Matlab: How to run code using multi threading/parallel computing?

Question

I have Matlab code that simulates something called the 2-D Lid Driven Cavity Flow. In this code I have the following structure:

for i = 1:timeStep
  %Lets call this Part 1
  for a1 = 1:N 
    for b1 = 1:N
    %calculates things
    end
  end
  %Lets call this Part 2
  for a2 = 1:N 
    for b2 = 1:N
    %calculates things
    end
  end
  %Lets call this Part 3
  for a3 = 1:N 
    for b3 = 1:N
    %calculates things
    end
  end 
end

Since Part 1, Part 2, and Part 3 are independent pf each other I would like to compute them in parallel, or multi thread them, every time there is a timeStep (every iteration of primary for loop). Is there any way I can achieve this? Thanks!

I include my code to to reference:

Nx = 50;
Ny = 50;
numTimesteps = 10000;
reynoldsNum = 1000;
dt = 0.0025;
numIter = 100000;
Beta = 1.5;
maxErr = 0.001;
ds = 1/(Nx + 1);
x1 = 0:ds:1;
x2 = 0:ds:1;
time = 0;
boundarySpeed = 1;

PHI = zeros(Nx+2, Ny+2);
OMEGA = zeros(Nx+2, Ny+2);
U = zeros(Nx+2, Ny+2);
V = zeros(Nx+2, Ny+2);
x2d = zeros(Nx+2, Ny+2);
y2d = zeros(Nx+2, Ny+2);
PRESSURE = zeros(Nx+2, Ny+2);
B = zeros(Nx+2, Ny+2);
pressureOLD = zeros(Nx+2, Ny+2);
W = zeros(Nx+2, Ny+2);

for i = 1:Nx+2
    for j = 1:Ny+2
        x2d(i,j) = x1(i);
        y2d(i,j) = x2(j);
    end
end

for timeStep = 1:numTimesteps   

    if(mod(timeStep,10000) == 0)
        disp(timeStep);
    end

    OLDPHI = PHI;
    OLDOMEGA = OMEGA;
    OLDPRESSURE = PRESSURE;

    parfor parJob = 1:4 

        switch parJob
%{
----------------------------------
   STREAM FUNCTION CALCULATION
----------------------------------
%}
        case 1
        for iter = 1:numIter
            ERRMATRIX = OLDPHI;
            for i = 2:Nx+1
                for j = 2:Ny+1
                    PHI(i,j) = (1/4) * Beta * (OLDPHI(i+1,j) + OLDPHI(i-1,j) + OLDPHI(i,j+1) + OLDPHI(i,j-1) + ...
                               ds * ds * OLDOMEGA(i,j)) + (1 - Beta) * OLDPHI(i,j);
                end
            end
            Err = 0;
            for i = 1:Nx+2
                for j = 1:Ny+2
                    Err = Err + abs(ERRMATRIX(i,j) - PHI(i,j));
                end
            end
            if (Err <= maxErr)
                break;  
            end
            OLDPHI = PHI;   
        end
%{
----------------------------------
BOUNDARY CONDITIONS FOR VORTICITY
----------------------------------
%}
        case 2
        for i = 2:Nx+1
            for j = 2:Ny+1
                OMEGA(i,1) = -2 * OLDPHI(i,2) / (ds * ds); % bottom wall
                OMEGA(i,Ny+2) = -2 * OLDPHI(i,Ny+1) / (ds * ds) - 2 * boundarySpeed / ds; % top wall
                OMEGA(1,j) = -2 * OLDPHI(2,j) / (ds * ds); % right wall
                OMEGA(Nx+2,j) = -2 * OLDPHI(Nx+1,j) / (ds * ds); % left wall
            end
        end 
%{
----------------------------------
     VORTICITY CALCULATIONS
----------------------------------  
%}  
        for i = 2:Nx+1
            for j = 2:Ny+1
                W(i,j) = -(1 / 4) * ((OLDPHI(i,j+1) - OLDPHI(i,j-1)) * (OLDOMEGA(i+1,j) - OLDOMEGA(i-1,j)) ...
                         - (OLDPHI(i+1,j) - OLDPHI(i-1,j)) * (OLDOMEGA(i,j+1) - OLDOMEGA(i,j-1))) / (ds * ds) ...
                         +(1 / reynoldsNum) * (OLDOMEGA(i+1,j) + OLDOMEGA(i-1,j) + OLDOMEGA(i,j+1) + ...
                         OLDOMEGA(i,j-1) - 4 * OLDOMEGA(i,j)) / (ds * ds);

