Is there an FEA technique for modelling current flow in an irregularly shaped conductor, other than by applying nodal (or mesh) analysis?

I want to create a model of the current flowing in a PCB that is not a "regular" shape, such as where the large terminal/pad of a high power FET gets reduced down to a PCB copper pour that is narrower than the pad. I have found nothing really on google or in text books that helps.

The method also needs to be able to handle varying resistance/conductance within the one model.

I have written an octave program for modelling a 4 layer PCB that can model the copper, vias and solder, but the array size becomes unusable/too large rather quickly. I am have found a 5um grid gives good results, but there is a limit of about a 20mm x 20mm board size.

Figured there had to be a better way to analyze this than creating a massive node matrix.

  • \$\begingroup\$ What do you mean by "a better way to analyze this?" I don't see your exact method, so how would it be possible to answer your question? Most of us would just reach for the usual partial differential equation approach, which is what finite element analysis is at bottom. It's not complex. Just detailed and more boiler-plate. Are you already using this and looking for a whole new approach? Or are you looking for us to redo your partial diffeq arrangement, none of which we can see right now? \$\endgroup\$
    – jonk
    Commented Aug 28, 2021 at 21:31
  • \$\begingroup\$ For mechanical FEA analysis it's extremely common to have the meshing vary throughout the model to get relatively fast analysis and decent accuracy. \$\endgroup\$ Commented Aug 28, 2021 at 21:32
  • \$\begingroup\$ I used nodal analysis,the nodes placed on a 5um grid as stated above. No PDE's, just an array of resistors interconnecting nodes with current sources at the nodes that correspond do the input nodes and output nodes. \$\endgroup\$
    – Willy--
    Commented Aug 29, 2021 at 0:29
  • \$\begingroup\$ Sephro, I had originally looked into changing my even grid to something less complex, but having it all auto-generate was becoming very complicated. Might be the best solution though, thanks for the reminder. \$\endgroup\$
    – Willy--
    Commented Aug 29, 2021 at 0:33
  • \$\begingroup\$ @Willy-- It's easy using PDEs. I've done this for all kinds of oddball shapes, as well. I've discussed easy things here: Simple problem, but the approach applies, another simple problem, done in different language, same idea, and yet another simple example. (And probably several more I didn't find so easily.) But the concept applies to any shape and meshing you want to use. I've done oddball antenna shapes/radiation patterns. \$\endgroup\$
    – jonk
    Commented Aug 29, 2021 at 5:22

1 Answer 1


If you want to model two-dimensional shapes for resistance, there are mathematical methods (conformal mapping) that give exact solutions for simple shapes. It is limited, though, because practical aspects like the plated-through-hole and bent leadwire of a through-hole transistor are not strictly two-dimensional.

This is a one such treatment:Numerical Computation of... and I dimly recall that some compilations of shapes have been pre-calculated for typical layouts, giving resistance.


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