In this work, we study liquid gallium stirring by rotating permanent magnets. We demonstrate possibility of easily creating different flow patterns by rotating permanent magnets, which can be industrially important for controlling heat and mass transfer processes in the system. Unlike the typical approach of simulating magnet rotation as a transient problem and time-averaging the Lorentz forces, we solve the magnet rotation as a harmonic (frequency domain) problem, which leads to forces equal to time-averaged ones and decreases the simulation time considerably. Numerical results are validated using qualitative flow structure results from the neutron radiography visualization of tracer particles and quantitative data from Ultrasound Doppler velocimetry.