Chemical complexity in astrophysical simulations: optimization and
  reduction techniques
  Chemistry has a key role in the evolution of the interstellar medium (ISM),
so it is highly desirable to follow its evolution in numerical simulations.
However, it may easily dominate the computational cost when applied to large
systems. In this paper we discuss two approaches to reduce these costs: (i)
based on computational strategies, and (ii) based on the properties and on the
topology of the chemical network. The first methods are more robust, while the
second are meant to be giving important information on the structure of large,
complex networks. To this aim we first discuss the numerical solvers for
integrating the system of ordinary differential equations (ODE) associated with
the chemical network. We then propose a buffer method that decreases the
computational time spent in solving the ODE system. We further discuss a
flux-based method that allows one to determine and then cut on the fly the less
active reactions. In addition we also present a topological approach for
selecting the most probable species that will be active during the chemical
evolution, thus gaining information on the chemical network that otherwise
would be difficult to retrieve. This topological technique can also be used as
an a priori reduction method for any size network. We implemented these methods
into a 1D Lagrangian hydrodynamical code to test their effects: both classes
lead to large computational speed-ups, ranging from x2 to x5. We have also
tested some hybrid approaches finding that coupling the flux method with a
buffer strategy gives the best trade-off between robustness and speed-up of
calculations.
