The Numerical Flow Iteration for the Vlasov-Poisson equation

TL;DR

The paper introduces NuFI, a novel numerical method for solving the Vlasov-Poisson equation that offers high resolution, preserves key physical properties, and is computationally efficient and highly parallelizable.

Contribution

NuFI is a new numerical flow iteration method that achieves infinite resolution and exact preservation of physical invariants for the Vlasov-Poisson equation.

Findings

NuFI preserves positivity, all L^p norms, charge, and entropy.

No energy drift observed in numerical experiments.

Requires significantly less memory and is GPU-parallelizable.

Abstract

We present the numerical flow iteration (NuFI) for solving the Vlasov--Poisson equation. In a certain sense specified later herein, NuFI provides infinite resolution of the distribution function. NuFI exactly preserves positivity, all $L^p$-norms, charge, and entropy. Numerical experiments show no energy drift. NuFI is fast, requires several orders of magnitude less memory than conventional approaches, and can very efficiently be parallelised on GPU clusters. Low fidelity simulations provide good qualitative results for extended periods of time and can be computed on low-cost workstations.