Benchmark

Here we provide a benchmark to identity the performance variation between Julia and Fortran implementations. For brevity, we direct make use of the dynamic library kitmod.so by ccall function in Julia, and compare the efficiency of computing numerical fluxes by BenchmarkTools.jl.

using Kinetic, BenchmarkTools

begin
    u = collect(-5.0:0.1:5.0)
    nu = length(u)
    weights = ones(nu) .* 0.5

    fw = zeros(3)
    fh = zeros(nu)
    fb = zeros(nu)

    inK = 2
    γ = 5.0 / 3.0
    primL = [1., 0., 1.]
    wL = prim_conserve(primL, γ)
    hL = maxwellian(u, primL) |> Array;
    bL = hL .* 2 ./ (2.)
    shL = zeros(nu)
    sbL = zeros(nu)
    lenL = 0.1

    primR = [0.5, 0., 1.]
    wR = prim_conserve(primR, γ)
    hR = maxwellian(u, primR) |> Array;
    bR = hR .* 2 ./ (2.)
    shR = zeros(nu)
    sbR = zeros(nu)
    lenR = 0.1

    muref = 0.001
    omega = 0.72
    prandtl = 1.0
    dt = 1e-4
end

#--- kfvs ---#
@btime ccall(
    (:__kinetic_MOD_flux_kfvs_2f1v, "kitmod.so"),
    Nothing,
    (
        Ref{Float64}, 
        Ref{Float64}, 
        Ref{Float64}, 
        Ref{Float64}, 
        Ref{Float64}, 
        Ref{Float64}, 
        Ref{Float64}, 
        Ref{Float64},
        Ref{Float64}, 
        Ref{Int}, 
        Ref{Float64}, 
        Ref{Float64}, 
        Ref{Float64}, 
        Ref{Float64},
        Ref{Float64},
    ),
    fw,
    fh,
    fb,
    hL,
    bL,
    hR,
    bR,
    u,
    weights,
    nu,
    dt,
    shL,
    sbL,
    shR,
    sbR,
)

@btime flux_kfvs!(fw, fh, fb, hL, bL, hR, bR, u, weights, dt, shL, sbL, shR, sbR)

#--- ugks ---#
@btime ccall(
    (:__kinetic_MOD_flux_ugks_2f1v, "kitmod.so"),
    Nothing,
    (
        Ref{Float64}, 
        Ref{Float64}, 
        Ref{Float64}, 
        Ref{Float64}, 
        Ref{Float64}, 
        Ref{Float64}, 
        Ref{Float64}, 
        Ref{Float64}, 
        Ref{Float64},
        Ref{Float64}, 
        Ref{Float64}, 
        Ref{Int}, 
        Ref{Float64}, 
        Ref{Float64}, 
        Ref{Float64}, 
        Ref{Float64}, 
        Ref{Float64}, 
        Ref{Float64}, 
        Ref{Float64}, 
        Ref{Float64},
        Ref{Float64}, 
        Ref{Float64}, 
        Ref{Float64}, 
        Ref{Float64},
    ),
    fw,
    fh,
    fb,
    wL,
    hL,
    bL,
    wR,
    hR,
    bR,
    u,
    weights,
    nu,
    inK,
    γ,
    muref,
    omega,
    prandtl,
    dt,
    lenL,
    lenR,
    shL,
    sbL,
    shR,
    sbR,
)

@btime flux_ugks!(fw, fh, fb, wL, hL, bL, wR, hR, bR, u, weights, inK, γ, muref, omega, prandtl, dt, lenL, lenR, shL, sbL, shR, sbR)

The results on a intel NUC8i7BEH with i7-8559U with 101 velocity points is as follows

Kinetic.jl

• KFVS flux ~ 6.747 μs (13 allocations: 11.38 KiB)
• UGKS flux ~ 13.344 μs (123 allocations: 20.94 KiB)

KitFort.jl

• KFVS flux ~ 5.421 μs (37 allocations: 800 bytes)
• UGKS flux ~ 11.413 μs (55 allocations: 1.09 KiB)

As presented, there is an improvement on efficiency by around 15%.