  Astrochemical simulations are a powerful tool for revealing chemical
evolution in the interstellar medium. Astrochemical calculations require
efficient processing of large matrices for the chemical networks. The large
chemical reaction networks often present bottlenecks for computation because of
time derivatives of chemical abundances. We propose an efficient algorithm
using a stoichiometry matrix approach in which this time-consuming part is
expressed as a loop, unlike the algorithm used in previous studies. Since
stoichiometry matrices are sparse in general, the performances of simulations
with our algorithm depend on which sparse-matrix storage format is used. We
conducted a performance comparison experiment using the common storage formats,
including the coordinate (COO) format, the compressed column storage (CCS)
format, the compressed row storage (CRS) format, and the Sliced ELLPACK (SELL)
format. Experimental results showed that the simulations with the CRS format
are the most suitable for astrochemical simulations and about three times
faster than those with the algorithm used in previous studies. In addition, our
algorithm significantly reduces not only the computation time but also the
compilation time. We also explore the beneficial effects of parallelization and
sparse-matrix reordering in these algorithms.
