arXiv subjects

Lukas Hensel

Publications and source records attributed to Lukas Hensel.

3 recordsLinked to original sources

arXiv2026

A Comparison of Active Flux Methods for the Vlasov-Poisson System

Active Flux is a third-order accurate, fairly novel finite volume method for hyperbolic conservation laws that is becoming increasingly popular. It evolves additional nodal degrees of freedom (DOF) located on cell interfaces and shared by neighboring cells. The numerical fluxes are then computed from these DOFs. A crucial component of Active Flux methods is the evolution operator of the point values, which enables the natural use of semi-Lagrangian ideas and makes Active Flux an attractive candidate for a grid-based approach to the Vlasov equation. Here, we compare two recently proposed Active Flux methods for the 1D1V Vlasov-Poisson system: a split-step method and an unsplit method.

math.NA↗

arXiv2024

A split-step Active Flux method for the Vlasov-Poisson system

Active Flux is a modified Finite Volume method that evolves additional Degrees of Freedom for each cell that are located on the interface by a non-conservative method to compute high-order approximations to the numerical fluxes through the respective interface to evolve the cell-average in a conservative way. In this paper, we apply the method to the Vlasov-Poisson system describing the time evolution of the time-dependent distribution function of a collisionless plasma. In particular, we consider the evaluation of the flux integrals in higher dimensions. We propose a dimensional splitting and three types of formulations of the flux integral: a one-dimensional reconstruction of second order, a third-order reconstruction based on information along each dimension, and a third-order reconstruction based on a discrepancy formulation of the Active Flux method. Numerical results in 1D1V phase-space compare the properties of the various methods.

math.NA↗

arXiv2020

Coronavirus Perceptions And Economic Anxiety

We provide one of the first systematic assessments of the development and determinants of economic anxiety at the onset of the coronavirus pandemic. Using a global dataset on internet searches and two representative surveys from the US, we document a substantial increase in economic anxiety during and after the arrival of the coronavirus. We also document a large dispersion in beliefs about the pandemic risk factors of the coronavirus, and demonstrate that these beliefs causally affect individuals' economic anxieties. Finally, we show that individuals' mental models of infectious disease spread understate non-linear growth and shape the extent of economic anxiety.

econ.GN↗