flows ; Laminar flows in cavities ; Mathematical analysis ; Mathematical methods in physics ; Mathematical models ; Meshless methods ; Physics ; Radial basis function ; Singularities ; Stokes problem</subject><ispartof>Engineering analysis with boundary elements, 2009-02, Vol.33 (2), p.200-208</ispartof><rights>2008 Elsevier Ltd</rights><rights>2009 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c384t-2340fd1287fb5f1ed5e7ea613be035f5c0a7ee5719b1c53521e7db03a37b6d953</citedby><cites>FETCH-LOGICAL-c384t-2340fd1287fb5f1ed5e7ea613be035f5c0a7ee5719b1c53521e7db03a37b6d953</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=20980561$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Bernal, F.</creatorcontrib><creatorcontrib>Gutierrez, G.</creatorcontrib><creatorcontrib>Kindelan, M.</creatorcontrib><title>Use of singularity capturing functions in the solution of problems with discontinuous boundary conditions</title><title>Engineering analysis with boundary elements</title><description>A method is proposed to improve the accuracy of the numerical solution of elliptic problems with discontinuous boundary conditions using both global and local meshless collocation methods with multiquadrics as basis functions. It is based on the use of special functions which capture the singular behavior near discontinuities in boundary conditions. In the case of global collocation, the method consists in enlarging the functional space spanned by the RBF basis functions, while in the case of local collocation, the method consists in modifying appropriately the problem in order to eliminate the singularities from the formulation. Numerical results for benchmark problems such as a stationary heat equation in a box (harmonic) and Stokes flow in a lid-driven square cavity, show significant improvements in accuracy and in compliance with the continuity equation.</description><subject>Accuracy</subject><subject>Analytical and numerical techniques</subject><subject>Basis functions</subject><subject>Boundary conditions</subject><subject>Boundary-integral methods</subject><subject>Collocation</subject><subject>Computational techniques</subject><subject>Discontinuous boundary conditions</subject><subject>Exact sciences and technology</subject><subject>Fluid dynamics</subject><subject>Fundamental areas of phenomenology (including applications)</subject><subject>General theory</subject><subject>Heat transfer</subject><subject>Laminar flows</subject><subject>Laminar flows in cavities</subject><subject>Mathematical analysis</subject><subject>Mathematical methods in physics</subject><subject>Mathematical models</subject><subject>Meshless methods</subject><subject>Physics</subject><subject>Radial basis function</subject><subject>Singularities</subject><subject>Stokes problem</subject><issn>0955-7997</issn><issn>1873-197X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><recordid>eNqNkEFrGzEQhUVpoa7b_6AeAr3sZrSKrNWxmDQpBHppoDehlUaJzFpyJG1K_31lO5QcyxwGhjdvvnmEfGbQM2Cby12P8cFEM6Ulun4AGHsQPcDwhqzYKHnHlPz1lqxACdFJpeR78qGUHQDjAJsVCfcFafK0hPiwzCaH-odac6hLbgPql2hrSLHQEGl9RFrSvBwHx5VDTtOM-0J_h_pIXSg2xRrikpZCTzgmN68UXThZfCTvvJkLfnrpa3L_7frn9ra7-3Hzffv1rrN8vKrdwK_AOzaM0k_CM3QCJZoN4xMCF15YMBJRSKYmZgUXA0PpJuCGy2njlOBr8uXs2_ieFixV7xsazrOJ2NA0g3EYgKtWa6LOUptTKRm9PuSwb9hNpI_x6p1-Fa8-xqtB6BZv2714OWOKNbPPJtpQ_hkMoEYQDXtNtmcdtp-fA2ZdbMBo0YWMtmqXwn9c-wt_zZms</recordid><startdate>20090201</startdate><enddate>20090201</enddate><creator>Bernal, F.</creator><creator>Gutierrez, G.</creator><creator>Kindelan, M.</creator><general>Elsevier Ltd</general><general>Elsevier</general><scope>IQODW</scope><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></search><sort><creationdate>20090201</creationdate><title>Use of singularity capturing functions in the solution of problems with discontinuous boundary conditions</title><author>Bernal, F. ; Gutierrez, G. ; Kindelan, M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c384t-2340fd1287fb5f1ed5e7ea613be035f5c0a7ee5719b1c53521e7db03a37b6d953</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2009</creationdate><topic>Accuracy</topic><topic>Analytical and numerical techniques</topic><topic>Basis functions</topic><topic>Boundary conditions</topic><topic>Boundary-integral