Shape optimization with finite elements
Abstract
A common strategy to solve shape optimization problems is to select an initial domain and to update it iteratively until it satisfies certain optimality crietria. In the presence of PDE-constraints, computing these updates requires solving a boundary value problem on a domain that changes at every iteration. We explain how to use isoparametric finite elements to tackle this issue. We also show how finite elements allow computing these updates without deriving shape derivative formulas by hand.