Some background
I have simplified understanding of inductance which is incorrect yet has been a useful falsehood so far. The idea is that a changing flow of current through a loop creates magnetic flux through the area of the loop and the change in this flux in turn induces a voltage in the loop. The effect is proportional to the area of the loop and thus quadratic in the number of turns of a solenoid. Roughly I would say the inductance of a loop would be naively calculated as so:
$$ L = \frac{\mu_0 r_{loop}}{2} $$
However much more complicated formulae are typically quoted, for example:
$$ L = \mu_0 \left[ \ln \left ( \frac{8r_{loop}}{r_{wire}} \right) - 2 \right] $$
Clearly I'm wrong, as if you consider the inductance of a 1m loop of 1mm wire my formula gives an inductance of 0.1uH and the real formula gives 1.02uH, which is quite a difference. This gross misunderstanding may or may not be relevant to my question.
The actual question
I frequently see talk of partial inductance and this confuses me. I have no problems with a 1uH SMD inductor for example (so long as it is electrically small), as I just imagine that if you connect it in a loop then the inductance of that loop will be 1uH larger than it would otherwise be, or as the length of the loop tends to zero the inductance will tend to 1uH.
However there exist tools such as FastHenry which can take an arbitrary geometry and assign inductance to each individual wire, despite the presence of switches in the circuit. How is this possible, given that surely the inductance should depend on which route the current actually takes through the wires and the resultant loop area? For a realistic motivating example you can imagine an integrated circuit where the switches are MOSFETs that source and sink current to/from the power rails in some unpredictable fashion, and people care deeply about the "inductance" of a particular power or ground wire.
Is this really possible, or is there some horrible simplification that has occurred when people talk about 'partial' inductances? If this really is a self-consistent method what is the right way to think about it and the justification for it? And, if scope allows, what is the right way to think about inductance in general?
