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Abstract

We demonstrate a new geometric method for fast template placement for
searches for gravitational waves from the inspiral, merger and ringdown of
compact binaries. The method is based on a binary tree decomposition of the
template bank parameter space into non-overlapping hypercubes. We use a
numerical approximation of the signal overlap metric at the center of each
hypercube to estimate the number of templates required to cover the hypercube
and determine whether to further split the hypercube. As long as the expected
number of templates in a given cube is greater than a given threshold, we split
the cube along its longest edge according to the metric. When the expected
number of templates in a given hypercube drops below this threshold, the
splitting stops and a template is placed at the center of the hypercube. Using
this method, we generate aligned-spin template banks covering the mass range
suitable for a search of Advanced LIGO data. The aligned-spin bank required ~24
CPU-hours and produced 2 million templates. In general, we find that other
methods, namely stochastic placement, produces a more strictly bounded loss in
match between waveforms, with the same minimal match between waveforms
requiring about twice as many templates with our proposed algorithm. Though we
note that the average match is higher, which would lead to a higher detection
efficiency. Our primary motivation is not to strictly minimize the number of
templates with this algorithm, but rather to produce a bank with useful
geometric properties in the physical parameter space coordinates. Such
properties are useful for population modeling and parameter estimation.