论文标题
杂交逐个汇总有限差异方法
Hybridized Summation-By-Parts Finite Difference Methods
论文作者
论文摘要
我们提供了一种综合技术，用于逐个局部的有限差异方法，其界面的执行较弱和二阶线性椭圆形偏微分方程的界面和边界条件。该方法基于杂交不连续的Galerkin文献的技术，其中分别为体积和微量网格点定义了局部和全局问题。通过使用Schur补体技术，可以消除体积点，从而大大降低了系统大小。我们同时得出了本地问题和全局问题，并表明必须求解的线性系统是对称的积极确定性的。理论稳定性结果通过数值实验证实，方法的准确性也是如此。
We present a hybridization technique for summation-by-parts finite difference methods with weak enforcement of interface and boundary conditions for second order, linear elliptic partial differential equations. The method is based on techniques from the hybridized discontinuous Galerkin literature where local and global problems are defined for the volume and trace grid points, respectively. By using a Schur complement technique the volume points can be eliminated, which drastically reduces the system size. We derive both the local and global problems, and show that the linear systems that must be solved are symmetric positive definite. The theoretical stability results are confirmed with numerical experiments as is the accuracy of the method.
