Second-order domain derivative of normal-dependent boundary integrals

Jonathan Balzer

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)551-570
Number of pages20
JournalJournal of Evolution Equations
Volume10
Issue number3
DOIs
StatePublished - Mar 17 2010

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

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