2 research outputs found
Reproducing kernel Hilbert spaces and variable metric algorithms in PDE constrained shape optimisation
In this paper we investigate and compare different gradient algorithms
designed for the domain expression of the shape derivative. Our main focus is
to examine the usefulness of kernel reproducing Hilbert spaces for PDE
constrained shape optimisation problems. We show that radial kernels provide
convenient formulas for the shape gradient that can be efficiently used in
numerical simulations. The shape gradients associated with radial kernels
depend on a so called smoothing parameter that allows a smoothness adjustment
of the shape during the optimisation process. Besides, this smoothing parameter
can be used to modify the movement of the shape. The theoretical findings are
verified in a number of numerical experiments
Reproducing kernel Hilbert spaces and variable metric algorithms in PDE constrained shape optimisation
In this paper we investigate and compare different gradient algorithms designed for the domain expression of the shape derivative. Our main focus is to examine the usefulness of kernel reproducing Hilbert spaces for PDE constrained shape optimisation problems. We show that radial kernels provide convenient formulas for the shape gradient that can be efficiently used in numerical simulations. The shape gradients associated with radial kernels depend on a so called smoothing parameter that allows a smoothness adjustment of the shape during the optimisation process. Besides, this smoothing parameter can be used to modify the movement of the shape. The theoretical findings are verified in a number of numerical experiments