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

Jürgen Geiser

Mathematical and Computer Modelling of Dynamical Systems, 2014, vol. 20, issue 4, 317-344

Abstract: 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.

Date: 2014
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/13873954.2013.859159 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:nmcmxx:v:20:y:2014:i:4:p:317-344

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/NMCM20

DOI: 10.1080/13873954.2013.859159

Access Statistics for this article

Mathematical and Computer Modelling of Dynamical Systems is currently edited by I. Troch

More articles in Mathematical and Computer Modelling of Dynamical Systems from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().