Lorentz force velocimetry (LFV) [1] is a contactless measurement technique, which uses the principle of induction to analyze physical properties of moving and electrically conducting media. We report a systematic numerical optimization procedure with finite element (FEM) simulation to improve the measurement quality of LFV for weakly conducting media. The force can be increased by optimizing the primary magnetic field created by a magnet system. We use magnetic dipoles as field sources. Analytic and numerical studies of the influence of single magnetic dipoles on the conducting medium have been investigated [2-4]. The optimization of different dipole configurations with a high number of dipoles is new and presents the next step in the development of Lorentz force flowmeters for weakly conducting fluids for industrial application. We study and optimize the orientation of dipoles with the FEM software PROMETHEUS and develop an optimization method. The resulting optimized dipoles exhibit characteristic orientations, which are point symmetric with respect to the center of the geometric setup so that the magnitudes of the vector fields wind themselves like a spiral around the pipe.