[Gnucap-devel] very large pure linear circuits

[walter steffè]

I am developing a new code to perform electromagnetic simulations.
To be more precise the software output is not exactly a simulation but is an 
equivalent circuit which is described in a gnucap compatible file that uses 
only R,L,G commands.
The problem is that the software tends to generate very large circuits.
At the moment the size is still tractable because, up to now, I was dealing 
with the equivalent circuits associated with the individual subvolumes (the 
problem domain is partitioned in many subdomains). The next thing to do is 
the development of the routines that that must handle the connecction of the 
several subcircuits and I can foresee that, at the end, I will get circuit 
with many tousend of nodes so I am looking for a very fast circuit simulator. 
The time issue is made also more critical by the fact that the final goal is 
to be able to perform a parametric optimization of the circuit performances.
I have seen that there are some commercial simulators (like smartspice from 
Silvaco and nspice from Apache Design) which claim the capability of solving 
a circuit with a million of nodes in a few ours. Unfortunately these codes 
come with astronomical licence costs.

So my question are:
What do you think are the differences which make possible the high speed
of these codes ? Is it something that can be done to improve the gnucap 
simulation speed when dealing with very large but pure linear circuits ?
I am not well aware of the details of the numerical methods used for the 
simulation of electrical circuits and so I would appraciate very much any 
information you can give me to understand the main factors which limit the
simulation speed and possible warkaround.