# How I can change script for speed up

**URL:** <https://discourse.julialang.org/t/how-i-can-change-script-for-speed-up/104136>\
**Category:** General Usage\
**Created:** [September 22, 2023, 6:45am UTC](https://discourse.julialang.org/t/how-i-can-change-script-for-speed-up/104136 "2023-09-22T06:45:22Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![Take1234](https://avatars.discourse-cdn.com/v4/letter/t/839c29/32.png) [@Take1234](https://discourse.julialang.org/u/Take1234)\
**Post date:** [September 22, 2023, 6:45am UTC](https://discourse.julialang.org/t/how-i-can-change-script-for-speed-up/104136/1 "2023-09-22T06:45:23Z")

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Hi Experts ,I’m just start studing Julia. But I’m in truble.  
Berrow 2D turblence simulation code is that I translated from Matlab. But It is not working well, very slow and use a lot of memory so I couldn’t run 3D version.  
I would like to borrow your help.

using FFTW  
using Printf  
using LinearAlgebra  
using Plots  
using MAT

# set parameters

N = 128 ; # N\*N grid,  
dt = 0.02 ; # timestep  
simutimeSeconds = 10 ;

HowOftenSave = 10 ; # save velocity field per ‘HowOftenSave’ timesteps  
HowOftenVisu = 10 ; # show illustration per ‘HowOftenVisu’ timesteps  
simutimeSteps = round(simutimeSeconds/dt);

nu = 1/1000 ; # kinematic viscosity [nu] = m^2/s  
L = 2\*pi ; # domain side length  
dx = L/N ; # grid spacing assumed dx=dy

Umax = 1 ;  
F\_0 = 0.03 ; ;

# create fields

x = (L-dx)_(0:(N-1))/(N-1) ; # to be precise, dx is subtracted here  
y = (L-dx)_(0:(N-1))/(N-1) ; # otherwise the derivative of e.g. sin(x) wouldnt be differentiable on this periodic grid  
X=zeros(N,N);  
Y=zeros(N,N);  
for jx=1:N  
for ix=1:N  
X[ix,jx]=x[jx]  
Y[ix,jx]=y[ix]  
end  
end

# wavenumbers

kx1 = mod.(1/2 .+ (0:(N-1))/N, 1) .- 1/2;  
ky1 = mod.(1/2 .+ (0:(N-1))/N, 1) .- 1/2;  
kx = kx1\*(2_pi/dx); # wavenumbers  
ky = ky1_(2\*pi/dx); # wavenumbers

KX=zeros(N,N);  
KY=zeros(N,N);  
for jkx=1:N  
for ikx=1:N  
KX[ikx,jkx]=kx[jkx]  
KY[ikx,jkx]=ky[ikx]  
end  
end

# Anti-aliasing filter based on the 2/3\*kNyq rule

AA = (abs.(KX) .\< (2/3) \* maximum(kx)) .\* (abs.(KY) .\< (2/3) \* maximum(ky))

# Runge-Kutta 4 coefficients

a=[1/6 1/3 1/3 1/6]; b=[1/2 1/2 1 1];

#-- Taylor-Green --#  
kmax = 4;  
U = -Umax .\* cos.(kmax .\* X) .\* sin.(kmax .\* Y)  
V = Umax .\* sin.(kmax .\* X) .\* cos.(kmax .\* Y)  
U = U + randn(N,N)\*F\_0;  
V = V + randn(N,N)\*F\_0;

Uhat = fft(U)  
Vhat = fft(V)

Uhat = Uhat - (KX .\* Uhat + KY .\* Vhat) .\* KX ./ (KX .^ 2 + KY .^ 2)  
Uhat[isnan.(Uhat)] .= 0

Vhat = Vhat - (KX .\* Uhat + KY .\* Vhat) .\* KY ./ (KX .^ 2 + KY .^ 2)  
Vhat[isnan.(Vhat)] .= 0

matwrite(“uv0000.mat”, Dict(“U” =\> U, “V” =\> V));

