Monte Carlo stochastic Galerkin methods for non-Maxwellian kinetic models of multiagent systems with uncertainties

TL;DR

This paper develops a hybrid Monte Carlo and stochastic Galerkin approach for accurately simulating non-Maxwellian kinetic models of multiagent systems with uncertainties, preserving physical properties and improving computational efficiency.

Contribution

It introduces a novel hybrid scheme combining DSMC and stochastic Galerkin methods for non-Maxwellian kinetic models with uncertainties, ensuring physical consistency and accuracy.

Findings

The scheme preserves main physical properties of solutions.

The method achieves accuracy in the random space.

Applications demonstrate effectiveness on multiagent models.

Abstract

In this paper, we focus on the construction of a hybrid scheme for the approximation of non-Maxwellian kinetic models with uncertainties. In the context of multiagent systems, the introduction of a kernel at the kinetic level is useful to avoid unphysical interactions. The methods here proposed, combine a direct simulation Monte Carlo (DSMC) in the phase space together with stochastic Galerkin (sG) methods in the random space. The developed schemes preserve the main physical properties of the solution together with accuracy in the random space. The consistency of the methods is tested with respect to surrogate Fokker-Planck models that can be obtained in the quasi-invariant regime of parameters. Several applications of the schemes to non-Maxwellian models of multiagent systems are reported.