Splitting schemes for the semi-linear wave equation with dynamic boundary conditions [article]

Robert Altmann
2021 arXiv   pre-print
This paper introduces novel splitting schemes of first and second order for the wave equation with kinetic and acoustic boundary conditions of semi-linear type. For kinetic boundary conditions, we propose a reinterpretation of the system equations as a coupled system. This means that the bulk and surface dynamics are modeled separately and connected through a coupling constraint. This allows the implementation of splitting schemes, which show first-order convergence in numerical experiments. On
more » ... the other hand, acoustic boundary conditions naturally separate bulk and surface dynamics. Here, Lie and Strang splitting schemes reach first- and second-order convergence, respectively, as we reveal numerically.
arXiv:2112.04321v1 fatcat:7ikz6snyxzhnhnhk5l54lgfkre