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An improved shape optimization formulation of the Bernoulli problem by tracking the Neumann data
- 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.
- Subjects :
- Minimax formulation
Scheme (programming language)
Computer science
General Mathematics
Tracking (particle physics)
01 natural sciences
Free boundary
010305 fluids & plasmas
Bernoulli's principle
Shape optimization
Lagrangian method
Shape derivative
0103 physical sciences
Applied mathematics
0101 mathematics
Bernoulli problem
computer.programming_language
Minimization problem
General Engineering
State (functional analysis)
Minimax
010101 applied mathematics
Domain perturbation
Shape gradient
computer
Subjects
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