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, small-parameter and large-time asymptotic analysis
- Time-fractional evolution equations
- Multiphysics coupling
- Numerical analysis of Galerkin methods
- Absorbing boundary conditions for open-domain problems
- Shape optimization and optimal control for acoustic problems
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