Special Session 108: Mathematics of Nonlinear Acoustics
Contents
Free boundary problems are challenging from a theoretical as well as numerical point of view. Efficient numerical solution strategies can be built on an equivalent formulation as a shape optimization problem. We briefly recall some aspects of shape optimization and discuss the shape gradient for shape optimization problems related to the Bernoulli free boundary problem and to a free boundary problem for the Stokes equation. We also apply the proposed techniques which allow to bypass the sometimes rather formal use of the shape derivative of the state variables to a shape optimization problem arising in lithotripsy where one is interested to find the shape of the excitation part of the boundary such that a prescribed pressure distribution is achieved.