How are circuits which use complex ICs normally simulated?
In my experience the widespread use of simulation of entire boards is mostly a myth outside of physics simulations in RF. 

Simulation rules for IC design of course, because the prototyping costs are so insane, and for anything involving HDL design, but for general electronics, not so much. 

Where the sim really helps is for things like filters and control loops where you really want to make sure the breakpoints and phase shifts are what you expected, but these are typically a small blob of a half dozen or so parts that you can simulate in isolation. 

Attempts to simulate an entire board of reasonable complexity tend to fail either on numerical stability or just simply on run time, which explodes once you start adding reasonable parasitics.

Generally you simulate the bits you are not sure about, which is usually less then 10% of a design (The rest is 'data sheet engineering' of power supplies and IO stuff).