TY - JOUR
T1 - Second-order domain derivative of normal-dependent boundary integrals
AU - Balzer, Jonathan
N1 - KAUST Repository Item: Exported on 2020-10-01
PY - 2010/3/17
Y1 - 2010/3/17
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/561623
UR - http://link.springer.com/10.1007/s00028-010-0061-3
UR - http://www.scopus.com/inward/record.url?scp=79451475476&partnerID=8YFLogxK
U2 - 10.1007/s00028-010-0061-3
DO - 10.1007/s00028-010-0061-3
M3 - Article
SN - 1424-3199
VL - 10
SP - 551
EP - 570
JO - Journal of Evolution Equations
JF - Journal of Evolution Equations
IS - 3
ER -