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Time solver dynamics - advice

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I'm in "currents and voltages" applying a current density pulse within a copper short going through the glass dielectric of a spherical copper capacitor. This is a biological equivalent, there is no ground (like the brain) and one cannot be asserted anywhere.

My problem is solver stability.

Time dependent, direct, mesh = finer. MUMPS.

I am getting variable convergence dynamics simply by setting different _durations_ of the simulation.

Can someone tell me if I get a convergence incident at step X, whether the results for data prior to step X are suspect?
Is the only time I can be confident when the entire simulation is convergence-incident free?

eg...If I truncate a simulation duration just prior to step X, where it previously diverged, why does the new simulaiton move the convergence problem INSIDE the time that was perfectly OK last time?.... and then produce slightly different results (voltages/times)....

confused Colin.

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