Save/use intermediate values on ode solver

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Thales
Thales 2019-4-5
评论： Pan Zhao 2021-8-17
I am doing a time integration of a system of ODEs using a stiff solver (ode15s). It is working, but I want to speed things up.
The system of equations is given in state space form:
function [dx] = fun(t,x,M,C,K,other_parameters)
% Mx'' + Cx' + Kx = F(t)
% BUNCH OF CALCULATIONS
F = myfun(x,t);
A = [zeros(n) eye(n) ; -M\K -M\C];
b = M\F;
dx = A*x + b
end
The trick part here is the forcing function F. It is highly nonlinear and depends on the x and t parameters. It uses the x parameters to solve a Poisson-type 2D equation (by the Finite Volume method). The force F is proportional to the Poisson equation solution.
function [F] = solveP()
% initialize solution
Phi = zeros(Ni,Nj);
% solve iteratively
% ...
% calculate F
F = sum(Phi(:)); % discrete integration over domain
end
Solving the Poisson equation by a iterative method requires an initial condition, which I set to zero (Phi=zeros(Ni,Nj)). I thought I could improve the speed of calculations by providing a better initial estimative of the ϕ field (a better initial condition would take faster to reach the sought answer). The optimal initial condition I can think (besides ) is the value of the ϕ field obtained in the previous iteration (the last step) of the ode solver (.
Bottom line is: how do I use/save intermediate values in the ode solution?
PS: I tried using the persistent variables, but that is not a good solution. The ode solver calculates the function in several points before advancing in time. The persistent variable saves the converged ϕ field every time the ode calls the odefun fun. That is not exactly what I want.

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回答（1 个）

Pan Zhao
Pan Zhao 2021-8-10
I have a similar problem. Did you manage to solve your problem?
  2 个评论
Thales
Thales 2021-8-13
Unfortunately, no.
The best I could come up with was to write my own integrator. Clearly, it is not as good as MATLAB's built-in ode, but I can return other variables in the function fun being integrated and use them in the time marching scheme.

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