Abstract
We are interested in shape sensitivity analysis for an optimization problem arising in medical applications of high intensity focused ultrasound. The goal is to find the optimal shape of a focusing acoustic lens so that the desired acoustic pressure at a kidney stone is achieved. Coupling of the silicone acoustic lens and nonlinearly acoustic fluid region is modeled by the Westervelt equation with nonlinear strong damping and piecewise constant coefficients. We follow the variational approach to calculating the shape derivative of the cost functional which does not require computing the shape derivative of the state variable; however assumptions of certain spatial regularity of the primal and the adjoint state are needed to obtain the derivative, in particular for its strong form according to the Delfour–Hadamard–Zolésio structure theorem.
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Acknowledgments
The financial support by the FWF (Austrian Science Fund) under grant P24970 is gratefully acknowledged as well as the support of the Karl Popper Kolleg “Modeling-Simulation-Optimization”, which is funded by the Alpen-Adria-Universität Klagenfurt and by the Carinthian Economic Promotion Fund (KWF).
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Nikolić, V., Kaltenbacher, B. Sensitivity Analysis for Shape Optimization of a Focusing Acoustic Lens in Lithotripsy. Appl Math Optim 76, 261–301 (2017). https://doi.org/10.1007/s00245-016-9340-x
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DOI: https://doi.org/10.1007/s00245-016-9340-x