Optimizing the Accuracy and Stability of Compact Finite Difference Schemes for 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 only 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 are developing families of compact finite difference (CFD) numerical schemes with the potential to improve the accuracy and efficiency of current methods with little increase in computational cost. We discuss some of these methods and our efforts to optimize the accuracy of CFD schemes while maintaining their numerical stability and show results on linear and nonlinear test systems that demonstrate these improvements.