SIAM Journal on Scientific Computing, Volume 43, Issue 2, Page A1472-A1496, January 2021.
We develop a fourth order accurate finite difference method for the three dimensional elastic wave equation in isotropic media with the piecewise smooth material property. In our model, the material property can be discontinuous at curved interfaces. The governing equations are discretized in second order form on curvilinear meshes by using a fourth order finite difference operator satisfying a summation-by-parts property. The method is energy stable and high order accurate. The highlight is that mesh sizes can be chosen according to the velocity structure of the material so that computational efficiency is improved. At the mesh refinement interfaces with hanging nodes, physical interface conditions are imposed by using ghost points and interpolation. With a fourth order predictor-corrector time integrator, the fully discrete scheme is energy conserving. Numerical experiments are presented to verify the fourth order convergence rate and the energy conserving property.

中文翻译：

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网格细化界面的曲线坐标系中弹性波的四阶有限差分法

SIAM科学计算杂志，第43卷，第2期，第A1472-A1496页，2021年1月。
我们针对各向同性介质中具有分段光滑材料特性的三维弹性波方程，开发了一种四阶精确有限差分方法。在我们的模型中，材料属性在弯曲界面处可能是不连续的。通过使用满足逐部分求和性质的四阶有限差分算子，可以在曲线网格上以二阶形式离散控制方程。该方法能量稳定且高阶精度。最重要的是，可以根据材料的速度结构选择网格大小，从而提高了计算效率。在带有悬挂节点的网格细化界面上，通过使用幻影点和插值来施加物理界面条件。借助四阶预测器-校正器时间积分器，完全离散的方案是节能的。通过数值实验验证了四阶收敛速度和能量守恒特性。