We implement a Newton-based approach with accurate sensitivities to directly determine cyclic steady states of a Simulated Moving Bed Process.

The sensitivity calculation is the most time-consuming step and remains a bottleneck for design and optimization. However since the sensitivity calculation
with respect to each parameter is independent, parallelization is straightforward. Here, the sensitivity parameters are divided into different sets and are distributed to different processors, with each processor running a copy of the state equations
and computing a subset of the sensitivity variables. Although the computation of DAE models is repeated at each processor, this overhead work is rather small compared to the effort of calculating sensitivities.