Monday, 07/24: Writing a pm-code - AIP

PM: main code blocks 30
After n time steps, a n = a i + n∆a, during the step n + 1, we should have
coordinates ˜x n at a n and momenta ˜p n−1/2 at a n−1/2 = a n − ∆a/2 from the
previous step. Assigning density and solving the Poisson equation gives
potential ˜φ n at a n . For the assumed variables and units, positions and
momenta are updated as follows:
˜p n+1/2 = ˜p n−1/2 + f(a n )˜g n ∆a;
˜x n+1 = ˜x n + a −2
n+1/2 f(a n+1/2)˜p n+1/2 ∆a.
Here, ˜g n = − ˜∇ ˜φ n is acceleration at the particle’s position. This acceleration
can be obtained by interpolating accelerations from the neighboring cell
centers. The latter are given by
˜g x i,j,k = −( ˜φ i+1,j,k − ˜φ i−1,j,k )/2, ˜g y i,j,k = −( ˜φ i,j+1,k − ˜φ i,j−1,k )/2,
˜g z i,j,k = −( ˜φ i,j,k+1 − ˜φ i,j,k−1 )/2.