A shape derivative for optimal control of the nonlinear Brinkman-Forchheimer equation

A shape derivative for optimal control of the nonlinear Brinkman-Forchheimer equation Full article

Journal

Journal of Applied and Numerical Optimization
ISSN: 2562-5527 , E-ISSN: 2562-5535

Output data

Year: 2021, Volume: 3, Number: 2, Pages: 243-261 Pages count : 19 DOI: 10.23952/jano.3.2021.2.02

Tags

Equilibrium-constrained optimization; Incompressible flow; Optimal control; Semilinear equation; Shape derivative

Authors

GRANADA JOSE RODRIGO GONZ ´ ALEZ ¹ , Kovtunenko Victor Anatolʹevich ^2,3

Affiliations

1	Department of Mathematics, Universidad Tecnologica de Pereira, 660003 Pereira, Colombia
2	Institute for Mathematics and Scientific Computing, Karl-Franzens University of Graz, NAWI Graz
3	3Lavrentyev Institute of Hydrodynamics, Siberian Division of the Russian Academy of Sciences

For a generalized Brinkman–Forchheimer’s equation under divergence-free and mixed boundary conditions, the stationary equilibrium problem and the inverse problem of shape optimal control are considered. For a convex, geometry-dependent objective function, the equilibrium-constrained optimization is treated with the help of an adjoint state within the Lagrange approach. The shape differentiability of a Lagrangian with respect to linearized shape perturbations is derived in the analytic form by the velocity method. A Hadamard representation of the shape derivative using boundary integrals is derived. Its applications to path-independent integrals and to the gradient descent method are illustrated.

GRANADA J.R.G.´.A. , Kovtunenko V.A.
A shape derivative for optimal control of the nonlinear Brinkman-Forchheimer equation
Journal of Applied and Numerical Optimization. 2021. V.3. N2. P.243-261. DOI: 10.23952/jano.3.2021.2.02 Scopus РИНЦ OpenAlex

Scopus:	2-s2.0-85105825636
Elibrary:	46073226
OpenAlex:	W4249283703

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Scopus	8
OpenAlex	6
Elibrary	8