Intrinsic expression of the derivatives in domain optimization problems. (December 2019)

• Record Type: Journal Article
• Authors: Philippe, Guillaume
• Is Part Of: Numerical functional analysis and optimization. Volume 17:Number 1/2(1996)
• Page Start: 93
• Page End: 112
• Publication Date: 2019-12
• Subjects: domain optimization -- shape optimixation -- Hessian -- higher order derivatives -- material derivative -- local derivative; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630569608816685
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract : It is well-known in domain optimization that the derivative of a cost function with respect to the shape of a domain is a distribution with support lying in the boundary of the domain to be optimized. This existence result is completed with a constructive method giving an explicit expression of this distribution, which can be applied in general cases. The relationship between material and local derivates of any order, provided they are well-defined, is also investigated.