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Shape derivatives without taking the shape derivative
Author(s) -
Ito K.,
Kunisch K.,
Peichl G.
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700780
Subject(s) - derivative (finance) , partial derivative , shape optimization , mathematics , differential (mechanical device) , mathematical optimization , second derivative , generalizations of the derivative , computer science , mathematical analysis , physics , thermodynamics , finite element method , economics , financial economics
A general framework for calculating shape derivatives for optimization problems with partial differential equations as constraints is presented. Exploiting the structure of the cost functional the proposed technique allows to obtain the shape derivative of the cost without the necessity to involve the shape derivative of the state variable. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)