Design of new Daspk for Sensitivity Analysis

A new version of DASPK, DASPK3.0, with capability for sensitivity analysis ispresented in this report. DASPK3.0 differs from the sensitivity code DASPKSO,described in {MaPe96}, in several ways. DASPK3.0 has all the features, whichwere not available in DASPKSO, of the previous version DASPK2.0. One of thesefeatures is an improved algorithm for calculation of consistent initialconditions for index-zero or index-one systems. DASPK3.0 also incorporates amechanism for initialization and solution of index-2 systems. Otherimprovements in DASPK3.0 include a more accurate error and convergence test,particularly for the sensitivity analysis. We implemented the Krylov methodfor sensitivity computation with a different strategy from DASPKSO, and made itmore efficient and easier for parallel computing. We also added the staggeredcorrector method {FeBa97} for both the direct and Krylov method. Weimplemented the sensitivity analysis with an internal parallel mode, which iseasy to use for both serial and parallel computation with message passinginterface (MPI). We also incorporated automatic differentiation into DASPK3.0to evaluate the Jacobian matrix and sensitivity equations. The goal of ourdesign has been to be compatible as much as possible with DASPK2.0, to minimizememory and storage requirements for sensitivity analysis, and to speed up thecomputation for a large number of sensitivity parameters.