Symplectic model reduction methods for the Vlasov equation

TL;DR

This paper compares various model reduction techniques, emphasizing the importance of symplectic algorithms for efficient particle-based simulations of the high-dimensional Vlasov equation.

Contribution

It demonstrates the applicability of different model reduction methods to the Vlasov equation and highlights the necessity of symplectic algorithms through numerical experiments.

Findings

Symplectic reduction improves computational efficiency.

Different reduction techniques are applicable to the Vlasov equation.

Symplectic methods are essential for preserving physical properties.

Abstract

Particle-based simulations of the Vlasov equation typically require a large number of particles, which leads to a high-dimensional system of ordinary differential equations. Solving such systems is computationally very expensive, especially when simulations for many different values of input parameters are desired. In this work we compare several model reduction techniques and demonstrate their applicability to numerical simulations of the Vlasov equation. The necessity of symplectic model reduction algorithms is illustrated with a simple numerical experiment.