Optimized Compact Finite Difference Schemes for Use in Binary Black Hole Simulations

As improvements continue to be made to gravitational wave detectors, the need for increasingly accurate simulations of binary black hole mergers will continue to grow. Merger simulations for systems with high spins, large mass ratios, or highly eccentric orbits come with additional computational costs that are still out of reach for many current evolution codes. We develop a suite of compact finite difference (CFD) numerical schemes of different orders which are demonstrated to show improvements over the accuracy and efficiency of current methods with minimal increase in the computational cost. We discuss the methods used to optimize CFD schemes for accuracy while maintaining numerical stability, and we compare the results of these methods with standard schemes used in numerical relativity.