A spectral multiresolution preconditioner combined with multilevel fast multipole algorithm for the fast monostatic RCS calculation

For efficiently solving large dense complex linear systems with multiple right-hand sides that arise in monostatic radar cross section (RCS) calculation, a spectral multiresolution method combined with the multilevel fast multipole algorithm (MLFMA) is developed and used in the context of the generalized minimal residual iterative method (GMRES). In this scheme, the MLFMA is used to speed up the matrix vector product operations and the spectral multiresolution (MR) preconditioner, combined with a diagonal preconditioning, is employed to efficiently improve the distribution of the eigenvalues of the matrix, and can achieves the fast convergence rate by augmenting to the GMRES method a few eigenvectors associated with the smallest eigenvalues of the system. Numerical experiments indicate that this spectral MR preconditioning scheme is very effective with the MLFMA and can reduce both the iteration number and the CPU time of calculation significantly.