Isogeometric shape optimization for nonlinear ultrasound focusing

TL;DR

This paper presents a novel isogeometric shape optimization method for nonlinear ultrasound focusing, using Westervelt's equation and gradient-based algorithms to improve acoustic lens design in a 2D setting.

Contribution

It introduces an isogeometric analysis framework for shape optimization of nonlinear ultrasound lenses, integrating exact geometry representation with pressure field modeling.

Findings

Successful application of the method in 2D numerical experiments

Enhanced focusing achieved through optimized lens geometries

Demonstration of the approach's potential for nonlinear acoustic applications

Abstract

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.