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Simultaneous equations getting solved
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WatchfulEye:
I thought it might be an interesting idea to write a 2D quasi-static field solver for PCB impedance calculations.
Not really knowing what I was doing, after a couple of false starts, I stumbled on a suitable discretisation for Gauss's law which allowed it to be applied in inhomogeneous conditions, and could easily be written in matrix form.
What I hadn't given any consideration to was actually solving the resulting very sparse, but absolutely huge, system of equations. Never having tried anything like this before, the solution was to try every method in the textbook, and see which one worked best. I found it quite astonishing at how profound the differences in solution times were.
I subsequently had the code export the intermediate steps towards the solution, just for interest to try to understand what was actually going on. The result was this video: https://www.veed.io/view/973ce332-82c9-4656-a811-e18e176f90ca?
What is being solved here is the potential field (φ) surrounding a differential pair over ground plane. The electric field (E) is the spatial derivative of this - i.e. E=∇φ. An example solution for φ is attached, together with a solution for E (not quite the same problem as in the video, but close enough).
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