Multiplicative Schwarz algorithms for the p-version Galerkin boundary element method in 3D
We study a 2-level multiplicative Schwarz method for the p version Galerkin boundary element method for a weakly singular integral equation of the first kind in 3D. We prove that the rate of convergence of the multiplicative Schwarz operator for the p version grows only logarithmically in p and is i...
Saved in:
| Published in: | Applied numerical mathematics Vol. 56; no. 10; pp. 1370 - 1382 |
|---|---|
| Main Author: | |
| Format: | Journal Article Conference Proceeding |
| Language: | English |
| Published: |
Amsterdam
Elsevier B.V
01.10.2006
Elsevier |
| Subjects: | |
| ISSN: | 0168-9274, 1873-5460 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | We study a 2-level multiplicative Schwarz method for the
p version Galerkin boundary element method for a weakly singular integral equation of the first kind in 3D. We prove that the rate of convergence of the multiplicative Schwarz operator for the
p version grows only logarithmically in
p and is independent of
h. |
|---|---|
| AbstractList | We study a 2-level multiplicative Schwarz method for the
p version Galerkin boundary element method for a weakly singular integral equation of the first kind in 3D. We prove that the rate of convergence of the multiplicative Schwarz operator for the
p version grows only logarithmically in
p and is independent of
h. |
| Author | Maischak, Matthias |
| Author_xml | – sequence: 1 givenname: Matthias surname: Maischak fullname: Maischak, Matthias email: maischak@ifam.uni-hannover.de organization: Institut für Angewandte Mathematik, University of Hannover, Germany |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=18041693$$DView record in Pascal Francis |
| BookMark | eNp9kD1PxDAMhiMEEsfHL2DJwtjiNL2kHRgQ3xKIAVhYojRxuBxtWiW9Q_DrKRwSG5Mt-Xkt-9kj26EPSMgRg5wBEyfLXA9h1eUFgMiB58DqLTJjleTZvBSwTWYTVWV1IctdspfSEgDm8xJm5OV-1Y5-aL3Ro18jfTSLdx0_qW5f--jHRZeo6yMdF0iHbI0x-T7Qa91ifPOBNv0qWB0_KLbYYRhph-Oit3Qa8YsDsuN0m_Dwt-6T56vLp_Ob7O7h-vb87C4zRcXHjDtbCwDtQGDRCGAll01lpSwEE1PPGmutQ1tL4URleWlBVk6zhjkmZVPwfXK82TvoZHTrog7GJzVE302nKVZByUTNJ45vOBP7lCK6PwTUt0a1VD8a1bdGBVxNGqfU6SaF0wtrj1El4zEYtD6iGZXt_b_5L0JRfvM |
| CODEN | ANMAEL |
| Cites_doi | 10.1090/S0025-5718-1991-1090464-8 10.1007/s002110000125 10.1216/jiea/1181075334 10.1007/s002119900082 10.1137/S0036142997323983 10.1007/s211-001-8012-7 10.1137/1034116 10.1137/0519043 10.1216/jiea/1181075956 |
| ContentType | Journal Article Conference Proceeding |
| Copyright | 2006 IMACS 2006 INIST-CNRS |
| Copyright_xml | – notice: 2006 IMACS – notice: 2006 INIST-CNRS |
| DBID | AAYXX CITATION IQODW |
| DOI | 10.1016/j.apnum.2006.03.019 |
| DatabaseName | CrossRef Pascal-Francis |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences Mathematics |
| EISSN | 1873-5460 |
| EndPage | 1382 |
| ExternalDocumentID | 18041693 10_1016_j_apnum_2006_03_019 S0168927406000705 |
| GroupedDBID | --K --M -~X .DC .~1 0R~ 1B1 1RT 1~. 1~5 23M 4.4 457 4G. 5GY 5VS 7-5 71M 8P~ 9JN AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXUO ABAOU ABEFU ABJNI ABMAC ABXDB ABYKQ ACAZW ACDAQ ACGFS ACRLP ADBBV ADEZE ADGUI ADIYS ADMUD AEBSH AEKER AENEX AFFNX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AI. AIEXJ AIGVJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ARUGR ASPBG AVWKF AXJTR AZFZN BKOJK BLXMC CS3 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q GBLVA HMJ HVGLF HZ~ IHE J1W KOM M26 M41 MHUIS MO0 N9A O-L O9- OAUVE OZT P-8 P-9 P2P PC. Q38 R2- RIG RNS ROL RPZ SDF SDG SDP SES SEW SME SPC SPCBC SSW SSZ T5K TN5 VH1 VOH WH7 WUQ XPP ZMT ~02 ~G- 9DU AATTM AAXKI AAYWO AAYXX ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO AEIPS AEUPX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP CITATION EFKBS ~HD ABPIF ABPTK IQODW |
