I have often had convergence problems with it but that may be their models rather than the simulator.
I'll tell you: it is the simulator. It is based on a standard Newton-Raphson algorithm that doesn't guarantee global convergence. The more non-linear and complicated the circuit is, the more chances you have to get convergence failure.
The only problem is that probably all of the simulators use the same NR algorithm - they differ with some hacks that improve NR convergence in some cases. Probably LTSpice's hacks are not as good as of other commercial simulators.
In a way, most simulators are similar 'under the hood'.
Most SPICE based probably are. But actually the simulator we are working on is *totally* different.
1. It uses a globally convergent method that can find a solution regardless of model non-linearity (the solution must only exist), and doesn't require a starting point.
2. It is fully modular, written in a high-level language.
3. It uses symbolic manipulation whenever possible, instead of numeric analysis, which means that linear parts of the circuits come almost for free (for example you can freely add a resistor or capacitor here and there and it doesn't affect the simulation speed).
4. It controls the amplitude of numeric round-off errors, so they can never cause convergence failures.
5. It uses modified BDF integration scheme instead of default trapezoidal in most other simulators. Trapezoidal suffer from ringing and instabilities in fast switching circuits.
6. It allows for easily writing new models with differential equations and real code with variables / ifs / loops / procedures / high level data structures etc. You can add new model code without restarting the simulator (yet it is *compiled* on the fly, not interpreted, thus *fast*).
7. It is almost as fast as LTSpice (we haven't optimized it too much), but faster than many other SPICE simulators.