Core Concepts
Introducing a novel Particle-in-Fourier scheme for non-periodic boundary conditions with energy conservation.
Abstract
The content introduces a new Particle-in-Fourier (PIF) method that extends its applicability to non-periodic boundary conditions. It explains the modifications made to handle free space and Dirichlet boundary conditions, providing numerical results to demonstrate accuracy and conservation properties.
Introduction
Overview of traditional PIC schemes and challenges.
Development of the PIF scheme for energy conservation.
Prerequisites
Explanation of the particle-in-cell method.
Introduction to the particle-in-Fourier scheme.
Particle-in-Fourier Scheme
Details on improving energy conservation in PIC methods.
Explanation of the PIF approach and its advantages.
Vico-Greengard-Ferrando Free Space Poisson Solver
Description of solving Poisson's equation with free space boundaries.
Combining PIF with Spectral Free Space Poisson Solver
Algorithm outline for combining PIF with a free space Poisson solver.
Dirichlet Boundary Conditions
Application of potential theory for Dirichlet boundary conditions.
Energy Convergence Analysis
Mathematical proof showing second-order convergence in energy conservation.
Stats
Our scheme achieves spectral accuracy without precomputation step, as shown by L2 norm error decay faster than any polynomial order as Nm increases.