Using numerical relativity to model gravitational waves from binary black holes

Numerical solutions of the Einstein equations for the last orbits and merger of two black holes are essential to model the gravitational-wave signal from such systems, which are the prime source for gravitational-wave observations with Advanced LIGO and Virgo. Our current numerical codes allow us to simulate systems of moderate mass ratios, and for black holes with moderate spins. Improved numerical techniques, coordinate conditions and initial data will allow us to study systems with far higher mass ratios and spins. These systems are interesting to study for their physical properties alone, as well as being essential for modelling generic-binary waveforms for gravitational-wave astronomy with Advanced LIGO and Virgo, third-generation detectors such as Einstein Telescope and Cosmic Explorer, and the space-based detector LISA.