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Abstract

Extreme Mass Ratio Inspirals (EMRIs) are one of the key sources for future
space-based gravitational wave interferometers. Measurements of EMRI
gravitational waves are expected to determine the characteristics of their
sources with sub-percent precision. However, their waveform generation is
challenging due to the long duration of the signal and the high harmonic
content. Here, we present the first ready-to-use Schwarzschild eccentric EMRI
waveform implementation in the frequency domain for use with either graphics
processing units (GPUs) or central processing units (CPUs). We present the
overall waveform implementation and test the accuracy and performance of the
frequency domain waveforms against the time domain implementation. On GPUs, the
frequency domain waveform takes in median $0.044$ seconds to generate and is
twice as fast to compute as its time domain counterpart when considering
massive black hole masses $\geq 2 \times 10^6 \,{\rm M_\odot}$ and initial
eccentricities $e_0 > 0.2$. On CPUs, the median waveform evaluation time is $5$
seconds, and it is five times faster in the frequency domain than in the time
domain. Using a sparser frequency array can further speed up the waveform
generation, reaching up to $ 0.3$ seconds. This enables us to perform, for the
first time, EMRI parameter inference with fully relativistic waveforms on CPUs.
Future EMRI models which encompass wider source characteristics (particularly
black hole spin and generic orbit geometries) will require significantly more
harmonics. Frequency-domain models will be essential analysis tools for these
astrophysically realistic and important signals.