  We present a new numerical method for transporting arbitrary sets in a
velocity field. The method computes a deformation mapping of the domain and
advects particular sets by function composition with the map. This also allows
for the transport of multiple sets at low computational cost. Our strategy is
to separate the computation of short time advection from the storage and
representation of long time deformation maps, employing appropriate grid
resolution for each of these two parts. We show through numerical experiments
that the resulting algorithm is accurate and exhibits significant reductions in
computational time over other methods. Results are presented in two and three
dimensions, and accuracy and efficiency are studied.

Numerical Analysis;Numerical Analysis