Reducing the computational complexity of implicit schemes in the modeling of kinetic inelastic collisions in a partially ionized plasma

Modeling the time evolution of atomic number densities and the kinetic (non‐Maxwellian) electron energy distribution function under the action of electron impact collisions by classical approaches requires an implicit time‐stepping scheme to maintain numerical stability. The resulting linear system that must be iteratively solved at each time step incorporates a dense (nonsparse) matrix. For variables being propagated, the computational cost is . We present an alternative approach with a computational cost of , which is the same order as the computational cost of an explicit method for propagating a system of this type. The approach relies on a combination of classical iterative derivative evaluations, combinatorial approximations, and some ideas from deep machine learning.