Adaptive BEM with inexact PCG solver yields almost optimal computational costs
We consider the preconditioned conjugate gradient method (PCG) with optimal preconditioner in the frame of the boundary element method for elliptic first-kind integral equations. Our adaptive algorithm steers the termination of PCG as well as the local mesh-refinement. Besides convergence with optim...
Gespeichert in:
| Veröffentlicht in: | Numerische Mathematik 2019-04, Vol.141 (4), p.967-1008 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 1008 |
|---|---|
| container_issue | 4 |
| container_start_page | 967 |
| container_title | Numerische Mathematik |
| container_volume | 141 |
| creator | Führer, Thomas Haberl, Alexander Praetorius, Dirk Schimanko, Stefan |
| description | We consider the preconditioned conjugate gradient method (PCG) with optimal preconditioner in the frame of the boundary element method for elliptic first-kind integral equations. Our adaptive algorithm steers the termination of PCG as well as the local mesh-refinement. Besides convergence with optimal algebraic rates, we also prove almost optimal computational complexity. In particular, we provide an additive Schwarz preconditioner which can be computed in linear complexity and which is optimal in the sense that the condition numbers of the preconditioned systems are uniformly bounded. As model problem serves the 2D or 3D Laplace operator and the associated weakly-singular integral equation with energy space
H
~
-
1
/
2
(
Γ
)
. The main results also hold for the hyper-singular integral equation with energy space
H
1
/
2
(
Γ
)
. |
| doi_str_mv | 10.1007/s00211-018-1011-1 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2191864708</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2191864708</sourcerecordid><originalsourceid>FETCH-LOGICAL-c359t-55e81e46f814e6217d8918543a144c53b0afc213afa1c1f4213e45036fba803c3</originalsourceid><addsrcrecordid>eNp1kEtLAzEUhYMoWKs_wF3A9ei9k2Qey1pqFepjoeAupGmiU6bNmKTV_ntTR3Dl6p4L5zscDiHnCJcIUF4FgBwxA6wyhCTwgAyg5iJjOReHSUNeZ6KuX4_JSQhLACwLjgPyMFqoLjZbQ68n9_Szie-0WZsvpSN9Gk9pcO3WeLprTLsIVLUrFyJ1CViplmq36jZRxcatf74Qwyk5sqoN5uz3DsnLzeR5fJvNHqd349Es00zUMRPCVGh4YSvkpsixXFQ1VoIzhZxrweagrM6RKatQo-VJGi6AFXauKmCaDclFn9t597ExIcql2_hUI8gcU1TBS6iSC3uX9i4Eb6zsfGrudxJB7meT_WwyzSb3s0lMTN4zIXnXb8b_Jf8PfQMdb26q</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2191864708</pqid></control><display><type>article</type><title>Adaptive BEM with inexact PCG solver yields almost optimal computational costs</title><source>Springer Online Journals Complete</source><creator>Führer, Thomas ; Haberl, Alexander ; Praetorius, Dirk ; Schimanko, Stefan</creator><creatorcontrib>Führer, Thomas ; Haberl, Alexander ; Praetorius, Dirk ; Schimanko, Stefan</creatorcontrib><description>We consider the preconditioned conjugate gradient method (PCG) with optimal preconditioner in the frame of the boundary element method for elliptic first-kind integral equations. Our adaptive algorithm steers the termination of PCG as well as the local mesh-refinement. Besides convergence with optimal algebraic rates, we also prove almost optimal computational complexity. In particular, we provide an additive Schwarz preconditioner which can be computed in linear complexity and which is optimal in the sense that the condition numbers of the preconditioned systems are uniformly bounded. As model problem serves the 2D or 3D Laplace operator and the associated weakly-singular integral equation with energy space
H
~
-
1
/
2
(
Γ
)
. The main results also hold for the hyper-singular integral equation with energy space
H
1
/
2
(
Γ
)
