I have not used HFSS but I have some experience in finding ways to keep a simulator from hanging up.
The timestep is important. A reasonable length to try is 1/1000 to 1/100 times the length of whatever cycle your circuit might have going on.
Add resistors across switching components, or components which turn on and off. Add a resistor to ground where you think a component is creating problems.
Convergence problems tend to crop up when you place coils/ diodes/ capacitors neighboring each other. Add resistors across diodes.
Some problems are solved by putting a resistor in series in the same wire with a capacitor.
Some simulators require that your circuit have a ground icon somewhere.
Split a complicated circuit into sections, and simulate them individually. Join two sections together when you see each working okay separately.
Large populations of transistors /mosfets become a burden on the simulator algorithm. If you are using several as switches, replace them with a simple switch operated by a single wire. (I use Falstad's simulator, and this non-real component is called an 'analog switch'.)