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José Rodrigo González Granada, Victor A. Kovtunenko, A shape derivative for optimal control of the nonlinear Brinkman-Forchheimer equation – Journal of Applied and Numerical Optimization Skip to content

José Rodrigo González Granada, Victor A. Kovtunenko, A shape derivative for optimal control of the nonlinear Brinkman-Forchheimer equation

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DOI: 10.23952/jano.3.2021.2.02
Volume 3, Issue 2, 31 August 2021, Pages 243-261

 

Abstract. 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.

 

How to Cite this Article:
José Rodrigo González Granada, Victor A. Kovtunenko, A shape derivative for optimal control of the nonlinear Brinkman-Forchheimer equation, J. Appl. Numer. Optim. 3 (2021), 243-261.