  Gravitational lensing allows us to probe the structure of matter on a broad
range of astronomical scales, and as light from a distant source traverses an
intervening galaxy, compact matter such as planets, stars, and black holes act
as individual lenses. The magnification from such microlensing results in rapid
brightness fluctuations which reveal not only the properties of the lensing
masses, but also the surface brightness distribution in the source. However,
while the combination of deflections due to individual stars is linear, the
resulting magnifications are highly non-linear, leading to significant
computational challenges which currently limit the range of problems which can
be tackled. This paper presents a new and novel implementation of a numerical
approach to gravitational microlensing, increasing the scale of the problems
that can be tackled by more than two orders of magnitude, opening up a new
regime of astrophysically interesting problems.
