Snapshots of the fraction of ionization and the velocity field at the final time t_f = 10¹⁰ s without the initial velocity perturbation (left panel) and with it (right panel). The physical domain is distributed across different numbers of MPI processes and different preconditioners have been used. Figure D.1a is the same figure as Fig. 15. (a) 4 × 4 MPI processes, ILU(k) factorization. (b) 2 × 2 MPI processes, ILU(k) factorization. (c) 4 × 4 MPI processes, Schwarz domain decomposition. (d) 2 × 2 MPI processes, Schwarz domain decomposition.