methods</topic><topic>Collocation</topic><topic>Computational techniques</topic><topic>Discontinuous boundary conditions</topic><topic>Exact sciences and technology</topic><topic>Fluid dynamics</topic><topic>Fundamental areas of phenomenology (including applications)</topic><topic>General theory</topic><topic>Heat transfer</topic><topic>Laminar flows</topic><topic>Laminar flows in cavities</topic><topic>Mathematical analysis</topic><topic>Mathematical methods in physics</topic><topic>Mathematical models</topic><topic>Meshless methods</topic><topic>Physics</topic><topic>Radial basis function</topic><topic>Singularities</topic><topic>Stokes problem</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bernal, F.</creatorcontrib><creatorcontrib>Gutierrez, G.</creatorcontrib><creatorcontrib>Kindelan, M.</creatorcontrib><collection>Pascal-Francis</collection><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>Engineering analysis with boundary elements</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bernal, F.</au><au>Gutierrez, G.</au><au>Kindelan, M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Use of singularity capturing functions in the solution of problems with discontinuous boundary conditions</atitle><jtitle>Engineering analysis with boundary elements</jtitle><date>2009-02-01</date><risdate>2009</risdate><volume>33</volume><issue>2</issue><spage>200</spage><epage>208</epage><pages>200-208</pages><issn>0955-7997</issn><eissn>1873-197X</eissn><abstract>A method is proposed to improve the accuracy of the numerical solution of elliptic problems with discontinuous boundary conditions using both global and local meshless collocation methods with multiquadrics as basis functions. It is based on the use of special functions which capture the singular behavior near discontinuities in boundary conditions. In the case of global collocation, the method consists in enlarging the functional space spanned by the RBF basis functions, while in the case of local collocation, the method consists in modifying appropriately the problem in order to eliminate the singularities from the formulation. Numerical results for benchmark problems such as a stationary heat equation in a box (harmonic) and Stokes flow in a lid-driven square cavity, show significant improvements in accuracy and in compliance with the continuity equation.</abstract><cop>Kidlington</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.enganabound.2008.05.002</doi><tpages>9</tpages></addata></record> |
fulltext | fulltext |
identifier | ISSN: 0955-7997 |
ispartof | Engineering analysis with boundary elements, 2009-02, Vol.33 (2), p.200-208 |
issn | 0955-7997 1873-197X |
language | eng |
recordid | cdi_proquest_miscellaneous_1082203939 |
source | ScienceDirect Freedom Collection 2022-2024 |
subjects | Accuracy Analytical and numerical techniques Basis functions Boundary conditions Boundary-integral methods Collocation Computational techniques Discontinuous boundary conditions Exact sciences and technology Fluid dynamics Fundamental areas of phenomenology (including applications) General theory Heat transfer Laminar flows Laminar flows in cavities Mathematical analysis Mathematical methods in physics Mathematical models Meshless methods Physics Radial basis function Singularities Stokes problem |
title | Use of singularity capturing functions in the solution of problems with discontinuous boundary conditions |
url | http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-07T18%3A57%3A16IST&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=Use%20of%20singularity%20capturing%20functions%20in%20the%20solution%20of%20problems%20with%20discontinuous%20boundary%20conditions&rft.jtitle=Engineering%20analysis%20with%20boundary%20elements&rft.au=Bernal,%20F.&rft.date=2009-02-01&rft.volume=33&rft.issue=2&rft.spage=200&rft.epage=208&rft.pages=200-208&rft.issn=0955-7997&rft.eissn=1873-197X&rft_id=info:doi/10.1016/j.enganabound.2008.05.002&rft_dat=%3Cproquest_cross%3E1082203939%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c384t-2340fd1287fb5f1ed5e7ea613be035f5c0a7ee5719b1c53521e7db03a37b6d953%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=1082203939&rft_id=info:pmid/&rfr_iscdi=true |