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

PM: main code blocks 28
⇒ Given a density field ˜δ(r) in real space, we can solve for the gravitational
potential by
• performing the FFT to get ˜δ(k),
• multiplying every element in the field by the corresponding value of G(k) to
get ˜φ(k),
ˆφ lmn = G(k lmn )ˆρ lmn , where
N g −1
∑
ˆf lmn = (∆x) 3
f ijk = 1 L 3
i,j,k=0
N g −1
∑
l,m,n=0
f ijk e −i2π(il+jm+kn)/N g
,
ˆf lmn e i2π(il+jm+kn)/N g
.
• transforming 8 the result back to real space to get ˜φ(r) discretized at cell
centers.
8 Be careful about normalization of the FFT. The transforms ˜δ(r) → ˜δ(k) and ˜δ(k) → ˜δ(r) should recover the
original field ˜δ(r).