Numerical convergence of discrete exterior calculus on arbitrary surface meshes

Handle URI:
http://hdl.handle.net/10754/627178
Title:
Numerical convergence of discrete exterior calculus on arbitrary surface meshes
Authors:
Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi ( 0000-0002-4702-6473 )
Abstract:
Discrete exterior calculus (DEC) is a structure-preserving numerical framework for partial differential equations solution, particularly suitable for simplicial meshes. A longstanding and widespread assumption has been that DEC requires special (Delaunay) triangulations, which complicated the mesh generation process especially for curved surfaces. This paper presents numerical evidence demonstrating that this restriction is unnecessary. Convergence experiments are carried out for various physical problems using both Delaunay and non-Delaunay triangulations. Signed diagonal definition for the key DEC operator (Hodge star) is adopted. The errors converge as expected for all considered meshes and experiments. This relieves the DEC paradigm from unnecessary triangulation limitation.
KAUST Department:
Physical Sciences and Engineering (PSE) Division; Mechanical Engineering Program
Citation:
Mohamed MS, Hirani AN, Samtaney R (2018) Numerical convergence of discrete exterior calculus on arbitrary surface meshes. International Journal for Computational Methods in Engineering Science and Mechanics: 1–13. Available: http://dx.doi.org/10.1080/15502287.2018.1446196.
Publisher:
Informa UK Limited
Journal:
International Journal for Computational Methods in Engineering Science and Mechanics
KAUST Grant Number:
URF/1/1401-01-01
Issue Date:
13-Feb-2018 ; 19-Apr-2018
DOI:
10.1080/15502287.2018.1446196
ARXIV:
arXiv:1802.04506
Type:
Article
ISSN:
1550-2287; 1550-2295
Sponsors:
This research was supported by the KAUST Office of Competitive Research Funds under Award No. URF/1/1401-01-01.
Additional Links:
http://arxiv.org/abs/1802.04506v1; http://arxiv.org/pdf/1802.04506v1; https://www.tandfonline.com/doi/full/10.1080/15502287.2018.1446196
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.accessioned2018-05-02T05:57:14Z-
dc.date.available2018-02-22T10:34:42Z-
dc.date.available2018-05-02T05:57:14Z-
dc.date.issued2018-02-13-
dc.date.issued2018-04-19en
dc.identifier.citationMohamed MS, Hirani AN, Samtaney R (2018) Numerical convergence of discrete exterior calculus on arbitrary surface meshes. International Journal for Computational Methods in Engineering Science and Mechanics: 1–13. Available: http://dx.doi.org/10.1080/15502287.2018.1446196.en
dc.identifier.issn1550-2287en
dc.identifier.issn1550-2295en
dc.identifier.doi10.1080/15502287.2018.1446196en
dc.identifier.urihttp://hdl.handle.net/10754/627178-
dc.description.abstractDiscrete exterior calculus (DEC) is a structure-preserving numerical framework for partial differential equations solution, particularly suitable for simplicial meshes. A longstanding and widespread assumption has been that DEC requires special (Delaunay) triangulations, which complicated the mesh generation process especially for curved surfaces. This paper presents numerical evidence demonstrating that this restriction is unnecessary. Convergence experiments are carried out for various physical problems using both Delaunay and non-Delaunay triangulations. Signed diagonal definition for the key DEC operator (Hodge star) is adopted. The errors converge as expected for all considered meshes and experiments. This relieves the DEC paradigm from unnecessary triangulation limitation.en
dc.description.sponsorshipThis research was supported by the KAUST Office of Competitive Research Funds under Award No. URF/1/1401-01-01.en
dc.language.isoenen
dc.publisherInforma UK Limiteden
dc.relation.urlhttp://arxiv.org/abs/1802.04506v1en
dc.relation.urlhttp://arxiv.org/pdf/1802.04506v1en
dc.relation.urlhttps://www.tandfonline.com/doi/full/10.1080/15502287.2018.1446196-
dc.rightsArchived with thanks to International Journal for Computational Methods in Engineering Science and Mechanicsen
dc.subjectDiscrete exterior calculus (DEC)en
dc.subjectHodge staren
dc.subjectincompressible Navier–Stokes equationsen
dc.subjectnon-Delaunay meshen
dc.subjectPoisson equationen
dc.subjectstructure-preserving discretizationsen
dc.titleNumerical convergence of discrete exterior calculus on arbitrary surface meshesen
dc.typeArticleen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.contributor.departmentMechanical Engineering Programen
dc.identifier.journalInternational Journal for Computational Methods in Engineering Science and Mechanicsen
dc.eprint.versionPost-printen
dc.contributor.institutionDepartment of Mathematics, University of Illinois at Urbana-Champaign, IL, USAen
dc.identifier.arxividarXiv:1802.04506-
kaust.authorMohamed, Mamdouh S.en
kaust.authorSamtaney, Ravien
kaust.grant.numberURF/1/1401-01-01en

Version History

VersionItem Editor Date Summary
2 10754/627178grenzdm2018-05-02 05:56:19.017Published with DOI.
1 10754/627178.1grenzdm2018-02-22 10:34:42.0
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