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| In the simulation of high intensity ultrasound, a particular challenge due to nonlinearity and the presence of different wave lengths is efficient and robust time integration. For this purpose, a promising approach are operator splitting techniques exploiting the intrinsic structure of the equations.
As a model problem we study the Westervelt equation in more detail, which is a nonlinear wave equation with potential degeneracy and strong damping. We will show several decomposition variants based on a reformulation as a first order system and, for the two most promising ones, show convergence results for the Lie Trotter splitting (for details on the convergence analysis we refer to the talk by Mechthild Thalhammer in ss108)
These rely on some new spatial regularity results for the Westervelt equation.
Finally, numerical experiments will illustrate the theoretical findings. |
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