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Impulse Response Approximations of Discrete Shape Hessians with Application in CFD
2009
SIAM Journal of Control and Optimization
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This paper discusses the symbol of the Hessian of a shape optimization problem in a viscid, incompressible flow. The symbol of the Hessian for the Stokes shape optimization problem is analytically approximated by tracking a Fourier mode through the operators involved. We propose a discrete method for finding the symbol and confirm the correctness by comparison with the analytical data. A preconditioner is constructed for both the Stokes and Navier-Stokes equation, which greatly accelerates the optimization.
doi:10.1137/080719844
fatcat:lr5aq2jlqjfvxg4nownpiig6cu