            end
        end

        OMEGA(2:Nx+1,2:Ny+1) = OLDOMEGA(2:Nx+1,2:Ny+1) + dt * W(2:Nx+1,2:Ny+1);

        time = time + dt;

        for i = 1:Nx
            for j = 1:Ny
                x2d(i,j) = x1(i);
                y2d(i,j) = x2(j);
            end
        end

%{
----------------------------------
      U AND V CALCULATIONS
----------------------------------
%}
        case 3
        for i = 2:Nx+1
            for j = 2:Ny+1
                U(i,j) = (OLDPHI(i,j+1) - OLDPHI(i,j)) / (2 * ds);
                V(i,j) = -(OLDPHI(i+1,j) - OLDPHI(i,j)) / (2 * ds);
                U(:,Ny+2) = 1;  
                V(Nx+2,:) = 0.0;
            end
        end
%{
----------------------------------
      PRESSURE CALCULATIONS
----------------------------------
%}
        otherwise
        for i = 2:Nx+1
            for j = 2:Ny+1
                PRESSURE(i,j) = (1/4) * (pressureOLD(i+1,j) + pressureOLD(i-1,j) + pressureOLD(i,j+1) ...
                                + pressureOLD(i,j-1)) - (1/2) * (((((OLDPHI(i-1,j) - 2 * OLDPHI(i,j) + ...
                                OLDPHI(i+1,j)) / (ds^2)) * ((OLDPHI(i,j-1) - 2 * OLDPHI(i,j) + OLDPHI(i,j+1)) / (ds^2))) ...
                                - (OLDPHI(i+1,j+1) - OLDPHI(i+1,j-1) - OLDPHI(i-1,j+1) + OLDPHI(i-1,j-1)) / (4 * (ds^2))) * ds^2);
            end
            pressureOLD = PRESSURE;
        end
        end
    end

score 2 · Accepted Answer · 2016-12-13 01:34:50Z

2

You can use parfor to run jobs in parallel.

result = cell(3, 1);
parfor k = 1:3
    result{k} = ['result-' num2str(k)]; 
    switch k
      case 1
          disp('do part one')

      case 2
          disp('do part two')

      otherwise
          disp('do part three')
    end
end

edited Dec 13, 2016 at 1:34

answered Dec 11, 2016 at 10:14

user2900180

Sign up to request clarification or add additional context in comments.

4 Comments

David Over a year ago

I have tried what you suggested, but end up with errors such as "The variable PHI in a parfor cannot be evaluated" or "The variable OMEGA in a parfor cannot be evaluated". Any hints as to why that is happening?

user2900180 Over a year ago

you cannot share variables between threads, but you can either use cell array, or use three diferent variables (one per part) to save result of your computation and after parfor union them.

David Over a year ago

Could you please elaborate on the cell arrays? I am not sure what you are trying to get across.

user2900180 Over a year ago

@David, I edited the code to show how one can accumulate results from parallel computations using cell array. I also tested now, it also works with matrix, but i remember that this trick worked only with cell array. May be it depends on matlab's version? I've tested on 2015b now.

Collectives™ on Stack Overflow

Matlab: How to run code using multi threading/parallel computing?

1 Answer 1

4 Comments

Your Answer

Hot Network Questions

Collectives™ on Stack Overflow

1 Answer 1

4 Comments

Your Answer

Sign up or log in

Post as a guest

Related