Wed Nov 5 10:25:45 EST 2014

Rethinking circuit representation

I'm starting to understand the spice rationale[1].  The basic model is
that of a resistive network with one node dedicated as ground node.
Equations are set up using KCL for each non-ground node.  This gives a
relation between node voltages and currents flowing into each node:

    G V = I

This is just a relation.  It can be interpreted as currents drawn from
voltage sources, or node voltages caused by current sources.

The matrix G is symmetric, positive definite.
- symmetric: a resistor has no directionality
- positive definite: V^T G V = V^T I = P, total power is always > 0

Starting from this basic model, SPICE linearizes the equations and
performs NR iterations at a particular time instance, and uses one of
several integration methods to move forward in time.

The structure of G allows for Krylov subspace methods (conjugate
gradient, lanczos)

[1] entry://../math/20141105-000511