arXiv subjects

Daniel S. Finn

Publications and source records attributed to Daniel S. Finn.

3 recordsLinked to original sources

arXiv2026

Structure preservation using discrete gradients in the Vlasov-Poisson-Landau system

We present a novel structure-preserving framework for solving the Vlasov-Poisson-Landau system of equations using a particle in cell (PIC) discretization combined with discrete gradient time integrators. The Vlasov-Poisson-Landau system is an accurate model for studying hot plasma dynamics at a kinetic scale where small-angle Coulomb collisions dominate. Our scheme guarantees conservation of mass, momentum and energy as well as preservation of the monotonicity of entropy production in both the time-continuous and discrete systems. We employ the conservative integrator for both the Hamiltonian Vlasov-Poisson equations and the dissipative Landau equation using the PETSc library (www.mcs.anl.gov/petsc) to showcase structure-preserving properties.

physics.plasm-ph↗

arXiv2025

A projection method for particle resampling

Particle discretizations of partial differential equations are advantageous for high-dimensional kinetic models in phase space due to their better scalability than continuum approaches with respect to dimension. Complex processes collectively referred to as particle noise hamper long time simulations with particle methods. One approach to address this problem is particle mesh adaptivity or remapping, known as particle resampling. This paper introduces a resampling method that projects particles to and from a (finite element) function space. The method is simple; using standard sparse linear algebra and finite element techniques, it can adapt to almost any set of new particle locations and preserves all moments up to the order of polynomial represented exactly by the continuum function space. This work is motivated by the Vlasov-Maxwell-Landau model of magnetized plasmas with up to six dimensions, 3X in physical space and 3V in velocity space, and is developed in the context of a 1X + 1V Vlasov-Poisson model of Landau damping with logically regular particle and continuum phase space grids. Stable long time dynamics are demonstrated up to T = 500 and reproducibility artifacts and data with stable dynamics up to T = 1000 are publicly available.

physics.plasm-ph↗

arXiv2023

A Numerical Study of Landau Damping with PETSc-PIC

We present a study of the standard plasma physics test, Landau damping, using the Particle-In-Cell (PIC) algorithm. The Landau damping phenomenon consists of the damping of small oscillations in plasmas without collisions. In the PIC method, a hybrid discretization is constructed with a grid of finitely supported basis functions to represent the electric, magnetic and/or gravitational fields, and a distribution of delta functions to represent the particle field. Approximations to the dispersion relation are found to be inadequate in accurately calculating values for the electric field frequency and damping rate when parameters of the physical system, such as the plasma frequency or thermal velocity, are varied. We present a full derivation and numerical solution for the dispersion relation, and verify the PETSC-PIC numerical solutions to the Vlasov-Poisson for a large range of wave numbers and charge densities.

physics.plasm-ph↗