In this paper, we propose a novel high order explicit time discretization method for the acoustic wave equation with discontinuous coefficients. The space discretization is based on the unfitted finite element method in the discontinuous Galerkin framework which allows us to treat problems with complex interface geometry on Cartesian meshes. The strong stability and optimal $hp$-version error estimates both in time and space are established. Numerical examples confirm our theoretical results.

翻译：在本文中,我们建议对具有不连续系数的声波波方程式采用新的高顺序明确时间分解法。空间分解法基于不连续的加勒金框架中不合适的有限元素法,该方法使我们能够处理Cartesian meshes上复杂的界面几何问题。在时间和空间方面,都确立了强大的稳定性和最佳的美元反向误差估计。数字实例证实了我们的理论结果。