二阶形式wave equation的基于能量的分部求和有限差分法
An energy-based summation-by-parts finite difference method for the wave equation in second order form
摘要：
对二阶波动方程发展了一种新的有限差分法。有限差分算子满足部分求和（SBP）性质。边界条件和材料交界条件施加弱的近似项（SAT）方法，我们得到的半离散化的能量估计。此外，误差估计推导出的正常模式分析。该方法被称为基于能量的，因为它的相似性基于能量的间断伽辽金方法。在施加狄利克雷边界条件和材料交界条件时，传统的SBP-SAT离散化使用具有网格相关参数的罚项，而我们的方法不需要这一点。此外，可以通过边界和交界条件将数值耗散添加到离散化中。我们提出了数值实验，验证所提出的方法的收敛性和鲁棒性。
英文摘要：
We develop a new finite difference method for the wave equation in second order form. The finite difference operators satisfy a summation-by-parts (SBP) property. With boundary conditions and material interface conditions imposed weakly by the simultaneous-approximation-term (SAT) method, we derive energy estimates for the semi-discretization. In addition, error estimates are derived by the normal mode analysis. The proposed method is termed as energy-based because of its similarity with the energy-based discontinuous Galerkin method. When imposing the Dirichlet boundary condition and material interface conditions, the traditional SBP-SAT discretization uses a penalty term with a mesh-dependent parameter, which is not needed in our method. Furthermore, numerical dissipation can be added to the discretization through the boundary and interface conditions. We present numerical experiments that verify convergence and robustness of the proposed method.
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