.</description><identifier>ISSN: 0029-599X</identifier><identifier>EISSN: 0945-3245</identifier><identifier>DOI: 10.1007/s00211-018-1011-1</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Adaptive algorithms ; Boundary element method ; Complexity ; Computation ; Conjugate gradient method ; Elliptic functions ; Finite element method ; Integral equations ; Mathematical analysis ; Mathematical and Computational Engineering ; Mathematical and Computational Physics ; Mathematical Methods in Physics ; Mathematics ; Mathematics and Statistics ; Nonlinear programming ; Numerical Analysis ; Numerical and Computational Physics ; Operators (mathematics) ; Simulation ; Singular integral equations ; Theoretical ; Three dimensional models ; Two dimensional models</subject><ispartof>Numerische Mathematik, 2019-04, Vol.141 (4), p.967-1008</ispartof><rights>The Author(s) 2018</rights><rights>Copyright Springer Nature B.V. 2019</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c359t-55e81e46f814e6217d8918543a144c53b0afc213afa1c1f4213e45036fba803c3</citedby><cites>FETCH-LOGICAL-c359t-55e81e46f814e6217d8918543a144c53b0afc213afa1c1f4213e45036fba803c3</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/s00211-018-1011-1$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00211-018-1011-1$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Führer, Thomas</creatorcontrib><creatorcontrib>Haberl, Alexander</creatorcontrib><creatorcontrib>Praetorius, Dirk</creatorcontrib><creatorcontrib>Schimanko, Stefan</creatorcontrib><title>Adaptive BEM with inexact PCG solver yields almost optimal computational costs</title><title>Numerische Mathematik</title><addtitle>Numer. Math</addtitle><description>We consider the preconditioned conjugate gradient method (PCG) with optimal preconditioner in the frame of the boundary element method for elliptic first-kind integral equations. Our adaptive algorithm steers the termination of PCG as well as the local mesh-refinement. Besides convergence with optimal algebraic rates, we also prove almost optimal computational complexity. In particular, we provide an additive Schwarz preconditioner which can be computed in linear complexity and which is optimal in the sense that the condition numbers of the preconditioned systems are uniformly bounded. As model problem serves the 2D or 3D Laplace operator and the associated weakly-singular integral equation with energy space
H
~
-
1
/
2
(
Γ
)
. The main results also hold for the hyper-singular integral equation with energy space
H
1
/
2
(
Γ
)
.</description><subject>Adaptive algorithms</subject><subject>Boundary element method</subject><subject>Complexity</subject><subject>Computation</subject><subject>Conjugate gradient method</subject><subject>Elliptic functions</subject><subject>Finite element method</subject><subject>Integral equations</subject><subject>Mathematical analysis</subject><subject>Mathematical and Computational Engineering</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical Methods in Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Nonlinear programming</subject><subject>Numerical Analysis</subject><subject>Numerical and Computational Physics</subject><subject>Operators (mathematics)</subject><subject>Simulation</subject><subject>Singular integral equations</subject><subject>Theoretical</subject><subject>Three dimensional models</subject><subject>Two dimensional models</subject><issn>0029-599X</issn><issn>0945-3245</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><recordid>eNp1kEtLAzEUhYMoWKs_wF3A9ei9k2Qey1pqFepjoeAupGmiU6bNmKTV_ntTR3Dl6p4L5zscDiHnCJcIUF4FgBwxA6wyhCTwgAyg5iJjOReHSUNeZ6KuX4_JSQhLACwLjgPyMFqoLjZbQ68n9_Szie-0WZsvpSN9Gk9pcO3WeLprTLsIVLUrFyJ1CViplmq36jZRxcatf74Qwyk5sqoN5uz3DsnLzeR5fJvNHqd349Es00zUMRPCVGh4YSvkpsixXFQ1VoIzhZxrweagrM6RKatQo-VJGi6AFXauKmCaDclFn9t597ExIcql2_hUI8gcU1TBS6iSC3uX9i4Eb6zsfGrudxJB7meT_WwyzSb3s0lMTN4zIXnXb8b_Jf8PfQMdb26q</recordid><startdate>20190403</startdate><enddate>20190403</enddate><creator>Führer, Thomas</creator><creator>Haberl, Alexander</creator><creator>Praetorius, Dirk</creator><creator>Schimanko, Stefan</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20190403</creationdate><title>Adaptive BEM with inexact PCG solver yields almost optimal computational costs</title><author>Führer, Thomas ; Haberl, Alexander ; Praetorius, Dirk ; Schimanko, Stefan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c359t-55e81e46f814e6217d8918543a144c53b0afc213afa1c1f4213e45036fba803c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Adaptive