Hi Matlab Gurus,
I have read many posts in this forum about my problem but I'm still not capable to solve it. I'm trying with a direct support
Problem
I want to calculate streamlines starting from a 3d vector field function, using the differential equation
the field is not known a-priori in the region, so I prefer not to use the built-in stream3 function and interpolate the data.
The vector field is solenoidal, so the streamlines are closed.
Here is a MWE, with the attached fieldFunction (it calculates the magnetic field due to a circular coil, but it's only an example)
clear variables, close all
streamLineFunct = @(t,x)fieldFunction(a,d,x(:).').';
options = odeset('OutputFcn',@odeplot,'OutputSel',[1 2 3]);
sol = ode15s(streamLineFunct,[0 0.5],Q0,options);
figure, axis equal, hold on, view([-1 1 1])
plot(a*exp(1j*(0:pi/100:2*pi)),'LineWidth',2);
plot3(Q(:,1),Q(:,2),Q(:,3));
Because the integration variable 's' is non-physical, it is difficult to define a proper tspan for the ode solver. It's possible to see, in fact, that the streamlines make about 2.5 complete circles. A good choice for this streamline of this example is around 0.21, but this guess can be done only after the computation.
Question:
Version 1: how to get the correct streamline without unnecessary computation, stopping the ode solver once the position returns to the starting point?
Version 2: is Event Location the right option to pass to the ode solver? If so, how can I define a suitable event that avoids the repetition of unnecessary calculation and stop the ode once the streamline returns at the original position?
Clarifications
- I know that playing with AbsTol and RelTol the streamline can be more accurate, avoiding the visible misalignment.
- I already tried to define an Event but due to the initial small integration steps, I can't find a good setup for this property
- The real-problem vector function is very accurate but can be time consuming, so the use of a large tspan is not practical.
Thank you in advance for your help
