Electrostatic and Gravitational Solves Using PETSc-PIC

Numerical solutions to the Vlasov-Poisson equations have important applications in the fields of plasma physics, solar physics and cosmology. The goal of this research is to develop a structure-preserving, electrostatic and gravitational Vlasov-Poisson(-Landau) model using the Portable, Extensible Toolkit for Scientific Computation (PETSc) and study the presence of Landau damping in a variety of systems, such as thermonuclear fusion reactors and galactic dynamics. The PETSc Particle-In-Cell (PETSc-PIC) model is a highly-scalable, structure preserving PIC method with multigrid capabilities. 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 radial basis functions to represent the particle field. Collisions are added to the formulation by means of a particle-basis Landau collision operator, recently added to the PETSc library.