algorithms</topic><topic>Boundary element method</topic><topic>Complexity</topic><topic>Computation</topic><topic>Conjugate gradient method</topic><topic>Elliptic functions</topic><topic>Finite element method</topic><topic>Integral equations</topic><topic>Mathematical analysis</topic><topic>Mathematical and Computational Engineering</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical Methods in Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Nonlinear programming</topic><topic>Numerical Analysis</topic><topic>Numerical and Computational Physics</topic><topic>Operators (mathematics)</topic><topic>Simulation</topic><topic>Singular integral equations</topic><topic>Theoretical</topic><topic>Three dimensional models</topic><topic>Two dimensional models</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Führer, Thomas</creatorcontrib><creatorcontrib>Haberl, Alexander</creatorcontrib><creatorcontrib>Praetorius, Dirk</creatorcontrib><creatorcontrib>Schimanko, Stefan</creatorcontrib><collection>Springer Nature OA/Free Journals</collection><collection>CrossRef</collection><jtitle>Numerische Mathematik</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Führer, Thomas</au><au>Haberl, Alexander</au><au>Praetorius, Dirk</au><au>Schimanko, Stefan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Adaptive BEM with inexact PCG solver yields almost optimal computational costs</atitle><jtitle>Numerische Mathematik</jtitle><stitle>Numer. Math</stitle><date>2019-04-03</date><risdate>2019</risdate><volume>141</volume><issue>4</issue><spage>967</spage><epage>1008</epage><pages>967-1008</pages><issn>0029-599X</issn><eissn>0945-3245</eissn><abstract>We consider the preconditioned conjugate gradient method (PCG) with optimal preconditioner in the frame of the boundary element method for elliptic first-kind integral equations. Our adaptive algorithm steers the termination of PCG as well as the local mesh-refinement. Besides convergence with optimal algebraic rates, we also prove almost optimal computational complexity. In particular, we provide an additive Schwarz preconditioner which can be computed in linear complexity and which is optimal in the sense that the condition numbers of the preconditioned systems are uniformly bounded. As model problem serves the 2D or 3D Laplace operator and the associated weakly-singular integral equation with energy space
H
~
-
1
/
2
(
Γ
)
. The main results also hold for the hyper-singular integral equation with energy space
H
1
/
2
(
Γ
)
.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00211-018-1011-1</doi><tpages>42</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0029-599X |
| ispartof | Numerische Mathematik, 2019-04, Vol.141 (4), p.967-1008 |
| issn | 0029-599X 0945-3245 |
| language | eng |
| recordid | cdi_proquest_journals_2191864708 |
| source | Springer Online Journals Complete |
| subjects | Adaptive algorithms Boundary element method Complexity Computation Conjugate gradient method Elliptic functions Finite element method Integral equations Mathematical analysis Mathematical and Computational Engineering Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Nonlinear programming Numerical Analysis Numerical and Computational Physics Operators (mathematics) Simulation Singular integral equations Theoretical Three dimensional models Two dimensional models |
| title | Adaptive BEM with inexact PCG solver yields almost optimal computational costs |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-26T15%3A57%3A24IST&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=Adaptive%20BEM%20with%20inexact%20PCG%20solver%20yields%20almost%20optimal%20computational%20costs&rft.jtitle=Numerische%20Mathematik&rft.au=F%C3%BChrer,%20Thomas&rft.date=2019-04-03&rft.volume=141&rft.issue=4&rft.spage=967&rft.epage=1008&rft.pages=967-1008&rft.issn=0029-599X&rft.eissn=0945-3245&rft_id=info:doi/10.1007/s00211-018-1011-1&rft_dat=%3Cproquest_cross%3E2191864708%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=2191864708&rft_id=info:pmid/&rfr_iscdi=true |