Introduction to fast Illinois solver code (FISC)

Because the multilevel fast multipole algorithm (MLFMA) expedites matrix-vector multiplication, it can be used to speed up iterative solutions of scattering problems. We have combined MLFMA with the conjugate gradient and the biconjugate gradient methods to arrive at efficient solvers for matrix equations arising from the integral equation of scattering. The computational and memory-requirement complexities are both O(NlogN) for surface scatterers. The total CPU time is hence proportional to N/sub iter/NlogN. Compared to traditional matrix solvers requiring O(N/sup 2/) memory, and N/sub iter/N/sup 2/ CPU time for iterative solvers, and O(N/sup 3/) CPU time for LUD, this is a vast improvement, especially for large problems. Therefore, large problems that previously require the resources of a supercomputer to solve, can now be solved on a workstation-size computer.