Line segment pole functions in the MMP method applied to shielded cables

The multiple multipole method (MMP) of computation for electromagnetic field problems that has been proposed as an alternative to existing finite-element and related methods is being extended in this work by the use of segment functions. In this method linear combinations of defining functions that satisfy themselves the pertaining partial differential equations (e.g., Laplace's equation) are employed to synthesize a solution of a potential in a certain region with given boundary conditions. The solution, as given by these defining functions, will be matched at selected points on the boundary (e.g., conductor surface). This 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. To reduce the number of functions in the series expansion, a novel class of harmonic functions obtained by integration of monopole or dipole point functions is investigated. These functions are obtained by integrating a point source function along a line segment. The efficiency of the procedure using these functions has been demonstrated in the calculation of the electrostatic potential and the capacitance of practical two-core cables with elliptical and circular conductors and three-core cables with sector shaped conductors.