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Reorganize shooting method (not optional anymore)

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Nuwan Yapa 2025-04-16 16:08:32 -04:00
parent 897fdf9214
commit 0af47ef161
1 changed files with 27 additions and 27 deletions
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38
nucleons.jl
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@ -56,27 +56,28 @@ init_BC() = [1.0, 1.0] # TODO: Why not [0.0, 1.0]?
"Solve the Dirac equation and return the wave function u(r)=[g(r), f(r)] where "Solve the Dirac equation and return the wave function u(r)=[g(r), f(r)] where
divs is the number of mesh divisions so solution would be returned as a 2×(1+divs) matrix, divs is the number of mesh divisions so solution would be returned as a 2×(1+divs) matrix,
shooting method divides the interval into two partitions at r_max/2, ensuring convergence at both r=0 and r=r_max,
the other parameters are the same from dirac!(...)." the other parameters are the same from dirac!(...)."
function solveNucleonWf(κ, p::Bool, E, s::system; shooting=true, normalize=true, algo=Vern9()) function solveNucleonWf(κ, p::Bool, E, s::system; normalize=true, algo=Vern9())
(f1, f2) = optimized_dirac_potentials(p, s) (f1, f2) = optimized_dirac_potentials(p, s)
if shooting # partitioning
@assert s.divs % 2 == 0 "divs must be an even number when shooting=true" mid_idx = s.divs ÷ 2
prob = ODEProblem(dirac!, asymp_BC(κ, p, E, s.r_max), (s.r_max, s.r_max / 2)) r_mid = rs(s)[mid_idx]
sol = solve(prob, algo, p=(κ, E, f1, f2), saveat=Δr(s)) left_r = rs(s)[1:mid_idx]
right_r = rs(s)[mid_idx:end]
# left partition
prob = ODEProblem(dirac!, init_BC(), (0, r_mid))
sol = solve(prob, algo, p=(κ, E, f1, f2), saveat=left_r)
wf_left = hcat(sol.u...)
# right partition
prob = ODEProblem(dirac!, asymp_BC(κ, p, E, s.r_max), (s.r_max, r_mid))
sol = solve(prob, algo, p=(κ, E, f1, f2), saveat=right_r)
wf_right = reverse(hcat(sol.u...); dims=2) wf_right = reverse(hcat(sol.u...); dims=2)
next_r_max = s.r_max / 2 # for the next step
else
next_r_max = s.r_max
end
prob = ODEProblem(dirac!, init_BC(), (0, next_r_max)) # join two segments
sol = solve(prob, algo, p=(κ, E, f1, f2), saveat=Δr(s)) u1 = wf_left[:, end]
wf = hcat(sol.u...)
if shooting # join two segments
u1 = wf[:, end]
u2 = wf_right[:, 1] u2 = wf_right[:, 1]
if norm(u2) < 1e-10 if norm(u2) < 1e-10
@warn "Right partition too small to rescale, setting to zero" @warn "Right partition too small to rescale, setting to zero"
@ -85,8 +86,7 @@ function solveNucleonWf(κ, p::Bool, E, s::system; shooting=true, normalize=true
proj = only(u1' * u2) / norm(u2)^2 proj = only(u1' * u2) / norm(u2)^2
wf_right .*= proj wf_right .*= proj
end end
wf = hcat(wf[:, 1:(end - 1)], wf_right) wf = hcat(wf_left[:, 1:(end - 1)], wf_right)
end
if normalize if normalize
wf ./= norm(wf) * sqrt(Δr(s)) # integration by Reimann sum wf ./= norm(wf) * sqrt(Δr(s)) # integration by Reimann sum
@ -169,7 +169,7 @@ function calculateNucleonDensity(p::Bool, s::system)::Tuple{Vector{Float64}, Vec
ρr2 = zeros(2, s.divs + 1) # ρ×r² values ρr2 = zeros(2, s.divs + 1) # ρ×r² values
for (κ, E, occ) in zip(κs, Es, occs) for (κ, E, occ) in zip(κs, Es, occs)
wf = solveNucleonWf(κ, p, E, s; shooting=true, normalize=true) wf = solveNucleonWf(κ, p, E, s; normalize=true)
wf2 = wf .* wf wf2 = wf .* wf
ρr2 += (occ / (4 * pi)) * wf2 # 2j+1 factor is accounted in the occupancy number ρr2 += (occ / (4 * pi)) * wf2 # 2j+1 factor is accounted in the occupancy number
end end