Magnetic field calculation using line segment pole functions in the MMP method

The multiple multipole method (MMP) has been used for the computation for electromagnetic field problems as an alternative to existing finite-element and related methods. In an earlier work by the authors, new line segment pole functions were introduced into the MMP method for solving electrostatic problems. In this work the MMP is further extended to solve Poisson´s equations in a certain region with given boundary conditions. A series solution for the magnetic potential in the region is synthesized using defining functions that satisfy themselves the pertaining partial differential equations. The calculation of magnetic potential is more involved than that of the electrostatic field potential. There are no given boundary values, however, the magnetic potential vector inside and outside a conductor must match for continuity and the normal components of the gradient of the magnetic potential inside and outside must also be matched. This matching will generate a redundant set of equations from which the coefficients of the various functions in the series solutions are deduced by the method of least squares. The number of functions in the series expansion is reduced by using a novel class of harmonic functions obtained by integration of monopole or dipole point functions. This solution procedure is demonstrated in the calculation of the magnetic potential and the inductance of practical 2-core and 3-core cables