Large scale computations using FISC

Abstract

FISC (Fast Illinois Solver Code) is designed to compute the RCS of complex three-dimensional targets. The problem is formulated by the method of moments, where the RWG basis functions are used. The resultant matrix equation is solved iteratively by the conjugate gradient (CG) method. The multilevel fast multipole algorithm (MLFMA) is used to accelerate the matrix-vector multiply in CG. Both complexities for the CPU time per iteration and memory requirements are of O(NlogN), where N is the number of unknowns. Some computations other than the matrix-vector multiply in FISC may have higher complexity than O(NlogN). When the translation matrix in MLFMA is calculated directly, the complexity is O(N/sup 3/2/). For calculating the bistatic RCS or radiation pattern on a one-plane cut, the number of observation angles (M) is proportional to the frequency for a surface scatterer. So the complexity of calculating bistatic RCS or radiation pattern is O(NM) or O(N/sup 1.5/). In this paper, we use interpolation to calculate the translation matrix and the complexity is reduced to O(N). MLFMA has been implemented to calculate the bistatic RCS or radiation pattern reducing its complexity to O(M)+O(NlogN). With these improvements, we have solved the problem of scattering from a 120/spl lambda/ sphere with 9,633,792 unknowns and VFY218 at 8 GHz with 9,990,918 unknowns. MLFMA has also been implemented for targets with a perfect electric conductor (PEC) ground plane.