Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Isogeometric shape optimization for nonlinear ultrasound focusing   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.

9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg