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：本文针对具有动力学与声学边界条件的半线性波动方程，提出了新型的一阶和二阶体-面分裂格式。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，即体域与表面动力学分别建模并通过耦合约束连接。该思路使得分裂格式得以实现，数值实验表明其具有一阶收敛性。另一方面，声学边界条件天然分离体域与表面动力学。数值结果显示，在此类边界条件下，李分裂格式与斯特朗分裂格式分别达到一阶和二阶收敛精度。