Article

Journal of Evolution Equations

, Volume 10, Issue 3, pp 551-570

Second-order domain derivative of normal-dependent boundary integrals

  • Jonathan BalzerAffiliated withGeometric Modeling and Scientific Visualization Center, King Abdullah University of Science and Technology Email author 

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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.

Mathematics Subject Classification (2000)

49Q10 49Q12

Keywords

Shape optimization Domain derivative Shape Hessian Generalized Newton method Boundary integral Shape evolution Level set method Reconstruction