# Navier-Stokes simulation begins

@elapsed begin  
for t=1:simutimeSteps  
@printf(“| Time step # %0.4d |\n”,t)

```
#SolveNavierStokes2D;
Uold = Uhat; 
Vold = Vhat;
Uc = Uhat; 
Vc = Vhat;

for rk in 1:4
    U = real.(ifft(AA .* Uc))
    V = real.(ifft(AA .* Vc))

    dUdx = real.(ifft(1im * KX .* AA .* Uc));
    dUdy = real.(ifft(1im * KY .* AA .* Uc));
    dVdx = real.(ifft(1im *KX .* AA .* Vc));
    dVdy = real.(ifft(1im * KY .* AA .* Vc));

    dUconv = fft(dt*(-U .* dUdx -V .* dUdy));
    dVconv = fft(dt*(-U .* dVdx -V .* dVdy));

    dUdiff = nu * dt * (-KX .* KX .* Uc - KY .* KY .* Uc);
    dVdiff = nu * dt * (-KX .* KX .* Vc - KY .* KY .* Vc);

    dU = dUconv + dUdiff;
    dV = dVconv + dVdiff;

    Uhat = Uhat-(KX.*Uhat + KY.*Vhat).*KX./(KX.^2 + KY.^2); Uhat[isnan.(Uhat)] .= 0;
    Vhat = Vhat-(KX.*Uhat + KY.*Vhat).*KY./(KX.^2 + KY.^2); Vhat[isnan.(Vhat)] .= 0;

    if rk < 4
        Uhat = Uold + b[rk] * dU
        Vhat = Vold + b[rk] * dV
    end        

    Uc = Uc + a[rk] * dU
    Vc = Vc + a[rk] * dV

end

Uhat = Uc
Vhat = Vc

Uhat = Uhat - (KX .* Uhat + KY .* Vhat) .* KX ./ (KX .^ 2 + KY .^ 2)
Uhat[isnan.(Uhat)] .= 0

Vhat = Vhat - (KX .* Uhat + KY .* Vhat) .* KY ./ (KX .^ 2 + KY .^ 2)
Vhat[isnan.(Vhat)] .= 0

U = real(ifft(Uhat));  
V = real(ifft(Vhat)); 

# SaveInstantField2D
if mod(t, HowOftenSave) == 0
filename = "uv$(@sprintf("%04d", t)).mat"
matwrite(filename, Dict("U" => U, "V" => V))
end

```

end  
end

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<div class="post-metadata">

**Author:** ![abraemer](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/abraemer/32/51403_2.png) [@abraemer](https://discourse.julialang.org/u/abraemer)\
**Post date:** [September 22, 2023, 6:51am UTC](https://discourse.julialang.org/t/how-i-can-change-script-for-speed-up/104136/2 "2023-09-22T06:51:44Z")

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It appears that your code is in global scope which is very slow. Put your performance critical code inside a function as recommended in the [Performance tips section of the manual](https://docs.julialang.org/en/v1/manual/performance-tips/#Performance-critical-code-should-be-inside-a-function).

Appart from that please format your code by putting it inside a code block

> ```julia  
> code  
> ```

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**Author:** ![Oscar\_Smith](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/oscar_smith/32/25343_2.png) [@Oscar\_Smith](https://discourse.julialang.org/u/Oscar_Smith)\
**Post date:** [September 22, 2023, 12:28pm UTC](https://discourse.julialang.org/t/how-i-can-change-script-for-speed-up/104136/3 "2023-09-22T12:28:47Z")

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don’t roll your own rk4. use an integrated from DifferentialEquations.jl

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<div class="post-metadata">

**Author:** ![Take1234](https://avatars.discourse-cdn.com/v4/letter/t/839c29/32.png) [@Take1234](https://discourse.julialang.org/u/Take1234)\
**Post date:** [October 4, 2023, 5:05am UTC](https://discourse.julialang.org/t/how-i-can-change-script-for-speed-up/104136/4 "2023-10-04T05:05:26Z")

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> [@Oscar\_Smith](#):
>
> integrated

What can I do DifferentialEquations.jl? What is difference own rk4 and DifferentialEquations.jl rk4. If you know something about Navier-Stokes quation with DifferentialEquations.jl,Please teach me about them.

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<div class="post-metadata">

**Author:** ![Oscar\_Smith](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/oscar_smith/32/25343_2.png) [@Oscar\_Smith](https://discourse.julialang.org/u/Oscar_Smith)\
**Post date:** [October 4, 2023, 12:35pm UTC](https://discourse.julialang.org/t/how-i-can-change-script-for-speed-up/104136/5 "2023-10-04T12:35:46Z")

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> [@Take1234](#):
>
> What is difference own rk4 and DifferentialEquations.jl rk4

the big difference is that by using a library it Will be a single line of code to switch to a good algorithm (e.g. tsit5).

I don’t understand your first question.