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Setting up ode solver options to speed up compute time

조회 수: 8 (최근 30일)
Deepa Maheshvare
Deepa Maheshvare 2021년 5월 18일
댓글: Bjorn Gustavsson 2021년 5월 25일
Hi All,
I'm specifying the `'JPattern', sparsity_pattern` in the ode options to speed up the compute time of my actual system. I am sharing a
sample code below to show how I set up the system using a toy example. Specifying the `JPattern` helped me in reducing the compute time from 2 hours to 7 min for my real system. I'd like to know if there are options (in addition to `JPatthen`) that I can specify to further decrease the compute time . I found the `Jacobian` option but I am not sure how to compute the Jacobian easily for my real system.
global mat1 mat2
mat1=[
1 -2 1 0 0 0 0 0 0 0;
0 1 -2 1 0 0 0 0 0 0;
0 0 1 -2 1 0 0 0 0 0;
0 0 0 1 -2 1 0 0 0 0;
0 0 0 0 1 -2 1 0 0 0;
0 0 0 0 0 1 -2 1 0 0;
0 0 0 0 0 0 1 -2 1 0;
0 0 0 0 0 0 0 1 -2 1;
];
mat2 = [
1 -1 0 0 0 0 0 0 0 0;
0 1 -1 0 0 0 0 0 0 0;
0 0 1 -1 0 0 0 0 0 0;
0 0 0 1 -1 0 0 0 0 0;
0 0 0 0 1 -1 0 0 0 0;
0 0 0 0 0 1 -1 0 0 0;
0 0 0 0 0 0 1 -1 0 0;
0 0 0 0 0 0 0 1 -1 0;
];
x0 = [1 0 0 0 0 0 0 0 0 0]';
tspan = 0:0.01:5;
f0 = fun(0, x0);
joptions = struct('diffvar', 2, 'vectvars', [], 'thresh', 1e-8, 'fac', []);
J = odenumjac(@fun,{0 x0}, f0, joptions);
sparsity_pattern = sparse(J~=0.);
options = odeset('Stats', 'on', 'Vectorized', 'on', 'JPattern', sparsity_pattern);
ttic = tic();
[t, sol] = ode15s(@(t,x) fun(t,x), tspan , x0, options);
ttoc = toc(ttic)
fprintf('runtime %f seconds ...\n', ttoc)
plot(t, sol)
function f = fun(t,x)
global mat1 mat2
% f = zeros('like', x)
% size(f)
f = zeros(size(x), 'like', x);
size(f);
f(1,:) = 0;
f(2:9,:) = mat1*x + mat2*x;
f(10,:) = 2*(x(end-1) - x(end));
% df = [f(1, :); f(2:9, :); f(10, :)];
end
Are there inbuilt options available for computing the Jacobian?
I tried something like the below
x = sym('x', [5 1]);
s = mat1*x + mat2*x;
J1 = jacobian(s, x)
But this takes huge time for large system.
Suggestions will be really appreciated.
Side note:
I would also like to know if there is someone on the forum to whom I can demonstrate my code and seek help to resolve the issue mentioned above.
Unfortunately, I cannot post my actual system here .
  댓글 수: 19
Torsten
Torsten 2021년 5월 23일
Analytical Jacobian should be Jac_ana = advMat + diffMat.
Maybe you can just output J, J1 and Jac_ana and compare them directly.
Bjorn Gustavsson
Bjorn Gustavsson 2021년 5월 25일
@Deepa Maheshvare - if you're solving a diffusion-advection problem then maybe it is worthwhile to look at the PDE-solvers, if you have access to the pde-toolbox.

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