In this paper, we propose a novel high order unfitted finite element method on Cartesian meshes for solving the acoustic wave equation with discontinuous coefficients having complex interface geometry. The unfitted finite element method does not require any penalty to achieve optimal convergence. We also introduce a new explicit time discretization method for the ODE system resulting from the spatial discretization of the wave equation. The strong stability and optimal $hp$-version error estimates both in time and space are established. Numerical examples confirm our theoretical results.

翻译：本文提出了一种基于笛卡尔网格的新型高阶非拟合有限元方法，用于求解具有复杂界面几何的间断系数声波方程。该方法无需任何惩罚项即可实现最优收敛。此外，我们针对波动方程空间离散化产生的常微分方程组，引入了一种新的显式时间离散化方法。建立了时间与空间上的强稳定性及最优$hp$版本误差估计。数值算例验证了理论结果。