Isogeometric shape optimization for nonlinear ultrasound focusing
| Autor: | Markus Muhr, Linus Wunderlich, Barbara Wohlmuth, Vanja Nikolić |
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| Rok vydání: | 2017 |
| Předmět: |
Control and Optimization
Basis (linear algebra) Discretization Computer science Applied Mathematics 010102 general mathematics Isogeometric analysis Wave equation 01 natural sciences 010101 applied mathematics 35 49 (Primary) 49Q10 35L05 (Secondary) Nonlinear system Nonlinear acoustics Optimization and Control (math.OC) Modeling and Simulation FOS: Mathematics Applied mathematics Acoustic wave equation Shape optimization 0101 mathematics Mathematics - Optimization and Control |
| DOI: | 10.48550/arxiv.1712.05228 |
| Popis: | The goal of this work is to improve focusing of high-intensity ultrasound by modifying the geometry of acoustic lenses through shape optimization. We formulate the shape optimization problem 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 \begin{document}$ 2 $\end{document} D setting illustrate our findings. |
| Databáze: | OpenAIRE |
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