SIAM Journal on Control and Optimization
Shapes and geometries: analysis, differential calculus, and optimization
Shapes and geometries: analysis, differential calculus, and optimization
Numerical Mathematics (Texts in Applied Mathematics)
Numerical Mathematics (Texts in Applied Mathematics)
Optimal shape design for Stokes flow via minimax differentiability
Mathematical and Computer Modelling: An International Journal
Vortex control of instationary channel flows using translation invariant cost functionals
Computational Optimization and Applications
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This paper is concerned with a numerical simulation of shape optimization in a two-dimensional viscous incompressible flow governed by Navier-Stokes equations with mixed boundary conditions containing the pressure. The minimization problem of total dissipated energy was established in the fluid domain. We derive the structures of continuous shape gradient of the cost functional by using the differentiability of a minimax formulation involving a Lagrange functional with a function space parametrization technique. Finally a gradient type algorithm is effectively used for our problem.