Hierarchical Two-level Preconditioning of MLFMA Algorithm for Electromagnetic Wave Scattering Problems

A 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). The hierarchical two-level spectral preconditioning technique is developed to solve EFIE in radar cross section (RCS) calculations. 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.