Superconducting magnets provide large magnetic fields in a large aperture region. Their design is based on magnetic and thermal field simulation. To reach the necessary accuracies, a high resolution is needed in space and time. Moreover, all occurring induced effects in the superconducting coils (persistent currents, interfilamentary coupling currents and interstrand coupling currents) and their consequences for the homogeneity of the magnetic field need to be addressed. The overall problem constitutes one of the most challenging contemporary design problems.