Preconditioned Multilevel Fast Inhomogeneous Plane Wave Algorithm for Solving Electromagnetic Scattering Problems

A mesh-neighbor preconditioner is implemented into the multilevel fast inhomogeneous plane wave algorithm (MLFIPWA), to solve three dimensional electromagnetic scattering problems more efficiently. The spectrum integration of the Green's function and grouping technique are used in FIPWA to translate the direct source and field interaction into aggregation, translation and disaggregation, to accelerate the matrix-vector multiplication. The computation complexity of this algorithm is O(N 4/3 ). By applying a multilevel strategy, this complexity can be reduced to O(N log N) . To further speed up the solution process, a mesh-neighbor preconditioner is applied into this fast algorithm. Numerical results show the accuracy and efficiency of this algorithm.