Please use this identifier to cite or link to this item: https://doi.org/10.15480/882.4310
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dc.contributor.authorGander, Martin J.-
dc.contributor.authorLunet, Thibaut-
dc.contributor.authorRuprecht, Daniel-
dc.contributor.authorSpeck, Robert-
dc.date.accessioned2022-04-26T16:18:22Z-
dc.date.available2022-04-26T16:18:22Z-
dc.date.issued2022-03-30-
dc.identifier.citationarXiv: 2203.16069v1 (2022)de_DE
dc.identifier.urihttp://hdl.handle.net/11420/12370-
dc.description.abstractParallel-in-time integration has been the focus of intensive research efforts over the past two decades due to the advent of massively parallel computer architectures and the scaling limits of purely spatial parallelization. Various iterative parallel-in-time (PinT) algorithms have been proposed, like Parareal, PFASST, MGRIT, and Space-Time Multi-Grid (STMG). These methods have been described using different notations and the convergence estimates that are available for some of them are difficult to compare. We describe Parareal, PFASST, MGRIT and STMG for the Dahlquist model problem using a common notation and give precise convergence estimates using generating functions. This allows us, for the first time, to directly compare their convergence. We prove that all four methods eventually converge super-linearly and compare them directly numerically. Our framework also allows us to find new methods.en
dc.description.sponsorshipBundesministerium für Bildung und Forschung (BMBF)de_DE
dc.description.sponsorshipEuropean High-Performance Computing Joint Undertaking (JU)de_DE
dc.language.isoende_DE
dc.rightsCopyrightde_DE
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/de_DE
dc.subjectMathematics - Numerical Analysisde_DE
dc.subjectMathematics - Numerical Analysisde_DE
dc.subjectComputer Science - Computational Engineering; Finance; and Sciencede_DE
dc.subjectComputer Science - Numerical Analysisde_DE
dc.subject.ddc510: Mathematikde_DE
dc.titleA unified analysis framework for iterative parallel-in-time algorithmsde_DE
dc.typeArticlede_DE
dc.identifier.doi10.15480/882.4310-
dc.type.diniarticle-
dcterms.DCMITypeText-
tuhh.identifier.urnurn:nbn:de:gbv:830-882.0181837-
tuhh.oai.showtruede_DE
tuhh.abstract.englishParallel-in-time integration has been the focus of intensive research efforts over the past two decades due to the advent of massively parallel computer architectures and the scaling limits of purely spatial parallelization. Various iterative parallel-in-time (PinT) algorithms have been proposed, like Parareal, PFASST, MGRIT, and Space-Time Multi-Grid (STMG). These methods have been described using different notations and the convergence estimates that are available for some of them are difficult to compare. We describe Parareal, PFASST, MGRIT and STMG for the Dahlquist model problem using a common notation and give precise convergence estimates using generating functions. This allows us, for the first time, to directly compare their convergence. We prove that all four methods eventually converge super-linearly and compare them directly numerically. Our framework also allows us to find new methods.de_DE
tuhh.publication.instituteMathematik E-10de_DE
tuhh.identifier.doi10.15480/882.4310-
tuhh.type.opus(wissenschaftlicher) Artikel-
dc.type.driverarticle-
dc.type.casraiJournal Article-
dc.relation.projectTIME parallelisation: for eXascale computing and beyondde_DE
dc.relation.projectHorizonde_DE
dc.rights.nationallicensefalsede_DE
dc.identifier.arxiv2203.16069v1de_DE
local.status.inpressfalsede_DE
local.funding.infoThis project has received funding from the European High-Performance Computing Joint Undertaking (JU) under grant agreement No 955701. The JU receives support from the European Union's Horizon 2020 research and innovation programme and Belgium, France, Germany, and Switzerland. This project also received funding from the German Federal Ministry of Education and Research (BMBF) grant 16HPC048.de_DE
datacite.resourceTypeJournal Article-
datacite.resourceTypeGeneralText-
item.languageiso639-1en-
item.grantfulltextopen-
item.creatorOrcidGander, Martin J.-
item.creatorOrcidLunet, Thibaut-
item.creatorOrcidRuprecht, Daniel-
item.creatorOrcidSpeck, Robert-
item.mappedtypeArticle-
item.creatorGNDGander, Martin J.-
item.creatorGNDLunet, Thibaut-
item.creatorGNDRuprecht, Daniel-
item.creatorGNDSpeck, Robert-
item.fulltextWith Fulltext-
item.openairetypeArticle-
item.openairecristypehttp://purl.org/coar/resource_type/c_6501-
item.cerifentitytypePublications-
crisitem.author.deptMathematik E-10-
crisitem.author.deptMathematik E-10-
crisitem.author.orcid0000-0003-1904-2473-
crisitem.author.orcid0000-0002-3879-1210-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik-
crisitem.funder.funderid501100002347-
crisitem.funder.funderrorid04pz7b180-
crisitem.project.funderEuropean Commission-
crisitem.project.funderid501100000780-
crisitem.project.funderrorid00k4n6c32-
crisitem.project.grantnoGA 955701-
crisitem.project.fundingProgramH2020-
crisitem.project.openAireinfo:eu-repo/grantAgreement/EC/H2020/955701-
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