Hybridized Summation-by-Parts Finite Difference Methods
Hybridized Summation-by-Parts Finite Difference Methods
复制标题
混合分部求和有限差分法
DOI：
10.1007/s10915-021-01448-5
复制
发表时间：
2020
影响因子：
2.5
通讯作者：
L. Wilcox
中科院分区：
文献类型：
--
作者：
J. Kozdon;B. Erickson;L. Wilcox
针对二阶线性椭圆型偏微分方程，提出了一种具有弱界面和边界条件的分部求和有限差分方法。该方法是基于杂交不连续Galerkin文献中的局部和全局问题的体积和跟踪网格点，分别定义的技术。通过使用舒尔互补技术，可以消除体积点，这大大减小了系统的大小。我们得到的局部和整体的问题，并证明所得到的线性系统是对称正定的。数值实验结果证实了理论的稳定性，是该方法的准确性。
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 resulting linear systems are symmetric positive definite. The theoretical stability results are confirmed with numerical experiments as is the accuracy of the method.