HILBERTIAN REGULARIZATION FOR SHAPE OPTIMIZATION PROBLEMS DESCRIBED VIA BOUNDARY INTEGRAL EQUATIONS

Abstract

Is this study, we evaluate a shape derivative and Hilbertian-regularized gradient of cost functionals associated with solutions of boundary integral equations. We focus on two-dimensional problems with smooth bounded domains and parameterize them using periodic functions. The parameterization allows us to apply the Fréchet-differential calculus in a straightforward manner. We apply the Hilbertian regularization technique to obtain a gradient (descent direction) of the cost functionals. Some numerical examples are presented to verify the obtained sensitivity.