Is it possible to make the program faster?

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My problem is that i have a program with many operations that runs for more than 12 hours and i would like to ask if there is any possibility to make it run faster. I am using two for loops where the first one runs the timesteps for one year in steps of 2.5s. So there we already have 12.614.400 iterations and within this for loop we have another for loop that runs over the number of layers of a watertank. I would like to know if i could somehow exchange my for loops to make the program run faster.
clear all
roh_w = 983.2;
cp_w = 4183;
lambda_w = 0.6544;
dt = 2.5;
m_strom = 1;
r = 0.5;
h = 2.5;
Tankschichten = 60;
Zeitschritte = 1440;
T_Start = 80;
T_ein = 50;
A_Tank = pi*r*r;
h_Schicht = h/Tankschichten;
v_w = m_strom/(roh_w*A_Tank);
CFL = (v_w*dt)/h_Schicht;
Fo = (lambda_w*dt)/(roh_w*cp_w*h_Schicht*h_Schicht);
T = zeros(Tankschichten,1);
for x = 1 : Zeitschritte
T_old = T;
if x == 1
for y = 1 : Tankschichten
T(y) = 80;
end
else
for y = 1 : Tankschichten
if y == 1
T(y) = (Fo + CFL)*T_ein + (1 - 2*Fo - CFL)*T_old(y) + Fo*T_old(y+1);
elseif y == Tankschichten
T(y) = (Fo + CFL)*T_old(y-1) + (1 - 2*Fo - CFL)*T_old(y) + Fo*T_old(y);
else
T(y) = (Fo + CFL)*T_old(y-1) + (1 - 2*Fo - CFL)*T_old(y) + Fo*T_old(y+1);
end
end
end
T_store(:,x) = T;
end
figure
plot(T_store(50,:))
hold on
ylabel("Temperatur [°C]")
xlabel("Timestep")

采纳的回答

Rik
Rik 2023-2-14
Below you will see my attempt and vectorizing your code. As you may notice, this is not actually faster, which shows you that the loops themselves are not really the issue.
The main things missing from your code are documentation and comments. You should also consider pre-allocating T_store with something like T_store = zeros(Tankschichten,Zeitschritte);.
roh_w = 983.2;
cp_w = 4183;
lambda_w = 0.6544;
dt = 2.5;
m_strom = 1;
r = 0.5;
h = 2.5;
Tankschichten = 60;
Zeitschritte = 1440;
T_Start = 80;
T_ein = 50;
A_Tank = pi*r*r;
h_Schicht = h/Tankschichten;
v_w = m_strom/(roh_w*A_Tank);
CFL = (v_w*dt)/h_Schicht;
Fo = (lambda_w*dt)/(roh_w*cp_w*h_Schicht*h_Schicht);
T_store=vectorized(Zeitschritte,Tankschichten,Fo,CFL,T_ein);
plot(T_store(50,:))
hold on
ylabel("Temperatur [°C]")
xlabel("Timestep")
% Run them all as a warm up.
double_loop(Zeitschritte,Tankschichten,Fo,CFL,T_ein);
double_loop2(Zeitschritte,Tankschichten,Fo,CFL,T_ein);
vectorized(Zeitschritte,Tankschichten,Fo,CFL,T_ein);
fprintf('looped: %.5f\n',timeit(@() double_loop(Zeitschritte,Tankschichten,Fo,CFL,T_ein)))
looped: 0.00335
fprintf('looped: %.5f\n',timeit(@() double_loop2(Zeitschritte,Tankschichten,Fo,CFL,T_ein)))
looped: 0.00302
fprintf('vector: %.5f\n',timeit(@() vectorized(Zeitschritte,Tankschichten,Fo,CFL,T_ein)))
vector: 0.00447
isequal(...
double_loop(Zeitschritte,Tankschichten,Fo,CFL,T_ein) ,...
vectorized( Zeitschritte,Tankschichten,Fo,CFL,T_ein) )
ans = logical
1
function T_store=vectorized(Zeitschritte,Tankschichten,Fo,CFL,T_ein)
T = 80*ones(Tankschichten,1);
T_store = 80*ones(Tankschichten,Zeitschritte);
for x = 2 : Zeitschritte
T_old = T;
T(end) = [];
T = (Fo + CFL)*[T_ein;T] + (1 - 2*Fo - CFL)*T_old + Fo*[T_old(2:end);T_old(end)];
T_store(:,x) = T;
end
end
function T_store=double_loop(Zeitschritte,Tankschichten,Fo,CFL,T_ein)
T = zeros(Tankschichten,1);
for x = 1 : Zeitschritte
T_old = T;
if x == 1
for y = 1 : Tankschichten
T(y) = 80;
end
else
for y = 1 : Tankschichten
if y == 1
T(y) = (Fo + CFL)*T_ein + (1 - 2*Fo - CFL)*T_old(y) + Fo*T_old(y+1);
elseif y == Tankschichten
T(y) = (Fo + CFL)*T_old(y-1) + (1 - 2*Fo - CFL)*T_old(y) + Fo*T_old(y);
else
T(y) = (Fo + CFL)*T_old(y-1) + (1 - 2*Fo - CFL)*T_old(y) + Fo*T_old(y+1);
end
end
end
T_store(:,x) = T;
end
end
function T_store=double_loop2(Zeitschritte,Tankschichten,Fo,CFL,T_ein)
T = zeros(Tankschichten,1);
T_store = zeros(Tankschichten,Zeitschritte);
for x = 1 : Zeitschritte
T_old = T;
if x == 1
for y = 1 : Tankschichten
T(y) = 80;
end
else
for y = 1 : Tankschichten
if y == 1
T(y) = (Fo + CFL)*T_ein + (1 - 2*Fo - CFL)*T_old(y) + Fo*T_old(y+1);
elseif y == Tankschichten
T(y) = (Fo + CFL)*T_old(y-1) + (1 - 2*Fo - CFL)*T_old(y) + Fo*T_old(y);
else
T(y) = (Fo + CFL)*T_old(y-1) + (1 - 2*Fo - CFL)*T_old(y) + Fo*T_old(y+1);
end
end
end
T_store(:,x) = T;
end
end

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