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Second order directional shape derivatives

URN to cite this document: urn:nbn:de:bvb:703-epub-4227-3

Title data

Schiela, Anton ; Ortiz, Julián:
Second order directional shape derivatives.
Bayreuth , 2019 . - 25 S.

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Project information

Project title:
Project's official title
Project's id
DFG-Projekt "Optimierung auf Mannigfaltigkeiten für die numerische Lösung von gleichungsbeschränkten Variationsproblemen"
SCHI 1379/3-1
Project financing: Deutsche Forschungsgemeinschaft

Abstract

We propose a variant in the definition of a second order shape derivative. The result is a quadratic form in terms of one perturbation vector field that yields a second order quadratic model of the perturbed functional. We discuss the structure of this derivative, derive domain expressions and Hadamard forms in a general geometric framework, and give a detailed geometric interpretation of the arising terms.

Further data

Item Type: Preprint, postprint
Keywords: shape optimization; shape derivative; shape hessian
Subject classification: AMS MSC 2010: 53A07, 49Q10, 49Q12
DDC Subjects: 500 Science > 510 Mathematics
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics > Chair Applied Mathematics - Univ.-Prof. Dr. Anton Schiela
Profile Fields > Advanced Fields > Nonlinear Dynamics
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Profile Fields
Profile Fields > Advanced Fields
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-4227-3
Date Deposited: 28 Feb 2019 11:49
Last Modified: 18 Dec 2020 10:42
URI: https://epub.uni-bayreuth.de/id/eprint/4227

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