The Fast Multipole Method

In previous chapters we observed and discussed the issues and complexities encountered in applying the Method of Moments to larger problems. Foremost among these are the limits in storing the MOM system matrix in memory, and the CPU requirements of the LU factorization, which increases exponentially with the number of unknowns. Though one of the iterative solvers discussed in Section 4.2 may yield a shorter compute time for a small number of right-hand sides, the run time may still be quite high due to the number of matrix-vector products per iteration. If the system matrix will not fit into memory, there are few options besides changing the surface geometry to reduce the number of unknowns, or using virtual (disk) memory and an out-of-core solver, though this may make the problem intractable due to the far slower read/write speed of the hard disk. This motivates the search for a technique that will reduce or eliminate many of these difficulties.