ptcont_examples

Pseudo-transient continuation — Enhancement-127

.option ptcont adds a pseudo-transient continuation homotopy to the DC operating-point solve — the "principled Ẋ-embedded continuation" that ngspice's convergence cascade otherwise lacked (it had static gmin stepping, source stepping, and a transient-op fallback, but not this).

What it does

The DC problem f(x) = 0 is embedded in a fictitious backward-Euler pseudo-transient

f(x) + Gps·(x − x_prev) = 0,   Gps = Cps / dτ,

and the pseudo-timestep dτ is marched from small (Gps large — strongly damped and well-conditioned) to large (Gps → 0 — the true DC operating point). Each step is a Newton solve of the augmented system: the Gps diagonal is added at factorization time (the same mechanism as gmin stepping), and the Gps·x_prev coupling is added to the right-hand side inside the Newton loop. That coupling is the key difference from static gmin stepping — it makes every step a move along a stable trajectory from the previous point, so the solve tracks the operating curve instead of jumping. A switched-evolution-relaxation rule grows dτ when a step converges easily and shrinks it (backtracking) when a step fails.

It is off by default and, like any convergence aid, result-neutral: when the standard solve already converges, the answer is identical.

ptcont_demo.cir

A behavioral exponential with no junction limiting — a deliberately stiff nonlinearity:

B1 1 0 I = 1e-14 * (exp(V(1)/0.026) - 1)
R1 2 1 100
V1 2 0 100

From V = 0, plain Newton overshoots the enormous exp derivative and settles on a spurious root (V(1) ≈ 70.5 V), whereas pseudo-transient continuation follows the stable trajectory to the physically correct operating point

V(1) = 0.837922 V   (the root of 1e-14·(exp(V/0.026)−1) = (100−V)/100).

gmin and source stepping are disabled in the demo (gminsteps=0 srcsteps=0) so the result depends on the pseudo-transient homotopy alone.

Verification

verify_ptcont.py (run under both KLU and Sparse1.3) checks:

1. .option ptcont is accepted;
2. result-neutrality — on a battery of normal nonlinear circuits (diode, BJT, two-diode divider, resistor network) the operating point with ptcont on is identical to a normal run;
3. convergence power — on the stiff circuit, ptcont reaches the correct DC 0.837922 V (matched to the analytic value), differing from the spurious 70.5 V plain Newton returns.