DC FieldValueLanguage
dc.contributor.authorAhrens, Robin-
dc.contributor.authorLe Borne, Sabine-
dc.date.accessioned2020-11-16T07:54:54Z-
dc.date.available2020-11-16T07:54:54Z-
dc.date.issued2020-03-13-
dc.identifier.citationApplied Numerical Mathematics (153): 473-491 (2020)de_DE
dc.identifier.issn0168-9274de_DE
dc.identifier.urihttp://hdl.handle.net/11420/7839-
dc.description.abstract© 2020 IMACS We consider the numerical solution of the multivariate aggregation population balance equation on a uniform tensor grid. This class of equations is numerically challenging to solve - the computational complexity of “straightforward” algorithms grows exponentially with respect to the number of internal coordinates describing particle properties. Here, we develop algorithms which reduce the storage and computational complexity to almost linear order, O(dn) and O(dnlog⁡(n)), respectively, where d denotes the number of internal coordinates and n the number of pivots per internal coordinate. In particular, we develop fast algorithms in tensor train format to evaluate the multidimensional aggregation integral exploiting fast Fourier transformation for the underlying convolution. A further significant result lies in the conservation of the first 2d moments for our proposed method. Numerical tests confirm the favorable theoretical results concerning computational complexity and conservation of moments.en
dc.language.isoende_DE
dc.publisherElsevierde_DE
dc.relation.ispartofApplied numerical mathematicsde_DE
dc.subjectFFTde_DE
dc.subjectMoment conservationde_DE
dc.subjectMultivariate convolutionde_DE
dc.subjectPopulation balance equationde_DE
dc.subjectTensor trainsde_DE
dc.subject.ddc510: Mathematikde_DE
dc.titleTensor trains and moment conservation for multivariate aggregation in population balance modelingde_DE
dc.typeArticlede_DE
dc.type.diniarticle-
dcterms.DCMITypeText-
tuhh.abstract.english© 2020 IMACS We consider the numerical solution of the multivariate aggregation population balance equation on a uniform tensor grid. This class of equations is numerically challenging to solve - the computational complexity of “straightforward” algorithms grows exponentially with respect to the number of internal coordinates describing particle properties. Here, we develop algorithms which reduce the storage and computational complexity to almost linear order, O(dn) and O(dnlog⁡(n)), respectively, where d denotes the number of internal coordinates and n the number of pivots per internal coordinate. In particular, we develop fast algorithms in tensor train format to evaluate the multidimensional aggregation integral exploiting fast Fourier transformation for the underlying convolution. A further significant result lies in the conservation of the first 2d moments for our proposed method. Numerical tests confirm the favorable theoretical results concerning computational complexity and conservation of moments.de_DE
tuhh.publisher.doi10.1016/j.apnum.2020.03.002-
tuhh.publication.instituteMathematik E-10de_DE
tuhh.type.opus(wissenschaftlicher) Artikel-
dc.type.driverarticle-
dc.type.casraiJournal Article-
tuhh.container.issueJulyde_DE
tuhh.container.volume153de_DE
tuhh.container.startpage473de_DE
tuhh.container.endpage491de_DE
dc.identifier.scopus2-s2.0-85081656716de_DE
local.status.inpressfalsede_DE
datacite.resourceTypeJournal Article-
datacite.resourceTypeGeneralText-
item.openairetypeArticle-
item.openairecristypehttp://purl.org/coar/resource_type/c_6501-
item.fulltextNo Fulltext-
item.languageiso639-1en-
item.grantfulltextnone-
item.mappedtypeArticle-
item.cerifentitytypePublications-
item.creatorGNDAhrens, Robin-
item.creatorGNDLe Borne, Sabine-
item.creatorOrcidAhrens, Robin-
item.creatorOrcidLe Borne, Sabine-
crisitem.author.deptMathematik E-10-
crisitem.author.deptMathematik E-10-
crisitem.author.orcid0000-0003-0473-408X-
crisitem.author.orcid0000-0002-4399-4442-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik (E)-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik (E)-
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