Model order reduction for numerical simulation of particle transport based on numerical integration approaches

In this article, we present a non-linear model order reduction (MOR) method based on a linearization technique for a model of particle transport. Historically, non-linear differential equations have been applied to model particle transport. Such non-linear differential equations are expensive and time-consuming to solve. This is a motivation for reducing such a model, based on molecular collisions for heavy particle transport in plasma reactors. Here, we reduce the order by linearization with numerical integration approaches and obtain a controllable and calculable transport-reaction model. We linearize the transport model of the heavy particles with numerical fixed point schemes to a general linear control systems (GLCSs); see M.A. Lieberman and A.J. Lichtenberg [Principle of Plasma Discharges and Materials Processing, 2nd ed., Wiley-Interscience, 2005]. Such linearization allows modelling the collision of the plasma reactor by a system of ordinary differential equations; see the models in M. Ohring [Materials Science of Thin Films, 2nd ed., Academic Press, San Diego, CA, 2002]. Because of their non-linearity, we extend the linear splitting methods with linearization techniques to solve these non-linear equations. Numerical simulations are used to validate this modelling and linearization approach. The contribution is to reuse linear reaction models without neglecting the delicate extension to non-linear reaction models. With the help of higher-order quadrature rules, e.g. Simpson's rule, we obtain sufficient accuracy and replace the non-linear models by a simpler lower-order linear model. Numerical simulations are presented to validate the coupling ideas of the linearized model.