This document compares the speed of performing finite difference calculations using parallel computing toolbox functions on a GPU versus a CPU. It presents a script that runs timed loops of a 2D finite difference heat equation calculation on arrays of varying sizes, both on a GPU and CPU. The results are stored in a performance table showing the millions of operations per second for different loop and array sizes. The GPU is faster for larger problems, with certain GPU optimizations like using arrayfun and GPU arrays providing additional speedups over normal MATLAB syntax.

1. PARALLEL COMPUTING (SAMPLE ASSIGNMENT)
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Finite difference equation
This sample assignment Compares the speed of the parallel computing toolbox functions vs
CPU for finite difference
test_gpu_array3.m
% script to test the speed of finite difference calculations on gpu vs cpu
% Mark Ward, University of Birmingham, r.m.ward@bham.ac.uk
LoopVals=500*(1:2); % how many times we want to loop the calculations for timing
NVals=1000*(1:4); % what array edge sizes we want to try
myPerf=zeros(length(LoopVals)+1,length(NVals)+1); % somewhere to store a table of
performance numbers
myPerf(2:end,1)=LoopVals; % record the loop sizes
myPerf(1,2:end)=NVals; % and array sizes
%======================
iGPU=true % true to run on GPU, false for CPU
%======================
for iLoopVals=1:length(LoopVals)
for iNVals=1:length(NVals)
N=NVals(iNVals);
% set up arrays for the finite difference calculation
if iGPU,
clear g1 iicentre
pause(0.5)
g=gpuDevice(1);
reset(g);
pause(0.5)
g1=gpuArray.zeros(N,N); %,'single');
iicentre=2:N-1;
iicentre=gpuArray(iicentre); %(int32(iicentre)) isn't noticeably
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iiup=iicentre+1;
iidown=iicentre-1;
else
g1=zeros(N,N);
iicentre=2:N-1; % indices to point to the array away from the
edges
iiup=iicentre+1; % and the edges
iidown=iicentre-1;
end
ii=round(0.4*N):round(0.6*N);g1(ii,ii)=1; % make the array hotter in the
centre
iLoop=LoopVals(iLoopVals);
fprintf('About to run %g loops of %g^2 2D finite difference
calculationn',iLoop,N)
tic % start timing
for ii=1:iLoop, % simplified finite difference. Should also have
temperature-dependent material properties.
if iGPU % run gpu code using arrayfun as it's faster than
overloading the normal syntax
g1(iicentre,iicentre)=arrayfun(@heat_eqn_fdiff,g1(iicentre,iicentre), ...
g1(iiup,iicentre),g1(iidown,iicentre), ...
g1(iicentre,iiup),g1(iicentre,iidown));
else % cpu is quicker using matrix operations, not arrayfun
g1(iicentre,iicentre)= 0.2*g1(iicentre,iicentre)+0.2* ...
(g1(iiup,iicentre)+g1(iidown,iicentre)+g1(iicentre,iiup)+g1(iicentre,iidown));
end
end
if iGPU,
g_res=gather(g1); % bring the results back from the gpu
else
g_res=g1;
end
t=toc; % stop timing after gathering the results back to main memory
myPerf(iLoopVals+1,iNVals+1)=N^2*iLoop/t/1e6 % speed in millions of fd
operations per second
imagesc(g_res,[0 1]);axis image;drawnow;pause(0.1) % show the
"temperature" plot
end
end

3. clear g1
g=gpuDevice(1);
reset(g);
% GTX580, arrayfun, indices as gpu arrays, single precision
% myPerf =
% 0 1000 2000 3000 4000
% 500 606.6 1332.2 1331.2 1222.8
% 1000 1000.6 1358.1 1342.7 1228.7
% all double precision below here:
% GTX580, arrayfun, indices as gpu arrays
% myPerf =
% 0 1000 2000 3000 4000
% 500 775.89 829.07 783.14 685.37
% 1000 813.41 831.59 803.56 688.19
% GTX580, arrayfun, indices on the cpu
% myPerf =
% 0 1000 2000 3000 4000
% 500 707.77 731.84 716.49 623.03
% 1000 733.92 741.25 720.24 596.46
% GTX 580, normal matlab syntax operating on gpu arrays
% myPerf =
% 0 1000 2000 3000 4000
% 500 551.02 568.05 537.08 500.59
% 1000 564.13 571.14 538.36 502.32
%cpu i5-2500K @ 4.2 GHz
% myPerf =
% 0 1000 2000 3000 4000
% 500 37.401 38.362 0 0
% 1000 0 0 0 0
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