9 citations · 21 across the 10 of their papers we have counts for
7 papers · 1 filter
The Numerical Flow Iteration for the Vlasov-Poisson equation
Matthias Kirchhart, Rostislav-Paul Wilhelm
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 distrib…
An interpolating particle method for the Vlasov-Poisson equation
Rostislav-Paul Wilhelm, Matthias Kirchhart
In this paper we present a novel particle method for the Vlasov--Poisson equation. Unlike in conventional particle methods, the particles are not interpreted as point charges, but…
Analytic Integration of the Newton Potential over Cuboids and an Application to Fast Multipole Methods
Matthias Kirchhart, Donat Weniger
We present simplified formulae for the analytic integration of the Newton potential of polynomials over boxes in two- and three-dimensional space. These are implemented in an easy-…
A Particle Method without Remeshing
Matthias Kirchhart, Christian Rieger
We propose a simple tweak to a recently developed regularisation scheme for particle methods. This allows us to chose the particle spacing proportional to the regularisation le…
On Particles and Splines in Bounded Domains
Matthias Kirchhart
We propose numerical schemes that enable the application of particle methods for advection problems in general bounded domains. These schemes combine particle fields with Cartesian…
A Smooth Partition of Unity Finite Element Method for Vortex Particle Regularization
Matthias Kirchhart, Shinnosuke Obi
We present a new class of -smooth finite element spaces on Cartesian grids, based on a partition of unity approach. We use these spaces to construct smooth approximations…
A Splitting-free Vorticity Redistribution Method
Matthias Kirchhart, Shinnosuke Obi
We present a splitting-free variant of the vorticity redistribution method. Spatial consistency and stability when combined with a time-stepping scheme are proven. We propose a new…