Hybridized Summation-by-Parts Finite Difference Methods

Jeremy E. Kozdon, Brittany A. Erickson, & Lucas C. Wilcox

Awaiting Publication April 26, 2021, SCEC Contribution #10992

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.

Kozdon, J. E., Erickson, B. A., & Wilcox, L. C. (2021). Hybridized Summation-by-Parts Finite Difference Methods. Journal of Scientific Comptuing, (awaiting publication).