ON THE ACCURACY OF THE ADDITION THEOREM FOR A SCALAR GREEN'S FUNCTION USED IN THE FMM

of ON too. The basis of the FMM is the application of the addition theorem to the free-space Green's function 1 . Coifman, Rokhlin, and Wandzura 2 , Song and Chew 3 , and Sertel and Volakis 10 have discussed how to choose the multipole expansion orders for achieving high accuracy in the FMM. The accuracy of the multipole expansion of the scalar Green's function directly affects the FMM acceleration schemes. This thus shows the motivation of this paper, that is, to address the accuracy of addition theorems for the free- space scalar Green's function and the convergence of the FMM algorithms.