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Major optimization to the Dirac equation

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Nuwan Yapa 2025-02-18 17:52:26 -05:00
parent 6c219816ed
commit 459d35e08e
1 changed files with 28 additions and 12 deletions
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40
nucleons.jl
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@ -11,16 +11,32 @@ const r_reg = 1E-8 # fm # regulator for the centrifugal term
κ is the generalized angular momentum,
p is true for proton and false for neutron,
E in the energy in MeV,
Φ0, W0, B0, A0 are the mean-field potentials (couplings included) in MeV as functions of r in fm,
f1(r) = M-Φ0(r)-W0(r)-(p-0.5)*2B0(r)-p*A0(r) is a function of r in MeV (see optimized_dirac_potentials()),
f2(r) = -M+Φ0(r)-W0(r)-(p-0.5)*2B0(r)-p*A0(r) is a function of r in MeV (see optimized_dirac_potentials()),
r is the radius in fm.
Reference: P. Giuliani, K. Godbey, E. Bonilla, F. Viens, and J. Piekarewicz, Frontiers in Physics 10, (2023)"
function dirac!(du, u, (κ, p, E, Φ0, W0, B0, A0), r)
M = p ? M_p : M_n
common1 = E - W0(r) - (p - 0.5) * 2B0(r) - p * A0(r)
common2 = M - Φ0(r)
function dirac!(du, u, (κ, E, f1, f2), r)
(g, f) = u
du[1] = -(κ/(r + r_reg)) * g + (common1 + common2) * f / ħc
du[2] = (κ/(r + r_reg)) * f - (common1 - common2) * g / ħc
@inbounds du[1] = -(κ/(r + r_reg)) * g + (E + f1(r)) * f / ħc
@inbounds du[2] = (κ/(r + r_reg)) * f - (E + f2(r)) * g / ħc
end
"Get the potentials f1 and f2 that goes into the Dirac equation, defined as
f1(r) = M-Φ0(r)-W0(r)-(p-0.5)*2B0(r)-p*A0(r),
f2(r) = -M+Φ0(r)-W0(r)-(p-0.5)*2B0(r)-p*A0(r)."
function optimized_dirac_potentials(p, s::system)
M = p ? M_p : M_n
f1s = zero_array(s)
f2s = zero_array(s)
@. f1s = M - s.Φ0 - s.W0 - (p - 0.5) * 2 * s.B0 - p * s.A0
@. f2s = -M + s.Φ0 - s.W0 - (p - 0.5) * 2 * s.B0 - p * s.A0
f1 = linear_interpolation(rs(s), f1s)
f2 = linear_interpolation(rs(s), f2s)
return (f1, f2)
end
"Solve the Dirac equation and return the wave function u(r)=[g(r), f(r)] where
@ -28,12 +44,12 @@ end
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!(...)."
function solveNucleonWf(κ, p, E, s::system; shooting=true, normalize=true, algo=Tsit5())
(Φ0, W0, B0, A0) = fields_interp(s)
(f1, f2) = optimized_dirac_potentials(p, s)
if shooting
@assert s.divs % 2 == 0 "divs must be an even number when shooting=true"
prob = ODEProblem(dirac!, [0, 1], (s.r_max, s.r_max / 2))
sol = solve(prob, algo, p=(κ, p, E, Φ0, W0, B0, A0), saveat=Δr(s))
sol = solve(prob, algo, p=(κ, E, f1, f2), saveat=Δr(s))
wf_right = reverse(hcat(sol.u...); dims=2)
next_r_max = s.r_max / 2 # for the next step
else
@ -41,7 +57,7 @@ function solveNucleonWf(κ, p, E, s::system; shooting=true, normalize=true, algo
end
prob = ODEProblem(dirac!, [0, 1], (0, next_r_max))
sol = solve(prob, algo, p=(κ, p, E, Φ0, W0, B0, A0), saveat=Δr(s))
sol = solve(prob, algo, p=(κ, E, f1, f2), saveat=Δr(s))
wf = hcat(sol.u...)
if shooting # join two segments
@ -66,8 +82,8 @@ end
the other parameters are the same from dirac!(...)."
function boundaryValueFunc(κ, p, s::system; dtype=Float64, algo=Tsit5())
prob = ODEProblem(dirac!, convert.(dtype, [0, 1]), (0, s.r_max))
(Φ0, W0, B0, A0) = fields_interp(s)
func(E) = solve(prob, algo, p=(κ, p, E, Φ0, W0, B0, A0), saveat=[s.r_max], save_idxs=[1])[1, 1]
(f1, f2) = optimized_dirac_potentials(p, s)
func(E) = solve(prob, algo, p=(κ, E, f1, f2), saveat=[s.r_max], save_idxs=[1])[1, 1]
return func
end