Comparison of discrete Hodge star operators for surfaces

Handle URI:
http://hdl.handle.net/10754/609008
Title:
Comparison of discrete Hodge star operators for surfaces
Authors:
Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi ( 0000-0002-4702-6473 )
Abstract:
We 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.
KAUST Department:
Mechanical Engineering Program; Physical Sciences and Engineering (PSE) Division
Citation:
Comparison of discrete Hodge star operators for surfaces 2016 Computer-Aided Design
Publisher:
Elsevier BV
Journal:
Computer-Aided Design
Issue Date:
10-May-2016
DOI:
10.1016/j.cad.2016.05.002
Type:
Article
ISSN:
00104485
Sponsors:
This 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.
Additional Links:
http://linkinghub.elsevier.com/retrieve/pii/S0010448516300227
Appears in Collections:
Articles; Physical Sciences and Engineering (PSE) Division; Mechanical Engineering Program

Full metadata record

DC FieldValue Language
dc.contributor.authorMohamed, Mamdouh S.en
dc.contributor.authorHirani, Anil N.en
dc.contributor.authorSamtaney, Ravien
dc.date.accessioned2016-05-11T07:40:52Zen
dc.date.available2016-05-11T07:40:52Zen
dc.date.issued2016-05-10en
dc.identifier.citationComparison of discrete Hodge star operators for surfaces 2016 Computer-Aided Designen
dc.identifier.issn00104485en
dc.identifier.doi10.1016/j.cad.2016.05.002en
dc.identifier.urihttp://hdl.handle.net/10754/609008en
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.en
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.en
dc.language.isoenen
dc.publisherElsevier BVen
dc.relation.urlhttp://linkinghub.elsevier.com/retrieve/pii/S0010448516300227en
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.2016.05.002en
dc.subjectDiscrete exterior calculus (DEC)en
dc.subjectHodge staren
dc.subjectCircumcentric dualen
dc.subjectBarycentric dualen
dc.titleComparison of discrete Hodge star operators for surfacesen
dc.typeArticleen
dc.contributor.departmentMechanical Engineering Programen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.identifier.journalComputer-Aided Designen
dc.eprint.versionPost-printen
dc.contributor.institutionDepartment of Mathematics, University of Illinois at Urbana-Champaign, IL, USAen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
kaust.authorMohamed, Mamdouh S.en
kaust.authorSamtaney, Ravien
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