Back to Search Start Over

An improved shape optimization formulation of the Bernoulli problem by tracking the Neumann data

Authors :
Hideyuki Azegami
Julius Fergy T. Rabago
Source :
Journal of Engineering Mathematics. 117:1-29
Publication Year :
2019
Publisher :
Springer Science and Business Media LLC, 2019.

Abstract

We propose a new shape optimization formulation of the Bernoulli problem by tracking the Neumann data. The associated state problem is an equivalent formulation of the Bernoulli problem with a Robin condition. We devise an iterative procedure based on a Lagrangian-like approach to numerically solve the minimization problem. The proposed scheme involves the knowledge of the shape gradient which is established through the minimax formulation. We illustrate the feasibility of the proposed method and highlight its advantage over the classical setting of tracking the Neumann data through several numerical examples.

Details

ISSN :
15732703 and 00220833
Volume :
117
Database :
OpenAIRE
Journal :
Journal of Engineering Mathematics
Accession number :
edsair.doi.dedup.....2e4cecb4973dbd659b5de37e3fd19a6d
Full Text :
https://doi.org/10.1007/s10665-019-10005-x