maxima 工具(微积分、插值)

通用的 PIC 方法的过程(把这个调研清楚)

Particle-In-Cell (PIC) is a technique commonly used to simulate motion of charged particles, or plasma.

plasma(等离子体): a gas of ions and atoms

Basic Physics: Coulomb force(库仑力), Lorentz force(洛伦兹力)

Motivation: we could simulate plasma by computing the storm of particles directly, but plasma simulations generally require at least 1M particles to reduce numerical errors (n²-problem - not feasible), especially when a typical simulation requires Ks of steps

PIC: Compute an electric field from the particles and then compute forces from the electric field (size-n problem). Group a large number of real particles into one computational particle (let ratio be “specific weight”, a.k.a. sp_wt)

$\nabla$ (nabla operator - generates one of gradient $\nabla f$, divergence $\nabla\cdot f$ or curl $\nabla\times f$)

Fundamental equations: See below

Steps:

  1. Compute charge density (电荷密度): distribute charges to adjacent nodes on the grid mesh
  2. Compute electric potential (电势): Solve Poisson equation (?)
  3. Compute electric field: (equals to) the gradient of potential
  4. Move particles (compute motion) using offset-by-half time frames for velocity and displacement (position/location)