论文标题
能源稳定有限差离散的边界和接口方法的动态束方程
Boundary and interface methods for energy stable finite difference discretizations of the dynamic beam equation
论文作者
论文摘要
我们考虑通过零件有限差异方法（SBP-FD）的能量稳定求和，用于均匀和分段均匀的动态束方程（DBE）。以前，恒定系数问题已用SBP-FD以及惩罚项（SBP-SAT）解决了边界条件。在这项工作中，我们重新审视了此问题，并将SBP-SAT与投影方法（SBP-P）进行比较。我们还考虑了具有不连续系数的DBE，并介绍了新型的SBP-SAT，SBP-P和混合SBP-SAT-P离散化，以施加界面条件。数值实验表明，在准确性方面，所有考虑的方法都相似，但是对于恒定和分段恒定系数问题，SBP-P可以更有效地有效地有效（对于显式时间集成方法的限制性时间步长要求）。
We consider energy stable summation by parts finite difference methods (SBP-FD) for the homogeneous and piecewise homogeneous dynamic beam equation (DBE). Previously the constant coefficient problem has been solved with SBP-FD together with penalty terms (SBP-SAT) to impose boundary conditions. In this work we revisit this problem and compare SBP-SAT to the projection method (SBP-P). We also consider the DBE with discontinuous coefficients and present novel SBP-SAT, SBP-P and hybrid SBP-SAT-P discretizations for imposing interface conditions. Numerical experiments show that all methods considered are similar in terms of accuracy, but that SBP-P can be more computationally efficient (less restrictive time step requirement for explicit time integration methods) for both the constant and piecewise constant coefficient problems.
