Poisson Solver initial value problem implementation is not robust.

[PaulWAyers]

The current boundary-value-problem for the Poisson solver is pretty robust. The initial value problem is a lot less robust.

It's a good first issue to try to make this work more efficiently. I will post some notes on how to do this.

[Aditish51]

@PaulWAyers Can you please give me more details on it? I would like to work on it.

[Charlie-1-3]

The current code uses a large initial interval (r_interval[0]) for the IVP solver. This might be unnecessary, especially if f decays rapidly with increasing r. Reducing the initial interval to a value just larger than the region of interest can potentially improve performance.

[PaulWAyers]

@Charlie-1-3 did you test it to see if this helped?

@Ali-Tehrani do you have some examples for this? I seem to recall that Carlos had an example that was problematic, but I don't remember for certain.

[Charlie-1-3]

@PaulWAyers Yes it worked for a few test cases where function f was inversely proportional to r. Cases, when f depends directly on r, might add extra computation in IVP because of larger domain traversal.
Use of Relaxation Techniques for Poisson’s Equation one of which is Successive Over-Relaxation (SOR) would help too.