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.