The use of tricubic interpolation with spectral derivatives to integrate particle trajectories in complicated electromagnetic fields
Codes that calculate the trajectories of particles in complicated electromagnetic fields often include spectral methods, which take advantage of the speed of FFTs to rapidly solve for the fields. In this case, Hermite tricubic interpolation can be used to calculate the fields between grid points, with spectral derivates used to determine the interpolation coefficients. This method is extremely accurate, and in the case of electrostatic fields produces an energy conserving force when incorporated into a particle follower code.
interpolation spectral electromagnetic hermite particle follower