Boundary condition depending on the State

[Waschenbacher]

I am implementing a custom PDE class and would like to add a not-so-easy boundary condition. Is it possible in py-PDE to add a Dirichlet boundary condition with its value being a function of

• its fields.data at coordinate (x = L)
• f(t)
  Example: I have a field A on 1-d "grid = CartesianGrid([[0, 10]], [100])]". The boundary condition at left-hand-side should be a function of the field at the right and a function of time t.

[david-zwicker]

If I understand you correctly, you would like to have a custom periodic boundary condition. This should in principle be possible, although the condition would not depend on the exact value at the boundary but rather on the value of the support point next to the boundary (a distance dx/2 away from the boundary). Otherwise, the situation cannot be resolved unambiguously. Would this cover your scenario? Obviously, you'd also need a boundary condition on the right side, but I guess this could be whatever you want it to be.

Such conditions are currently not implemented, but this should be fairly straightforward. However, I would need to have a good term for such a condition. Do you have a suggestion?

[david-zwicker]

I just merged #490, which allows more control over the value that determine the boundary condition. Using the latest master branch, you should be able to use a boundary condition like {"type": "value_expression", "value": "sin(value)", "value_cell": -1}, which would set the value of the BC to the sine of the value of the right-most grid cell. Let me know if this covers your use case!

[Waschenbacher]

Awesome! Thanks! It worked with sin. However, I am wondering how can I use a user-defined-func instead of sin to this boundary condition. According to the Expression section from https://py-pde.readthedocs.io/en/latest/manual/advanced_usage.html#boundary-conditions, I tried out {"type": "value_expression", "user_funcs": "user_defined_boundary(value)", "value_cell": -1} with user_defined_boundary being the user defined function, but it seems that the BC does not accept user_funcs.

[david-zwicker]

Good point. This should be easy to fix. I'll open another issue and hope to work on this soon.

[david-zwicker]

I just pushed #492 , which should allow you to use {"type": "value_expression", "value": "func(value)", "value_cell": -1, "user_funcs": {"func": user_defined_boundary}}. I hope this is what you meant.

[Waschenbacher]

thank you so much for the new feature! I really appreciate it a lot! It works with a general user_funcs. However when I tried it with the following case:
`class PID:

def __init__(self, Kp, Ki, Kd, setpoint):
    self.Kp = Kp
    self.Ki = Ki
    self.Kd = Kd
    self.setpoint = setpoint

def get_ctrl_func(self, measurement):
    ...
    return ...

`pid = PID(Kp=1., Ki=0., Kd=0., setpoint=1.)

def user_boundary(x: float) -> float:
return pid.get_ctrl_func(x)`

I received the error message below:

Could you please give me some further guidance?

[david-zwicker]

The error indicates that the user-supplied function cannot be compiled using numba. I guess it would be useful if py-pde then falls back onto the basic python backend, which would be much slower, but could support more python code. Could you please raise an issue with reference to this discussion, so we can improve this in the future?

[Waschenbacher]

Thank! I just opened an issue

[david-zwicker]

I found some time and implemented a change in the latest master branch that would allow calling a non-compilable function. I hope it's helpful!