Accelerating Kinetic Simulations of Electrostatic Plasmas with Reduced-Order Modeling

We present a cost-effective method for collisionless electrostatic plasma kinetics based on the Vlasov-Poisson equation. Eulerian simulations are computationally expensive due to high dimensionality, while particle-based methods suffer from statistical noise and require many particles. Our reduced-order modeling (ROM) approach projects the equation onto a linear subspace spanned by major proper orthogonal decomposition (POD) modes. We introduce a tensorial approach to efficiently update the nonlinear term using a precomputed third-order tensor. To capture multi-scale behaviors with a few POD modes, we decompose the solution into multiple time windows, constructing a temporally-local ROM. Demonstrated on 1D--1V simulations with a prescribed electric field and the benchmark two-stream instability case, our tensorial approach solves the equation about 100 times faster than Eulerian simulations. Time-windowing significantly improves the ROM performance, especially for nonlinear simulations.