Re: Inductance calculations

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Antonio Carlos M. de Queiroz by way of Terry Fritz <teslalist-at-qwest-dot-net>" <acmq-at-compuland-dot-com.br>

Tesla list wrote:

 > Original poster: "Godfrey Loudner by way of Terry Fritz 
<teslalist-at-qwest-dot-net>" <ggreen-at-gwtc-dot-net>

Hello Godfrey

 > The following quadratically convergent algorithm for F(c) and E(c)
 > might be useful. More details can be found in the book: Pi and the
 > AGM, J. Borwein and P. Borwein, John Wiley & Sons. The AGM
 > for F and E is an iteration, a task at which computers excel.

Thank you! I tested this algorithm, and it works extremely well. With
just 7 iterations I get more precision (1e-15) than with a Simpson
integral with 100000 segments, even with c=0.9999999999. I was using
a series for c<0.999 (3417 terms!) and Simpson integration with
10000 intervals above this. Good enough, but slow. With the AGM
method, the analysis is now instantaneous for solenoids, e fast
even for conical coils with many turns. I implemented a comparison
of the three methods for calculation of elliptic integrals in the
Inca program (menu item "Tests").
http://www.coe.ufrj.br/~acmq/programs/inca.zip

 > Higher order versions of the AGM are possible, which
 > converge even faster. But they become complicated.

This is good enough, and can't be simpler for an apparently
difficult problem.

Antonio Carlos M. de Queiroz