Towards Improving Binary Black Hole Simulations Using Compact Finite Differences

The next generation of gravitational wave observatories will require greater accuracy in the simulated waveforms from binary black hole mergers. Current numerical relativity methods for solving Einstein's highly nonlinear equations are computationally expensive and largely insufficient for these greater accuracy demands. Compact Finite Differences (CFDs) show promise as a numerical method that can reduce computational cost while improving accuracy and efficiency. We are working to incorporate CFD methods into the evolution code for general relativity, Dendro-GR. Simulations of mergers with large mass ratios, spins, and/or eccentricities are examples of the additional physics that such systems will have and for which detectors will require highly accurate waveform templates. As there exist a variety of possible constructions and optimizations of CFDs we are able to build more than one family of derivative operators suitable for different contexts and accuracy orders. We discuss some of the testing of these candidate operators for accuracy and stability in simpler systems with the goal of their subsequent implementation into binary black hole simulations.