Multilevel Complex Source Beam Method for Electromagnetic Scattering Problems

This letter proposes a multilevel complex source beam (MLCSB) method for electromagnetic (EM) scattering problems. The multilevel structure is obtained with the octree grouping technique. Each basis function in the nonempty group is expanded with CSBs that tightly surround the group. The interactions between far groups are expressed with interactions of these CSBs. To accelerate the computation, the symmetry and shift invariance of the Green´s function is employed. The adaptive cross approximation (ACA) algorithm is then applied to accelerate the computation of interactions of CSBs. Due to the directionality of the radiation pattern of the CSBs, the interactions of CSBs are truncated with an angle threshold. Numerical examples demonstrate the efficiency of this method.