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)))
fprintf('looped: %.5f\n',timeit(@() double_loop2(Zeitschritte,Tankschichten,Fo,CFL,T_ein)))
fprintf('vector: %.5f\n',timeit(@() vectorized(Zeitschritte,Tankschichten,Fo,CFL,T_ein)))
isequal(...
double_loop(Zeitschritte,Tankschichten,Fo,CFL,T_ein) ,...
vectorized( Zeitschritte,Tankschichten,Fo,CFL,T_ein) )
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
