Abstract

A new version of DASPK, DASPK3.0, with capability for sensitivity analysis is pre-sented in this report. DASPK3.0 differs from the sensitivity code DASPKSO, described in [12], in several ways. DASPK3.0 has all the features, which were not available in DASPKSO, of the previous version DASPK2.0. One of these features is an improved algorithm for calculation of consistent initial conditions for index-zero or index-one systems. DASPK3.0 also incorporates a mechanism for initialization and solution of index-2 systems. Other improvements in DASPK3.0 include a more accurate error and convergence test, particularly for the sensitivity analysis. We implemented the Krylov method for sensitivity computation with a different strategy from DASPKSO, and made it more efficient and easier for parallel computing. We also added the staggered correc-tor method [7] for both the direct and Krylov method. We implemented the sensitivity analysis with an internal parallel mode, which is easy to use for both serial and parallel computation with message passing interface (MPI). We also incorporated automatic dif-ferentiation into DASPK3.0 to evaluate the Jacobian matrix and sensitivity equations. The goal of our design has been to be compatible as much as possible with DASPK2.0, to minimize memory and storage requirements for sensitivity analysis, and to speed up the computation for a large number of sensitivity parameters.

Citations