Handle URI:
http://hdl.handle.net/10754/597716
Title:
Calculus on Surfaces with General Closest Point Functions
Authors:
März, Thomas; Macdonald, Colin B.
Abstract:
The closest point method for solving partial differential equations (PDEs) posed on surfaces was recently introduced by Ruuth and Merriman [J. Comput. Phys., 227 (2008), pp. 1943- 1961] and successfully applied to a variety of surface PDEs. In this paper we study the theoretical foundations of this method. The main idea is that surface differentials of a surface function can be replaced with Cartesian differentials of its closest point extension, i.e., its composition with a closest point function. We introduce a general class of these closest point functions (a subset of differentiable retractions), show that these are exactly the functions necessary to satisfy the above idea, and give a geometric characterization of this class. Finally, we construct some closest point functions and demonstrate their effectiveness numerically on surface PDEs. © 2012 Society for Industrial and Applied Mathematics.
Citation:
März T, Macdonald CB (2012) Calculus on Surfaces with General Closest Point Functions. SIAM J Numer Anal 50: 3303–3328. Available: http://dx.doi.org/10.1137/120865537.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Numerical Analysis
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
Jan-2012
DOI:
10.1137/120865537
Type:
Article
ISSN:
0036-1429; 1095-7170
Sponsors:
Received by the editors February 10, 2012; accepted for publication (in revised form) September 24, 2012; published electronically December 4, 2012. This work was supported by award KUK-C1-013-04 made by King Abdullah University of Science and Technology (KAUST).
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Full metadata record

DC FieldValue Language
dc.contributor.authorMärz, Thomasen
dc.contributor.authorMacdonald, Colin B.en
dc.date.accessioned2016-02-25T12:55:25Zen
dc.date.available2016-02-25T12:55:25Zen
dc.date.issued2012-01en
dc.identifier.citationMärz T, Macdonald CB (2012) Calculus on Surfaces with General Closest Point Functions. SIAM J Numer Anal 50: 3303–3328. Available: http://dx.doi.org/10.1137/120865537.en
dc.identifier.issn0036-1429en
dc.identifier.issn1095-7170en
dc.identifier.doi10.1137/120865537en
dc.identifier.urihttp://hdl.handle.net/10754/597716en
dc.description.abstractThe closest point method for solving partial differential equations (PDEs) posed on surfaces was recently introduced by Ruuth and Merriman [J. Comput. Phys., 227 (2008), pp. 1943- 1961] and successfully applied to a variety of surface PDEs. In this paper we study the theoretical foundations of this method. The main idea is that surface differentials of a surface function can be replaced with Cartesian differentials of its closest point extension, i.e., its composition with a closest point function. We introduce a general class of these closest point functions (a subset of differentiable retractions), show that these are exactly the functions necessary to satisfy the above idea, and give a geometric characterization of this class. Finally, we construct some closest point functions and demonstrate their effectiveness numerically on surface PDEs. © 2012 Society for Industrial and Applied Mathematics.en
dc.description.sponsorshipReceived by the editors February 10, 2012; accepted for publication (in revised form) September 24, 2012; published electronically December 4, 2012. This work was supported by award KUK-C1-013-04 made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectClosest point methoden
dc.subjectImplicit surfacesen
dc.subjectLaplace-Beltrami operatoren
dc.subjectRetractionsen
dc.subjectSurface intrinsic differential operatorsen
dc.titleCalculus on Surfaces with General Closest Point Functionsen
dc.typeArticleen
dc.identifier.journalSIAM Journal on Numerical Analysisen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
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