Abstract
There exist two versions of the fast multipole method—one that is based on a multipole expansion of the interaction kernel exp(ikr)/r, and another based on a plane wave expansion of the kernel. The stable plane wave expansion has a lower computational expense than the multipole expansion and does not have the accuracy and stability problems of the plane wave expansion. For a linear system of size N, the use of an iterative method combined with the fast multipole method reduces the total expense of the computation to N log N. The solution of the Helmholtz and Maxwell equations, using integral formulations, requires solving large complex linear systems. A direct solution of such problems, using Gauss elimination, is practical only for very small systems with few unknowns. The use of an iterative method can reduce the computational expense.
Published Version
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