The Generalized Multipole Technique

The Generalized Multipole Technique (GMT) was developed in the 1980s by C. Hafner [1] and implemented in software known as the Multiple Multipole (MMP) programs. It is essentially a frequency-domain moment-method technique where the basis functions are analytic solutions of the fields generated by sources located some distance away from the surface where the boundary conditions is being enforced. These basis functions are spherical wave field solutions corresponding to multipole sources. By locating these sources away from the boundary, the field solutions form a smooth set of basis functions on the boundary and singularities on the boundary are avoided.

Like the method of moments, a system of linear equations is developed and then solved to determine the coefficients of the basis functions that yield the best solution. Since the basis functions are already field solutions, it is not necessary to do any further computation to determine the fields. Conventional moment methods determine the currents and/or charges on the surface first and then must integrate these quantities over the entire surface to determine the fields. This integration is not necessary at any stage of the GMT solution.

There is little difference in the way dielectric and conducting boundaries are treated by the GMT. The same multipole expansion functions are used. For this reason, a general purpose implementation of the GMT models configurations with multiple dielectrics and conductors much more readily than a general purpose moment method technique.

Despite the advantages of this technique for certain types of modeling, it is not widely used. This may be partly because this technique is a little less intuitive to use and it can be difficult to learn to locate the multipole sources optimally.

Note that the Generalized Multipole Technique should not be confused with the Fast Multipole Method (FMM), which is a technique for exploiting symmetry or periodicity in structures to accelerate some types of electromagnetic modeling codes.

References

[1] Christian Hafner, The Generalized Multipole Technique for Computational Electromagnetics, Artech House, 1990.