We computed derivatives of the single-species contaminant concentrations at
each node at time step *t* + 1
to the flow field velocity vectors at time step *t*
on meshes
ranging in size from
4 to 32 rectangular box elements, corresponding to 48 to 432 independent
variables. We verified the derivatives computed by ADIFOR with central
differences. However, ADIFOR-generated derivatives can be computed much
faster. The table below shows the complexity of evaluation the model
(labelled f(x)) and the speedup that ADIFOR achieves over one-sided
divided differences.

To view the paper describing this application in detail, click here.

Argonne National Laboratory/Mathematics and Computer Science Division/ autodiff@mcs.anl.gov