abstract:A multipole expansion is a mathematical series representing a function that depends on angles — usually the two angles on a sphere. These series are useful because they can often be truncated, meaning that only the first few terms need to be retained for a good approximation to the original function.
Thethree-dimensionalboundaryelementmethod for elastic materials was extended to develop afastmultipoleexpansionformulationof thefundamentalsolutions forquadraticelements.