Faster finite difference schemes for numerical relativity

Future advances in gravitational wave detector technology will provide both more accurate observations of merger events and observations from a wider variety of sources. The challenge for numerical relativity is to improve our numerical solutions of Einstein's equations by a commensurate amount. Dendro-GR is a new code for numerical relativity, which uses Wavelet Adaptive Multi-Resolution (WAMR) to construct unstructured meshes for massively parallel simulations. To further improve Dendro-GR's performance, we are testing compact finite difference schemes for evolving the Einstein equations in the BSSN formulation. Compact finite difference stencils can achieve equal or higher accuracy than standard finite differences with less communication for parallel runs. We will present some initial tests of compact finite differences with the BSSN equations in Dendro-GR, including measures of accuracy and performance gains. We will discuss some of the challenges that were encountered, and plans to further improve the code's performance for production-level simulations.