The construction of practically useful fast converging expansions for the GMT

The generalized multipole technique (GMT) uses expansions of the unknown field function. The author describes a procedure through which a set of expansion functions f/sub k/ may be found, fulfilling the following properties: the f/sub k/s are easy and inexpensive to calculate; the total number of f/sub k/s is minimum; the set is adapted to both the geometry and the solution of the field problem; the f/sub k/s are independent and lead to fairly well-conditioned matrices; the pole construction procedure may be automated; and local verification of the solution by adding few additional functions is possible.<>