Published September 12, 2011
| Version v1
Conference paper
Strong Shape Derivative for the Wave Equation with Neumann Boundary Condition
- Creators
- Zolésio, Jean-Paul
- Bociu, Lorena
- Others:
- Institut Non Linéaire de Nice Sophia-Antipolis (INLN) ; Université Nice Sophia Antipolis (1965 - 2019) (UNS) ; COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)
- Centre de Recherches Mathématiques [Montréal] (CRM) ; Université de Montréal (UdeM)
- North Carolina State University [Raleigh] (NC State) ; University of North Carolina System (UNC)
- Dietmar Hömberg
- Fredi Tröltzsch
- TC 7
Description
The paper provides shape derivative analysis for the wave equation with mixed boundary conditions on a moving domain Ωs in the case of non smooth neumann boundary datum. The key ideas in the paper are (i) bypassing the classical sensitivity analysis of the state by using parameter differentiability of a functional expressed in the form of Min-Max of a convex-concave Lagrangian with saddle point, and (ii) using a new regularity result on the solution of the wave problem (where the Dirichlet condition on the fixed part of the boundary is essential) to analyze the strong derivative.
Abstract
Part 6: Shape and Structural Optimization
Abstract
International audience
Additional details
- URL
- https://hal.inria.fr/hal-01347567
- URN
- urn:oai:HAL:hal-01347567v1
- Origin repository
- UNICA