  The goal of this work is to improve focusing of high-intensity ultrasound by
modifying the geometry of acoustic lenses through shape optimization. The shape
optimization problem is formulated by introducing a tracking-type cost
functional to match a desired pressure distribution in the focal region.
Westervelt's equation, a nonlinear acoustic wave equation, is used to model the
pressure field. We apply the optimize first, then discretize approach, where we
first rigorously compute the shape derivative of our cost functional. A
gradient-based optimization algorithm is then developed within the concept of
isogeometric analysis, where the geometry is exactly represented by splines at
every gradient step and the same basis is used to approximate the equations.
Numerical experiments in a 2D setting illustrate our findings.
