Automatic differentiation applied to unsaturated flow - ADOL-C case study

We have experimented with many variants of the code dual.c for two-dimensional unsaturated flow in a porous medium. The goal has been to speed up the evaluation of derivatives required for a Newton iteration. We have primarily investigated the use of ADOL-C, a C++ tool for automatic differentiation and have come to the following conclusions: three colors suffice for computing the nonlinear portion of the Jacobian. That speeds up the Jacobian evaluation in the original code by a factor of two. The use of ADOL-C for automatic differentiation does not speed up the code. The best result we have achieved for automatic differentiation takes twice as long as the original centered difference approximation. The derivative values computed by ADOL-C are more accurate than the centered difference approximations. We can realize big savings in the linear equation solver