Abstract:
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. We will highlight certain mathematical and computational aspects related to the relevant nonlinear acoustic phenomena, namely - modeling of high intensity ultrasound phenomena as second and higher order wave equations
- efficient and robust time integration
- absorbing boundary conditions for the treatment of open domain problems
- optimal shape design and boundary control problems in the context of HIFU