Implicit-explicit (IMEX) evolution of single black holes

Understand

Numerical simulations of binary black holes---an important predictive tool for the detection of gravitational waves---are computationally expensive, especially for binaries with high mass ratios or with rapidly spinning constituent holes.

• Existing codes for evolving binary black holes rely on explicit timestepping methods, for which the timestep size is limited by the smallest spatial scale through the Courant-Friedrichs-Lewy condition.
• Binary inspiral typically involves spatial scales (the spatial resolution required by a small or rapidly spinning hole) which are orders of magnitude smaller than the relevant (orbital, precession, and radiation-reaction) timescales characterizing the inspiral.
• Therefore, in explicit evolutions of binary black holes, the timestep size is typically orders of magnitude smaller than the relevant physical timescales.