  Multidimensional nucleosynthesis studies with hundreds of nuclei linked
through thousands of nuclear processes are still computationally prohibitive.
To date, most nucleosynthesis studies rely either on hydrostatic/hydrodynamic
simulations in spherical symmetry, or on post-processing simulations using
temperature and density versus time profiles directly linked to huge nuclear
reaction networks. Parallel computing has been regarded as the main permitting
factor of computationally intensive simulations. This paper explores the
different pros and cons in the parallelization of stellar codes, providing
recommendations on when and how parallelization may help in improving the
performance of a code for astrophysical applications.
  We report on different parallelization strategies succesfully applied to the
spherically symmetric, Lagrangian, implicit hydrodynamic code SHIVA,
extensively used in the modeling of classical novae and type I X-ray bursts.
Speed-up factors of 26 and 35 have been obtained with a parallelized version of
SHIVA, in a 200-shell simulation of a type I X-ray burst carried out with two
nuclear reaction networks: a reduced one, consisting of 324 isotopes and 1392
reactions, and a more extended network with 606 nuclides and 3551 nuclear
interactions. Maximum speed-ups of 41 (324-isotope network) and 85 (606-isotope
network), are also predicted for 200 cores, stressing that the number of shells
of the computational domain constitutes an effective upper limit for the
maximum number of cores that could be used in a parallel application.
