Second-order domain derivative of normal-dependent boundary integrals

Handle URI:
http://hdl.handle.net/10754/561623
Title:
Second-order domain derivative of normal-dependent boundary integrals
Authors:
Balzer, Jonathan
Abstract:
Numerous reconstruction tasks in (optical) surface metrology allow for a variational formulation. The occurring boundary integrals may be interpreted as shape functions. The paper is concerned with the second-order analysis of such functions. Shape Hessians of boundary integrals are considered difficult to find analytically because they correspond to third-order derivatives of an, in a sense equivalent, domain integral. We complement previous results by considering cost functions depending explicitly on the surface normal. The correctness and practicability of our calculations are verified in the context of a Newton-type shape reconstruction method. © 2010 Birkhäuser / Springer Basel AG.
KAUST Department:
Visual Computing Center (VCC)
Publisher:
Springer Verlag
Journal:
Journal of Evolution Equations
Issue Date:
17-Mar-2010
DOI:
10.1007/s00028-010-0061-3
Type:
Article
ISSN:
14243199
Appears in Collections:
Articles; Visual Computing Center (VCC)

Full metadata record

DC FieldValue Language
dc.contributor.authorBalzer, Jonathanen
dc.date.accessioned2015-08-03T09:00:33Zen
dc.date.available2015-08-03T09:00:33Zen
dc.date.issued2010-03-17en
dc.identifier.issn14243199en
dc.identifier.doi10.1007/s00028-010-0061-3en
dc.identifier.urihttp://hdl.handle.net/10754/561623en
dc.description.abstractNumerous reconstruction tasks in (optical) surface metrology allow for a variational formulation. The occurring boundary integrals may be interpreted as shape functions. The paper is concerned with the second-order analysis of such functions. Shape Hessians of boundary integrals are considered difficult to find analytically because they correspond to third-order derivatives of an, in a sense equivalent, domain integral. We complement previous results by considering cost functions depending explicitly on the surface normal. The correctness and practicability of our calculations are verified in the context of a Newton-type shape reconstruction method. © 2010 Birkhäuser / Springer Basel AG.en
dc.publisherSpringer Verlagen
dc.subjectBoundary integralen
dc.subjectDomain derivativeen
dc.subjectGeneralized Newton methoden
dc.subjectLevel set methoden
dc.subjectReconstructionen
dc.subjectShape evolutionen
dc.subjectShape Hessianen
dc.subjectShape optimizationen
dc.titleSecond-order domain derivative of normal-dependent boundary integralsen
dc.typeArticleen
dc.contributor.departmentVisual Computing Center (VCC)en
dc.identifier.journalJournal of Evolution Equationsen
kaust.authorBalzer, Jonathanen
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.