| ID | FETCH-LOGICAL-c283t-3fd9600af06e2b601437b8d7726164371bdddfed976f68d34d078fa1b1f177b23 |
| ISICitedReferencesCount | 0 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000239513800011&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0168-9274 |
| IngestDate | Sun Oct 22 16:09:44 EDT 2023 Sat Nov 29 02:29:43 EST 2025 Fri Feb 23 02:32:55 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 10 |
| Keywords | Multiplicative Schwarz operator Preconditioned conjugate gradient algorithm 65N55 p-version boundary integral equation method 65N38 Conjugate gradient method Convergence acceleration Singular equation Schwarz method Numerical analysis Applied mathematics First integral Convergence rate Galerkin method Preconditioning Boundary element method Boundary integral equations |
| Language | English |
| License | https://www.elsevier.com/tdm/userlicense/1.0 CC BY 4.0 |
| LinkModel | OpenURL |
| MeetingName | Selected papers from the First Chilean Workshop on Numerical Analysis of Partial Differential Equations (WONAPDE 2004) |
| MergedId | FETCHMERGED-LOGICAL-c283t-3fd9600af06e2b601437b8d7726164371bdddfed976f68d34d078fa1b1f177b23 |
| PageCount | 13 |
| ParticipantIDs | pascalfrancis_primary_18041693 crossref_primary_10_1016_j_apnum_2006_03_019 elsevier_sciencedirect_doi_10_1016_j_apnum_2006_03_019 |
| PublicationCentury | 2000 |
| PublicationDate | 2006-10-01 |
| PublicationDateYYYYMMDD | 2006-10-01 |
| PublicationDate_xml | – month: 10 year: 2006 text: 2006-10-01 day: 01 |
| PublicationDecade | 2000 |
| PublicationPlace | Amsterdam |
| PublicationPlace_xml | – name: Amsterdam |
| PublicationTitle | Applied numerical mathematics |
| PublicationYear | 2006 |
| Publisher | Elsevier B.V Elsevier |
| Publisher_xml | – name: Elsevier B.V – name: Elsevier |
| References | Heuer (bib005) 1996; 8 Bergh, Löfström (bib001) 1976; vol. 223 Bramble, Pasciak, Wang, Xu (bib003) 1991; 57 Heuer (bib006) 2001; 88 Stephan, Suri (bib011) 1989; 52 Stephan, Tran (bib012) 2000; 85 Xu (bib013) 1992; 34 Maischak, Stephan, Tran (bib010) 2000; 38 Heuer, Maischak, Stephan (bib007) 1999; 83 Bespalov, Heuer (bib002) 2005; 17 M. Maischak, Manual of the software package maiprogs, Technical report ifam48, Institut für Angewandte Mathematik, Universität Hannover, 2001. ftp://ftp.ifam/uni-hannover.de/pub/preprints/ifam48.ps.Z Maischak, Stephan, Tran (bib009) 1997; 63 Costabel (bib004) 1988; 19 Maischak (10.1016/j.apnum.2006.03.019_bib009) 1997; 63 Maischak (10.1016/j.apnum.2006.03.019_bib010) 2000; 38 Bramble (10.1016/j.apnum.2006.03.019_bib003) 1991; 57 Stephan (10.1016/j.apnum.2006.03.019_bib012) 2000; 85 Costabel (10.1016/j.apnum.2006.03.019_bib004) 1988; 19 Stephan (10.1016/j.apnum.2006.03.019_bib011) 1989; 52 Bespalov (10.1016/j.apnum.2006.03.019_bib002) 2005; 17 Heuer (10.1016/j.apnum.2006.03.019_bib006) 2001; 88 Xu (10.1016/j.apnum.2006.03.019_bib013) 1992; 34 Bergh (10.1016/j.apnum.2006.03.019_bib001) 1976; vol. 223 Heuer (10.1016/j.apnum.2006.03.019_bib007) 1999; 83 10.1016/j.apnum.2006.03.019_bib008 Heuer (10.1016/j.apnum.2006.03.019_bib005) 1996; 8 |
