  We describe an F-statistic search for continuous gravitational waves from
galactic white-dwarf binaries in simulated LISA Data. Our search method employs
a hierarchical template-grid based exploration of the parameter space. In the
first stage, candidate sources are identified in searches using different
simulated laser signal combinations (known as TDI variables). Since each source
generates a primary maximum near its true "Doppler parameters" (intrinsic
frequency and sky position) as well as numerous secondary maxima of the
F-statistic in Doppler parameter space, a search for multiple sources needs to
distinguish between true signals and secondary maxima associated with other,
"louder" signals. Our method does this by applying a coincidence test to reject
candidates which are not found at nearby parameter space positions in searches
using each of the three TDI variables. For signals surviving the coincidence
test, we perform a fully coherent search over a refined parameter grid to
provide an accurate parameter estimation for the final candidates. Suitably
tuned, the pipeline is able to extract 1989 true signals with only 5 false
alarms. The use of the rigid adiabatic approximation allows recovery of signal
parameters with errors comparable to statistical expectations, although there
is still some systematic excess with respect to statistical errors expected
from Gaussian noise. An experimental iterative pipeline with seven rounds of
signal subtraction and re-analysis of the residuals allows us to increase the
number of signals recovered to a total of 3419 with 29 false alarms.
