So I started writing an antenna simulator program to design antennas for my needs. To calculate the electric field vector at every point, I split the active element of the antenna into a large number of smaller parts and the calculate the electric field generated by each element at that point - taking into account speed of light. In the program I simulated a dipole antenna and it worked well.
Now I'm thinking how could I add support for passive element? If I would like to simulate a yagi-uda antenna, I need to somehow take into account a passive element which does not fit into my model.