Mathematical ultrasonics
My research centers around nonlinear wave phenomena. I am especially interested in mathematical aspects of nonlinear acoustics and the use of analytical and numerical tools in the development of different ultrasonic applications.
Particular topics include:
- Well-posedness, regularity, and limiting behavior of nonlinear acoustic models
- Time-fractional evolution equations
- Thermo-ultrasonics and Elasto-ultrasonics
- Numerical analysis of FE-based numerical discretizations
- Absorbing boundary conditions for open-domain problems
- Shape optimization of focusing devices in acoustics
Nonlinear sound propagation and focusing by a lens
Nonlinear evolution of the pressure wave with self-focusing
Linear evolution with an external source
Two sound sources and a transparent boundary
Elasto-acoustic coupling via the excitator/fluid
See also