ColPack computes the Jacobian of a flow associated with the drag on a Volkswagen
in fewer steps, i.e., number of colors, (png file)
More colors (steps) are needed when the Jacobian
is computed without ColPack's ordering (png file)
Without coloring, these Jacobians would be infeasible to compute.
Thanks to Markus Towara of the STCE department at the RWTH University in Aachen, Germany,
for these pictures.
ColPack is integrated with Automatic Differentiation software
Control Optimization software PSOPT,
Process Engineering Optimization software Ciengis (commercial).
Our coloring algorithms have been implemented
by Miles Lubin and colleagues at the MIT Operations Research Center;
in CppAD (AD software)
by Brad Bell of the University of Washington.
Our papers on Coloring for computing derivative matrices,
including one in SIAM Review, have been cited more than 300 times.
These include theory (e.g., polyhedral investigations of acyclic and star colorings),
and several application areas in Computational Science and Engineering:
chemical process engineering; fluid dynamics; stellar hydrodynamics; oceanography;
circuit and device simulations; course timetabling; financial optimization, etc.
Google Scholar page.