~15 years ago I used FastCap and the biggest challenge I found was how to properly tesselate a model. Intuitively, you would want the charge density per panel to be constant. And since charges repel toward the edges of objects, you typically want the panels on the edges to be smaller than the ones in the interior. For example, if you have two closely spaced coplanar square plates, then the tesselation along the edges near the gap between the plates would be finer than the tesselation in the center of the plates.
FasterCap mostly obviates the need for manual tesselation. However when the aspect ratio of a conductor is large or there is a significant size disparity between objects, it seems that some sort of manual tesselation is still needed (I'm basing this on the Bus example and empirical experimentation). But I could be wrong...
Consider this simple example. It consists of two plates. One is a 0.1mX0.1m square and the other is 0.1mX0.01m rectangle 1mm above the square:
0 A 0.1mX0.1m plate with 0.01mX0.1m rectangle 0.001m above
* auto-generated
Q 0 0 0 0 0.1 0 0 0.1 0.1 0 0 0.1 0
Q 1 0 0.045000000000000005 0.001 0.1 0.045000000000000005 0.001 0.1 0.055 0.001 0 0.055 0.001
And the capacitance matrix is:
1.692533010393579e-11 -1.3109472221548975e-11
-1.3139773278290896e-11 1.3252619335968535e-11
And here's the same thing except that the narrow rectangle has been manually tesselated.
0 A 0.1mX0.1m plate with 0.01mX0.1m rectangle 0.001m above
* auto-generated
Q 0 0 0 0 0.1 0 0 0.1 0.1 0 0 0.1 0
Q 1 0.0 0.045000000000000005 0.001 0.01 0.045000000000000005 0.001 0.01 0.055 0.001 0.0 0.055 0.001
Q 1 0.01 0.045000000000000005 0.001 0.02 0.045000000000000005 0.001 0.02 0.055 0.001 0.01 0.055 0.001
Q 1 0.02 0.045000000000000005 0.001 0.03 0.045000000000000005 0.001 0.03 0.055 0.001 0.02 0.055 0.001
Q 1 0.03 0.045000000000000005 0.001 0.04 0.045000000000000005 0.001 0.04 0.055 0.001 0.03 0.055 0.001
Q 1 0.04 0.045000000000000005 0.001 0.05 0.045000000000000005 0.001 0.05 0.055 0.001 0.04 0.055 0.001
Q 1 0.05 0.045000000000000005 0.001 0.060000000000000005 0.045000000000000005 0.001 0.060000000000000005 0.055 0.001 0.05 0.055 0.001
Q 1 0.06 0.045000000000000005 0.001 0.06999999999999999 0.045000000000000005 0.001 0.06999999999999999 0.055 0.001 0.06 0.055 0.001
Q 1 0.07 0.045000000000000005 0.001 0.08 0.045000000000000005 0.001 0.08 0.055 0.001 0.07 0.055 0.001
Q 1 0.08 0.045000000000000005 0.001 0.09 0.045000000000000005 0.001 0.09 0.055 0.001 0.08 0.055 0.001
Q 1 0.09 0.045000000000000005 0.001 0.09999999999999999 0.045000000000000005 0.001 0.09999999999999999 0.055 0.001 0.09 0.055 0.001
And the output is
1.637919591766101e-11 -1.2554323883396026e-11
-1.258950741355236e-11 1.2776059334652919e-11
There's about 5% difference in the two. Not much in terms of absolute values, but the differences are more pronounced when you consider the rectangle's free-space capacitance. If you save the FasterCap output you can see the difference in the auto-tesselation. I can't attach the post script images, but I would say that for this contrived example that the manual tesselation constrains FasterCap; the automatic tesselation is better.
Finally the question:
Under what conditions should we constrain the panels? The only one I saw in the forum was for small-angle triangles. Are there others?