Yes, each coherent mode is simulated separately, but the coherent modes themselves consist of plane waves which are simulated simultaneously. For example, in the section 5 they mention
There are 16 modes, so 16 simulations what they mention. Within each mode (each simulation) there are 225 plane waves used, not 225 simulations. At least, that is how I read it. Otherwise they would need to run 16x225 simulations, which is quite a lot.