A hierarchical two-level spectral preconditioning technique for cavity scattering problems

A new set of higher order hierarchical basis functions is proposed for expansion of the current in electrical field integral equations (EFIE) solved by multilevel fast multipole algorithm (MLFMA) for the cavity scattering problem. The hierarchical two-level spectral preconditioning technique is developed to solve EFIE with multiple right-hand sides arising in monostatic radar cross section (RCS) calculations. The sparse approximate inverse (SAI) preconditioner based on the higher order hierarchical basis functions is used to damp the high frequencies of the error and the low frequencies is eliminated by a spectral preconditioner in a two-level manner defined on the lower order basis functions. The spectral preconditioner is combined with SAI preconditioner to obtain a hierarchical two-level spectral preconditioner. This newly constructed hierarchical two-level spectral preconditioner is used to speed up the restarted GMRES iterative algorithm. Numerical experiments indicate that the new preconditioner is efficient for the MLFMA and can significantly reduce both the iteration number and computational time.