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dc.contributor.authorLohi, Jonni
dc.date.accessioned2022-04-26T07:47:42Z
dc.date.available2022-04-26T07:47:42Z
dc.date.issued2022
dc.identifier.citationLohi, J. (2022). Systematic implementation of higher order Whitney forms in methods based on discrete exterior calculus. <i>Numerical Algorithms</i>, <i>91</i>(3), 1261-1285. <a href="https://doi.org/10.1007/s11075-022-01301-2" target="_blank">https://doi.org/10.1007/s11075-022-01301-2</a>
dc.identifier.otherCONVID_117817060
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/80716
dc.description.abstractWe present a systematic way to implement higher order Whitney forms in numerical methods based on discrete exterior calculus. Given a simplicial mesh, we first refine the mesh into smaller simplices which can be used to define higher order Whitney forms. Cochains on this refined mesh can then be interpolated using higher order Whitney forms. Hence, when the refined mesh is used with methods based on discrete exterior calculus, the solution can be expressed as a higher order Whitney form. We present algorithms for the three required steps: refining the mesh, solving the coefficients of the interpolant, and evaluating the interpolant at a given point. With our algorithms, the order of the Whitney forms one wishes to use can be given as a parameter so that the same code covers all orders, which is a significant improvement on previous implementations. Our algorithms are applicable with all methods in which the degrees of freedom are integrals over mesh simplices — that is, when the solution is a cochain on a simplicial mesh. They can also be used when one simply wishes to approximate differential forms in finite-dimensional spaces. Numerical examples validate the generality of our algorithms.en
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherSpringer
dc.relation.ispartofseriesNumerical Algorithms
dc.rightsCC BY 4.0
dc.subject.otherhigher order Whitney forms
dc.subject.othercochains
dc.subject.otherdifferential forms
dc.subject.otherinterpolation
dc.subject.otherdiscrete exterior calculus
dc.subject.othersimplicial mesh
dc.titleSystematic implementation of higher order Whitney forms in methods based on discrete exterior calculus
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-202204262391
dc.contributor.laitosInformaatioteknologian tiedekuntafi
dc.contributor.laitosFaculty of Information Technologyen
dc.contributor.oppiaineLaskennallinen tiedefi
dc.contributor.oppiaineComputing, Information Technology and Mathematicsfi
dc.contributor.oppiaineComputational Scienceen
dc.contributor.oppiaineComputing, Information Technology and Mathematicsen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.type.coarhttp://purl.org/coar/resource_type/c_2df8fbb1
dc.description.reviewstatuspeerReviewed
dc.format.pagerange1261-1285
dc.relation.issn1017-1398
dc.relation.numberinseries3
dc.relation.volume91
dc.type.versionpublishedVersion
dc.rights.copyright© 2022 the Authors
dc.rights.accesslevelopenAccessfi
dc.subject.ysodiskreetti matematiikka
dc.subject.ysodifferentiaalilaskenta
dc.subject.ysointerpolointi
dc.subject.ysoosittaisdifferentiaaliyhtälöt
dc.subject.ysonumeeriset menetelmät
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p27156
jyx.subject.urihttp://www.yso.fi/onto/yso/p7856
jyx.subject.urihttp://www.yso.fi/onto/yso/p14376
jyx.subject.urihttp://www.yso.fi/onto/yso/p12392
jyx.subject.urihttp://www.yso.fi/onto/yso/p6588
dc.rights.urlhttps://creativecommons.org/licenses/by/4.0/
dc.relation.doi10.1007/s11075-022-01301-2
jyx.fundinginformationOpen Access funding provided by University of Jyväskylä (JYU). University of Jyväskylä.
dc.type.okmA1


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