Photovoltaic tweezers are a promising tool to place and move particles on the surface of a photovoltaic material in a controlled way. To exploit this new technique it is necessary to accurately know the electric field created by a specific illumination on the surface of the crystal and above it. This paper describes a numerical algorithm to obtain this electric field generated by several relevant light patterns, and uses them to calculate the dielectrophoretic potential acting over neutral, polarizable particles in the proximity of the crystal. The results are compared to experiments carried out in LiNbO₃with good overall agreement.