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dc.contributor.authorMohamed, Mamdouh S.
dc.contributor.authorHirani, Anil N.
dc.contributor.authorSamtaney, Ravi
dc.date.accessioned2016-05-11T07:40:52Z
dc.date.available2016-05-11T07:40:52Z
dc.date.issued2016-05-10
dc.identifier.citationComparison of discrete Hodge star operators for surfaces 2016 Computer-Aided Design
dc.identifier.issn00104485
dc.identifier.doi10.1016/j.cad.2016.05.002
dc.identifier.urihttp://hdl.handle.net/10754/609008
dc.description.abstractWe investigate the performance of various discrete Hodge star operators for discrete exterior calculus (DEC) using circumcentric and barycentric dual meshes. The performance is evaluated through the DEC solution of Darcy and incompressible Navier–Stokes flows over surfaces. While the circumcentric Hodge operators may be favorable due to their diagonal structure, the barycentric (geometric) and the Galerkin Hodge operators have the advantage of admitting arbitrary simplicial meshes. Numerical experiments reveal that the barycentric and the Galerkin Hodge operators retain the numerical convergence order attained through the circumcentric (diagonal) Hodge operators. Furthermore, when the barycentric or the Galerkin Hodge operators are employed, a super-convergence behavior is observed for the incompressible flow solution over unstructured simplicial surface meshes generated by successive subdivision of coarser meshes. Insofar as the computational cost is concerned, the Darcy flow solutions exhibit a moderate increase in the solution time when using the barycentric or the Galerkin Hodge operators due to a modest decrease in the linear system sparsity. On the other hand, for the incompressible flow simulations, both the solution time and the linear system sparsity do not change for either the circumcentric or the barycentric and the Galerkin Hodge operators.
dc.description.sponsorshipThis research was supported by the KAUST Office of Competitive Research Funds under Award No. URF/1/1401-01-01. The work of ANH was supported in part by NSF Grant No. CCF-1064429.
dc.language.isoen
dc.publisherElsevier BV
dc.relation.urlhttp://linkinghub.elsevier.com/retrieve/pii/S0010448516300227
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Computer-Aided Design. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computer-Aided Design, 10 May 2016. DOI: 10.1016/j.cad.2016.05.002
dc.subjectDiscrete exterior calculus (DEC)
dc.subjectHodge star
dc.subjectCircumcentric dual
dc.subjectBarycentric dual
dc.titleComparison of discrete Hodge star operators for surfaces
dc.typeArticle
dc.contributor.departmentMechanical Engineering Program
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Division
dc.identifier.journalComputer-Aided Design
dc.eprint.versionPost-print
dc.contributor.institutionDepartment of Mathematics, University of Illinois at Urbana-Champaign, IL, USA
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)
kaust.personMohamed, Mamdouh S.
kaust.personSamtaney, Ravi
refterms.dateFOA2018-05-10T00:00:00Z


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