Reduced-Order Modeling of Advection-Dominated Kinetic Plasma Problems by Shifted Proper Orthogonal Decomposition

Abstract

Model-order reduction is an important tool in the computational exploration of complex physical phenomena, such as kinetic plasmas. A popular strategy to achieve model reduction is the so- called projection methods, such as the proper orthogonal decomposition (POD), where the dynamics of interest are decomposed into a set of global modes and the problem is then projected onto those modes. While very successful, in general, the conventional POD technique is not suited for certain advection-dominated problems or “transport” problems where moving localized features cannot be well represented by global modes. In this work, we apply an extension of the POD technique to obtain an efficient reduced-order model of advection-dominated kinetic plasma problems from finite-element particle-in-cell (PIC) simulations. The results obtained showcase the efficacy of this strategy for obtaining a parsimonious representation of the degrees of freedom of the problem that serves to both reduce simulation costs and provide added physical insight into the problem.