Efficient computation of source magnetic scalar potential

Magnetic field problems are often excited by a known source field which itself is caused by free currents. Some formulations to solve the problem require knowledge of the source magnetic scalar potential whose gradient is the source field. In general, it has to be computed as a line integral. An approach for efficient computation of this potential has been developed that is based on an algorithm that gives short integration paths as well as on application of the fast multipole method. Numerical results indicate the efficiency of this approach especially when the number of current-carrying volume elements or the number of observation points are high.