system of equations runs slow

Question

Conrado Garcia 2020-4-23

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/520112-system-of-equations-runs-slow

评论： darova 2020-4-23

Hi to everyone!

Here I present a problem that occurs to me when running a simulation

I have to solve a system of equations multiple times. The system is linear and can be solved by x=A\b. there are 273 variables. The system has to be solved 87600 times. Since every iteration depends on the results of the previous time step (t) the matrix A is changing. In the code below you have my approach. R(j,i) and C(j,i) are previously calculated.

The problem is that for every iteration of t it takes about 1 minute.

syms T [length(depth) length(r)]
syms Tbor
k=1;
t=1;
Tsol=Tm*ones(length(depth),length(r),tsimulation);
for t=1:tsimulation
for j=1:length(depth)
 tic   
    
    
    for i=1:length(r)
        Tprev=Tm;
        
        if i==1 && j==1
%             eqns(k)= 2*(Tf0(t)-Tb)/Rb + (T(j,1)-Tb)/R(j,1)== 0;
%             k=k+1;
            eqns(k)= (Tb(t)-T(j,i))/R(j,i) +(T(j,i+1)-T(j,i))/R(j,i+1) + (Tsurface(t)-T(j,i))/Rprima + (T(j+1,i)-T(j,i))/Rprima - C(j,i)*(T(j,i)-Tprev)/paso ==0;
               
        end
        if i==1 && j>1 && j<length(depth)
%             eqns(k)= 2*(Tf0(t)-Tb(t))/Rb + (T(j,1)-Tb(t))/R(j,1)== 0;
%             k=k+1;
            eqns(k)= (Tb(t)-T(j,i))/R(j,i) +(T(j,i+1)-T(j,i))/R(j,i+1) + (T(j-1,i)-T(j,i))/Rprima + (T(j+1,i)-T(j,i))/Rprima - C(j,i)*(T(j,i)-Tprev)/paso ==0;
            
        end
        if i>1 && j==1 && i<length(r)
             eqns(k)= (T(j,i-1)-T(j,i))/R(j,i) +(T(j,i+1)-T(j,i))/R(j,i+1) + (Tsurface(t)-T(j,i))/Rprima + (T(j+1,i)-T(j,i))/Rprima - C(j,i)*(T(j,i)-Tprev)/paso ==0;
           
        end
        if i>1 && j>1  && i<length(r) && j<length(depth)
            eqns(k)= (T(j,i-1)-T(j,i))/R(j,i) +(T(j,i+1)-T(j,i))/R(j,i+1) + (T(j-1,i)-T(j,i))/Rprima + (T(j+1,i)-T(j,i))/Rprima - C(j,i)*(T(j,i)-Tprev)/paso ==0;
            
        end
        if i==length(r) || j==length(depth)
            eqns(k)= T(j,i)==Tm;
           
        end
       k=k+1;
    end
end
[A b]=equationsToMatrix(eqns,T);
    Tb(t)=(-2*R(j,1)*Tf0(t)-Rb*Tsol(j,1,t))/(-2*R(j,1)-Rb);
    if t==1
        Tprev=Tm;
    else
        Tprev=Tsol(j,i,t-1);
    end
 Tcalc=A\b; toc;
Tcalc=double(Tcalc);
% Tcalc=[Tcalc{:}];
% Tcalc=double(Tcalc);
for j=1:length(depth)
    for i=1:length(r)
        Tsol(j,i,t)=Tcalc(i);
    end
    
end
t
end