With the new release of nodal.py I could greatly improve the code presented in the previous blog post. We now have a simpler script that will also run faster.
The new release of nodal provides some new objects in a nicely packaged format, allowing me to rewrite the solver in a much simpler and maintainable form.
To make the code faster I started using sparse matrices to represent the circuit. Since electrical networks are often not densely connected, with few or no components at all connecting any two given nodes, using the sparse methods from scipy results in memory and runtime savings.
In the new release of nodal applying this change is just a matter of setting the sparse flag to true when building the circuit from the netlist:
netlist = nodal.Netlist("netlist.csv")
circuit = nodal.Circuit(netlist, sparse=True)
e = circuit.solve().result
In this table we can compare the new and old results of the simulation:
| n | result (Ω) | old runtime (s) | new runtime (s) |
|---|---|---|---|
| 21 | 0.77934 | 0.0289 | 0.1233 |
| 51 | 0.77428 | 0.2435 | 0.4533 |
| 71 | 0.77377 | 1.2203 | 0.7980 |
| 101 | 0.77350 | 8.7821 | 1.5985 |
| 171 | 0.77333 | 226.1542 | 4.5561 |
| 201 | 0.77330 | - | 6.5638 |
| 501 | 0.77325 | - | 45.3930 |
| 1001 | 0.77324 | - | 226.4865 |
[tests run on Intel i7 processor, 8GB RAM]
The results of the old and new methods are equal up to rounding errors.
The main take-away is that the new methods allowed me to run simulations of grids with \(n \geq 191\), where the old simulation would instead crash because it ran out of memory.