For efficiently solving large dense complex linear systems that arise in electric field integral equations (EFIE) of electromagnetic scattering problems, the fast multipole method (FMM) is used to accelerate the matrix‐vector product operations, and the sparse approximate inverse (SAI) preconditioning technique is employed to speed up the convergence rate of the Krylov iterations. A good quality SAI preconditioner in the FMM context is constructed based on the near‐field matrix of the EFIE. The main purpose of this paper is to show that the quality of the SAI preconditioner can be greatly improved by use of information from FMM implementation. Numerical experiments indicate that the resulted SAI preconditioner is very effective with FMM and can reduce the overall simulation time significantly. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 1746–1750, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22538

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A new spectral two-step preconditioning of multilevel fast multipole algorithm (MLFMA) is proposed to solve large dense linear systems with multiple right-hand sides arising in monostatic radar cross section (RCS) calculations. The first system is solved with a deflated generalized minimal residual (GMRES) method and the eigenvector information is generated at the same time. Based on this eigenvector information, a spectral preconditioner is defined and combined with a previously constructed sparse approximate inverse (SAI) preconditioner in a two-step manner, resulting in the proposed spectral two-step preconditioner. Restarted GMRES with the newly constructed spectral two-step preconditioner is considered as the iterative method for solving subsequent systems and the MLFMA is used to speed up the matrix-vector product operations. Numerical experiments indicate that the new preconditioner is very effective with the MLFMA and can reduce both the iteration number and the computational time significantly.Index Terms-Electromagnetic scattering, generalized minimal residual (GMRES) method, multilevel fast multipole algorithm (MLFMA), preconditioning techniques.