| References_xml | – volume: 52 start-page: 31 year: 1989 end-page: 48 ident: bib011 article-title: On the convergence of the publication-title: Math. Comp. – reference: M. Maischak, Manual of the software package maiprogs, Technical report ifam48, Institut für Angewandte Mathematik, Universität Hannover, 2001. ftp://ftp.ifam/uni-hannover.de/pub/preprints/ifam48.ps.Z – volume: 17 start-page: 243 year: 2005 end-page: 258 ident: bib002 article-title: The publication-title: J. Integral Equations Appl. – volume: 83 start-page: 641 year: 1999 end-page: 666 ident: bib007 article-title: Exponential convergence of the publication-title: Numer. Math. – volume: 85 start-page: 433 year: 2000 end-page: 468 ident: bib012 article-title: Additive Schwartz algorithms for the publication-title: Numer. Math. – volume: 57 start-page: 1 year: 1991 end-page: 21 ident: bib003 article-title: Convergence estimates for product iterative methods with applications to domain decomposition publication-title: Math. Comp. – volume: 88 start-page: 485 year: 2001 end-page: 511 ident: bib006 article-title: Additive Schwartz method for the publication-title: Numer. Math. – volume: 38 start-page: 1243 year: 2000 end-page: 1268 ident: bib010 article-title: Multiplicative Schwarz algorithms for the Galerkin boundary element method publication-title: SIAM J. Numer. Anal. – volume: 19 start-page: 613 year: 1988 end-page: 626 ident: bib004 article-title: Boundary integral operators on Lipschitz domains: Elementary results publication-title: SIAM J. Math. Anal. – volume: 8 start-page: 337 year: 1996 end-page: 361 ident: bib005 article-title: Efficient algorithms for the publication-title: J. Integral Equations Appl. – volume: 34 start-page: 581 year: 1992 end-page: 613 ident: bib013 article-title: Iterative methods by space decomposition and subspace correction publication-title: SIAM Review – volume: 63 start-page: 111 year: 1997 end-page: 132 ident: bib009 article-title: Domain decomposition for integral equations of the first kind: Numerical results publication-title: Appl. Anal. – volume: vol. 223 year: 1976 ident: bib001 article-title: Interpolation Spaces publication-title: Grundlehren der mathematischen Wissenschaften – volume: 57 start-page: 1 year: 1991 ident: 10.1016/j.apnum.2006.03.019_bib003 article-title: Convergence estimates for product iterative methods with applications to domain decomposition publication-title: Math. Comp. doi: 10.1090/S0025-5718-1991-1090464-8 – volume: 85 start-page: 433 year: 2000 ident: 10.1016/j.apnum.2006.03.019_bib012 article-title: Additive Schwartz algorithms for the p version of the Galerkin boundary element method publication-title: Numer. Math. doi: 10.1007/s002110000125 – volume: 17 start-page: 243 issue: 3 year: 2005 ident: 10.1016/j.apnum.2006.03.019_bib002 article-title: The p-version of the boundary element method for a three-dimensional crack problem publication-title: J. Integral Equations Appl. doi: 10.1216/jiea/1181075334 – volume: 83 start-page: 641 year: 1999 ident: 10.1016/j.apnum.2006.03.019_bib007 article-title: Exponential convergence of the hp-version for the boundary element method on open surfaces publication-title: Numer. Math. doi: 10.1007/s002119900082 – volume: 38 start-page: 1243 year: 2000 ident: 10.1016/j.apnum.2006.03.019_bib010 article-title: Multiplicative Schwarz algorithms for the Galerkin boundary element method publication-title: SIAM J. Numer. Anal. doi: 10.1137/S0036142997323983 – volume: 88 start-page: 485 year: 2001 ident: 10.1016/j.apnum.2006.03.019_bib006 article-title: Additive Schwartz method for the p-version of the boundary element method for the single layer potential operator on a plane screen publication-title: Numer. Math. doi: 10.1007/s211-001-8012-7 – volume: 34 start-page: 581 year: 1992 ident: 10.1016/j.apnum.2006.03.019_bib013 article-title: Iterative methods by space decomposition and subspace correction publication-title: SIAM Review doi: 10.1137/1034116 – volume: 63 start-page: 111 year: 1997 ident: 10.1016/j.apnum.2006.03.019_bib009 article-title: Domain decomposition for integral equations of the first kind: Numerical results publication-title: Appl. Anal. – volume: 19 start-page: 613 issue: 3 year: 1988 ident: 10.1016/j.apnum.2006.03.019_bib004 article-title: Boundary integral operators on Lipschitz domains: Elementary results publication-title: SIAM J. Math. Anal. doi: 10.1137/0519043 – volume: 8 start-page: 337 year: 1996 ident: 10.1016/j.apnum.2006.03.019_bib005 article-title: Efficient algorithms for the p-version of the boundary element method publication-title: J. Integral Equations Appl. doi: 10.1216/jiea/1181075956 – volume: vol. 223 year: 1976 ident: 10.1016/j.apnum.2006.03.019_bib001 article-title: Interpolation Spaces – volume: 52 start-page: 31 year: 1989 ident: 10.1016/j.apnum.2006.03.019_bib011 article-title: On the convergence of the p-version for some boundary element Galerkin methods publication-title: Math. Comp. – ident: 10.1016/j.apnum.2006.03.019_bib008 |
| SSID | ssj0005540 |
| Score | 1.7353879 |
| Snippet | We study a 2-level multiplicative Schwarz method for the
p version Galerkin boundary element method for a weakly singular integral equation of the first kind... |
| SourceID | pascalfrancis crossref elsevier |
| SourceType | Index Database Publisher |
| StartPage | 1370 |
| SubjectTerms | Exact sciences and technology Mathematics Multiplicative Schwarz operator Numerical analysis Numerical analysis. Scientific computation p-version boundary integral equation method Partial differential equations, boundary value problems Preconditioned conjugate gradient algorithm Sciences and techniques of general use |
| Title | Multiplicative Schwarz algorithms for the p-version Galerkin boundary element method in 3D |
| URI | https://dx.doi.org/10.1016/j.apnum.2006.03.019 |
| Volume | 56 |
| WOSCitedRecordID | wos000239513800011&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1873-5460 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0005540 issn: 0168-9274 databaseCode: AIEXJ dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3db9MwELdg44EJCRhDjI_JD7yVVHGcOc5jNYY2oNMkhlTxEtl1zDqNrGqzbuKv55yzk3YbIB54iaq0aRTfL3fn-_gdIW8Zt1okioMEYIuSmjSPVCrjSIFtYlxay3TDrv85OzqSo1F-7FMx82acQFZV8vo6n_5XUcM5ELZrnf0Hcbd_CifgMwgdjiB2ON4W_J32J3iW1SWmY857P1py1vkyRoZYTdiE7RYNI-eVmv3sqfPvF7NJfYpcDdhMFS0wsNZzFsXF13u6GcjkenmxAt0Po3YBFN6WEQ8Hh1_2DgafsC2ork8n6magIZSs-eiXN9XLwUgByjLBKTv9EhWozFyxBc4ICBoWqcMDkuLIq1dUmYzj5BBvfh0n4p2qHaMMZ301hdXzWSTej73CXSHSvmHg2rJD5siWRM7vk_WECwl79fXB4f7oY1cTtNt00LYPFmiqmoLAWzf-nSvzaKrmIFuLk1GW3JWTJ2Sra-Skxy1EnpJ7ZbVJHnt8UK_X55tkY9gB5Bn5tooL6nFBO1xQwAWFK2iLCxpwQQMuqMcFRVxQ-Iq_3yJfP-yf7B1EfgZHNAbHs464NbDHjZWNRZlo4dggMy0N7MkEczlfpo0xtjTg1VohDU8NvPNWMc0syzKd8OdkrbqoyheEWlHKVEsNLqtLN-_K0nIzzl3VQJKzXG6Td2E5iylSrRShBvGsaFbfDU0VRcwLWP1tIsKSF95bRC-wAMT8-cKdFQF1N_PwePm3H7wiD7sX5DVZq2eX5RvyYLyoJ_PZjgfVLxxqlB8 |
| linkProvider | Elsevier |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=proceeding&rft.title=Applied+numerical+mathematics&rft.atitle=Multiplicative+Schwarz+algorithms+for+the+p-version+galerkin+boundary+element+method+in+3D&rft.au=MAISCHAK%2C+Matthias&rft.date=2006-10-01&rft.pub=Elsevier&rft.issn=0168-9274&rft.eissn=1873-5460&rft.volume=56&rft.issue=10-11&rft.spage=1370&rft.epage=1382&rft_id=info:doi/10.1016%2Fj.apnum.2006.03.019&rft.externalDBID=n%2Fa&rft.externalDocID=18041693 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0168-9274&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0168-9274&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0168-9274&client=summon |