This paper introduces novel bulk-surface 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 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.

翻译：本文针对半线性波动方程在动力学和声学边界条件下，提出了全新的一阶和二阶体-面拆分格式。对于动力学边界条件，我们提出将系统方程重新解释为耦合系统。这意味着体域和面域动力学被分别建模，并通过耦合约束相互连接。这使得拆分格式的实施成为可能，数值实验表明其具有一阶收敛性。另一方面，声学边界条件自然地分离了体域和面域动力学。在此情况下，数值结果显示李拆分格式和斯特朗拆分格式分别实现了一阶和二阶收敛。