We describe in detail full numerical and perturbative techniques to compute the gravitational radiation from intermediate-mass-ratio black-hole-binary inspirals and mergers .
We perform a series of full numerical simulations of nonspinning black holes with mass ratios q = 1 / 10 and q = 1 / 15 from different initial separations and for different finite-difference resolutions .
In order to perform those full numerical runs , we adapt the gauge of the moving punctures approach with a variable damping term for the shift .
We also derive an extrapolation ( to infinite radius ) formula for the waveform extracted at finite radius .
For the perturbative evolutions we use the full numerical tracks , transformed into the Schwarzschild gauge , in the source terms of the Regge-Wheller-Zerilli Schwarzschild perturbations formalism .
We then extend this perturbative formalism to take into account small intrinsic spins of the large black hole , and validate it by computing the quasinormal mode frequencies , where we find good agreement for spins |a / M| < 0.3 .
Including the final spins improves the overlap functions when comparing full numerical and perturbative waveforms , reaching 99.5 % for the leading ( \ell,m ) = ( 2 , 2 ) and ( 3,3 ) modes , and 98.3 % for the nonleading ( 2,1 ) mode in the q = 1 / 10 case , which includes 8 orbits before merger .
For the q = 1 / 15 case , we obtain overlaps near 99.7 % for all three modes .
We discuss the modeling of the full inspiral and merger based on a combined matching of post-Newtonian , full numerical , and geodesic trajectories .