  Future space-based laser interferometric detectors, such as LISA, will be
able to detect gravitational waves (GWs) generated during the inspiral phase of
stellar-mass binary black holes (SmBBHs). The detection and characterization of
GWs from SmBBHs poses a formidable data analysis challenge, arising from the
large number of wave cycles that make the search extremely sensitive to
mismatches in signal and template parameters in a likelihood-based approach.
This makes the search for the maximum of the likelihood function over the
signal parameter space an extremely difficult task. We present a data analysis
method that addresses this problem using both algorithmic innovations and
hardware acceleration driven by GPUs. The method follows a hierarchical
approach in which a semi-coherent $\mathcal{F}$-statistic is computed with
different numbers of frequency domain partitions at different stages, with
multiple particle swarm optimization (PSO) runs used in each stage for global
optimization. An important step in the method is the judicious partitioning of
the parameter space at each stage to improve the convergence probability of PSO
and avoid premature convergence to noise-induced secondary maxima. The
hierarchy of stages confines the semi-coherent searches to progressively
smaller parameter ranges, with the final stage performing a search for the
global maximum of the fully-coherent $\mathcal{F}$-statistic. We test our
method on 2.5 years of a single LISA TDI combination and find that for an
injected SmBBH signal with a SNR between $\approx 11$ and $\approx 14$, the
method can estimate (i) the chirp mass with a relative error of $\lesssim
0.01\%$, (ii) the time of coalescence within $\approx 100$ sec, (iii) the sky
location within $\approx 0.2$ ${\rm deg}^2$, and (iv) orbital eccentricity at a
fiducial signal frequency of 10 mHz with a relative error of $\lesssim 1\%$.
(abr.)
