  In the era of synoptic surveys, the number of known gravitationally lensed
quasars is set to increase by over an order of magnitude. These new discoveries
will enable a move from single-quasar studies to investigations of statistical
samples, presenting new opportunities to test theoretical models for the
structure of quasar accretion discs and broad emission line regions (BELRs). As
one crucial step in preparing for this influx of new lensed systems, a
large-scale exploration of microlensing convergence-shear parameter space is
warranted, requiring the computation of O(10^5) high resolution magnification
maps. Based on properties of known lensed quasars, and expectations from
accretion disc/BELR modelling, we identify regions of convergence-shear
parameter space, map sizes, smooth matter fractions, and pixel resolutions that
should be covered. We describe how the computationally time-consuming task of
producing ~290000 magnification maps with sufficient resolution (10000^2
pixel/map) to probe scales from the inner edge of the accretion disc to the
BELR can be achieved in ~400 days on a 100 teraflop/s high performance
computing facility, where the processing performance is achieved with graphics
processing units. We illustrate a use-case for the parameter survey by
investigating the effects of varying the lens macro-model on accretion disc
constraints in the lensed quasar Q2237+0305. We find that although all
constraints are consistent within their current error bars, models with more
densely packed microlenses tend to predict shallower accretion disc radial
temperature profiles. With a large parameter survey such as the one described
here, such systematics on microlensing measurements could be fully explored.
