I know that fast multipole methods can be a less costly alternative to MoM. I want to know if there is also any EM simulator using a Fast multipole method (FMM) solver?
What type of EM simulations are you looking for? Most of the commercial EM-simulators will use some kind of a fast algorithm for solution acceleration.
Another alternative to FMM will be FFT-based methods like procreated FFT and AIM (adaptive integral method).
For example, if you are interested in magneto-quasi-static parameter extraction, FMM-accelerated FastHenry/FastCap solvers are the ones you are looking for.
Are you looking for a way to accelerate your own MoM solver or for a solver to solve some particular large-scale problem?