SBP

This repository contains summation-by-parts (SBP) operators and codes used in the following list of publications.

Provably Non-stiff implementation of weak coupling conditions for hyperbolic problems

The directory non-stiff contains source codes and scripts to reproduce most of the work presented in

• O. O'Reilly, J. Nordström
  Provably Non-stiff implementation of weak coupling conditions for hyperbolic problems (submitted to Numerische Mathematik July 2020)

SBP Staggered interpolation and differentiation operators

The directory covariant contains a MATLAB implementation of the SBP operators presented in

• O. O'Reilly, N. A. Petersson, Energy conservative SBP discretizations of the acoustic wave equation in covariant form on staggered curvilinear grids https://arxiv.org/abs/1907.01105

Compatible staggered and upwind SBP operators

The directory staggered-upwind contains a MATLAB implementation of the SBP operators presented in

• K. Mattsson, O. O'Reilly, Compatible diagonal-norm staggered and upwind SBP operators, Journal of Computational Physics, Volume 352, 1 January 2018, Pages 52-75, https://doi.org/10.1016/j.jcp.2017.09.044

Staggered grid SBP operators

The directory staggered contains a MATLAB implementation of the SBP operators presented in

• O. O'Reilly, T. Lundquist, J. Nordström, and E. M. Dunham, Energy stable and high-order-accurate finite difference methods on staggered grids, Journal of Computational Physics, Volume 346, 2017, Pages 572-589, http://dx.doi.org/10.1016/j.jcp.2017.06.030

Axisymmetric SBP operators

The directory axisymmetric contains a MATLAB implementation of the SBP operators presented in

• B. Prochnow, O. O'Reilly, E. M. Dunham, and N.A Petersson, Treatment of the polar coordinate singularity in axisymmetric wave propagation using high-order summation-by-parts operators on a staggered grid, Computers and Fluids, Volume 149, 13 June 2017, Pages 138–149, http://dx.doi.org/10.1016/j.compfluid.2017.03.015