Seminar in Numerical Analysis: Barbara Kaltenbacher (Universität Klagenfurt)
High intensity (focused) ultrasound HIFU is used in numerous medical and industrial applications ranging from litotripsy and thermotherapy via ultrasound cleaning and welding to sonochemistry. In this talk, we will highlight two computational aspects related to the relevant nonlinear acoustic phenomena, namely
- absorbing boundary conditions for the treatment of open domain problems;
- optimization tasks for ultrasound focusing.
Strictly speaking, acoustic sound propagation takes place in full space or at least in a domain that is typically much larger than the region of interest Ω. To restrict attention to a bounded domain Ω, e.g, for computational purposes, artificial reflections on the boundary ∂Ω have to be avoided. This can be done by imposing so-called absorbing boundary conditions ABC that induce dissipation of outgoing waves. Here it will turn out to be crucial to take into account nonlinearity of the PDE also in these ABC. This is joint work with Igor Shevchenko (Imperial College London).
In the context of applications in HIFU, focusing of nonlinearly propagating waves amounts to optimization problems. The design of ultrasound excitation via piezoelectric transducers leads to a boundary control problem; focusing high intensity ultrasound by a silicone lens requires shape optimization. For both problem classes, we will discuss the derivation of gradient information in order to formulate optimality conditions and drive numerical optimization methods. This is joint work with Christian Clason (University of Duisburg-Essen), Vanja Nikolić (TU München), and Gunther Peichl (University of Graz).
Finally we will provide an outlook on imaging with nonlinearly acoustic waves, which amounts to identifying spatially varying coefficients (sound speed and/or coefficient of nonlinearity) in the Westervelt equation. This is recent joint work with Masahiro Yamamoto (University of Tokyo) and William Rundell (Texas A&M University).
For further information about the seminar, please visit this webpage.
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