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Use AGM for Greens Calculations #3273

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@geograham

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@geograham

Description of issue / requirement to address

Papercut #205 had three key suggestions for greens.py. The other two have been addressed. This one may still be helpful for speed:

"Scipy function uses interpolation for E and K, this may increase errors for values of k near 1, i.e. the field very close to the loop. Two methods to improve this may be to use the AGM calculation (Wikipedia has the simplest method and finds E and K simultaneously) and/or to use a different modulus, k_1 = (1-sqrt(1-k^2))/(1+sqrt(1-k^2)), this approaches 1 much slower for the same distance and so the AGM converges very quickly. Again Wikipedia has the general method for doing this. Maxwell himself seemed to have cracked this so there are plenty of other sources if required."

Proposed solution

Implement and test the use of AGM alternative.

Alternative solutions

Leave the way it is.

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