Sparse approximate inverse preconditioning of deflated block-GMRES algorithm for the fast monostatic RCS calculation

A sparse approximate inverse (SAI) preconditioning of deflated block-generalized minimal residual (GMRES) algorithm is proposed to solve large dense linear systems with multiple right-hand sides arising from monostatic radar cross section (RCS) calculations. The multilevel fast multipole method (MLFMM) is used to accelerate the matrix-vector product operations, and the SAI preconditioning technique is employed to speed up the convergence rate of block-GMRES (BGMRES) iterations. The main purpose of this study is to show that the convergence rate of the SAI preconditioned BGMRES method can be significantly improved by deflating a few smallest eigenvalues. Numerical experiments indicate that the combined effect of the SAI preconditioning technique that clusters most of eigenvalues to one, coupled with the deflation technique that shifts the rest of the smallest eigenvalues in the spectrum, can be very beneficial in the MLFMM, thus reducing the overall simulation time substantially. Copyright (c) 2008 John Wiley & Sons, Ltd.