here for completeness. The pre-supernova stellar evolution models are post-processed using the NuGrid MPPNP code, which solves the network equations on each grid cell using a fully implicit Backward Euler method combined with Newton-Raphson iterations to obtain a converged solution [^2] over the time step. Following each network integration over the whole model, an operator split diffusion equation is solved per isotopic species to account for mixing. The diffusion coefficient profile is taken from the stellar evolution models.

The detailed end-of-life stellar abundances are then mapped to the spherically symmetric Lagrangian explosion tracer particles via linear-interpolation to the enclosed mass shells. The supernova models are post-processed with the NuGrid TPPNP code in which each Lagrangian mass shell is treated as a particle that evolves independently of the other mass shells. Therefore, the trajectory of each shell is integrated in time using a variable order Bader-Deuflhard integrator [@bader1983a; @Deuflhard1983a; @Timmes1999a]. Subcycling is performed if convergence[^3] is not reached in an adequate number of sub-levels and in this case a linear interpolation of the trajectory is performed. Above the threshold temperature of 6 GK we assume nuclear statistical equilibrium (NSE) of the strong reactions and evolve the electron fraction using a 4th/5th 