Second-order domain derivative of normal-dependent boundary integrals

被引：0
|
作者：
Jonathan Balzer
机构：
[1] King Abdullah University of Science and Technology,Geometric Modeling and Scientific Visualization Center
来源：
Journal of Evolution Equations | 2010年 / 10卷
关键词：
49Q10; 49Q12; Shape optimization; Domain derivative; Shape Hessian; Generalized Newton method; Boundary integral; Shape evolution; Level set method; Reconstruction;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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.
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页码：551 / 570
页数：19
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