Optimal shape design for Stokes flow via minimax differentiability
This paper is concerned with the shape sensitivity analysis of a viscous incompressible fluid driven by Stokes equations with a nonhomogeneous boundary condition. The structure of the shape gradient with respect to the shape of the variable domain for a given cost function is established by using the differentiability of a minimax formulation involving a Lagrangian functional combined with the function space parametrization technique and the function space embedding technique. We apply a gradient type algorithm to our problem. Numerical examples show that our theory is useful for practical purposes and the proposed algorithm is feasible. (c) 2008 Published by Elsevier Ltd
stokes equations minimax formulation shape optimization gradient algorithm