A distributed memory parallel algorithm for the efficient computation of sensitivities of differential-algebraic systems

An efficient algorithm for the evaluation of the parametric sensitivities for mixed systems of differential and algebraic equations (DAEs) on computers involving multiple processors operating in parallel is presented. The algorithm derives its efficiency by decoupling the integration of the sensitivity equations from that of the original DAE system, and by allowing tasks associated with the evaluation of sensitivities at multiple time points to overlap instead of being carried out in sequence. Numerical experiments demonstrating the efficiency of the proposed algorithm with systems of more than 850 DAEs and 45 parameters are presented. In all the cases studied, the simultaneous integration of the original DAEs and their sensitivity equations is carried out in less than 10% more time than that of the original DAEs alone.