Chapter 4
Optimized Algorithms for the Signed-Particle Method

This chapter highlights the improvements and contributions that have been made to optimize the algorithms of the signed-particle method. The contributions encompass algorithms for increased computational efficiency, statistical enhancement and address certain discretization effects which can lead to erroneous behaviour in simulations. Finally, the accuracy of the signed-particle method with the optimized algorithms is demonstrated by a comparison of numerical results to the exact solution of a physical problem.

 4.1 Wigner potential
  4.1.1 Full discretization
  4.1.2 Efficient calculation of two-dimensional Wigner potential
  4.1.3 Choice of coherence length
  4.1.4 Tapering window
 4.2 Generation process
 4.3 Annihilation process
  4.3.1 Numerical diffusion
  4.3.2 Spatial scaling
  4.3.3 Ensemble sorting
  4.3.4 Particle growth prediction
 4.4 Validation