Exploring Novel Electromagnetic Algorithms for Efficient Particle-in-Cell Simulations*

In particle-based fluid-kinetic plasma simulations¹, an electromagnetic-field solver is coupled to the particles via a mesh. Explicit finite-difference time-domain (FDTD) methods solve Maxwell’s equations and require very small time steps when high-resolution meshes are used. Long-time-scale simulations might require 10⁵ to 10⁷ time steps in order to reach the hydrodynamic time of interest. A critical area of research is to accelerate these computations using GPU hardware. The use of implicit methods generally requires additional operations to solve banded matrices and has a more-complex algorithm design, but benefits from being unconditionally stable and unrestricted by the need to resolve the speed of light on the mesh. This enables larger time steps and shorter computation times. The fundamental locally one-dimensional complying divergence (FLOD-CD) FDTD method² is an unconditionally stable semi-implicit non-iterative method. We report on our efforts to test this and similar algorithms for accuracy, efficiency, memory use, and how well they can be accelerated and parallelized. Our goal is to stably and accurately achieve very long simulation times for inertial confinement fusion, high-energy-density physics, and magnetic fusion energy applications.