Westervelt-based models of ultrasound: Incorporating space-variable attenuation
Thursday, 4 June 2026, 11:00–12:00 in HG03.082
Abstract
The Westervelt equation is one of the key nonlinear PDEs used to model the behavior of high-frequency sound waves. In biological media, sound waves are attenuated following a power law with respect to the source frequency, which can be accurately captured in the time domain by incorporating fractional attenuation. Allowing the fractional order to vary in space offers further flexibility in modeling a range of phenomena, including heterogeneous propagation media.
In the first part of the talk, we will discuss the well-posedness of the Westervelt equation with a space-dependent order of time-fractional damping, focusing on the challenges that arise by incorporating this type of attenuation. In the second part, we will introduce a discretization involving a convolution quadrature to accurately handle the Caputo time-fractional derivative. Numerical simulations will show the effectiveness of the scheme and the influence of the variable fractional damping.