Adaptive multilevel fast multipole algorithm with AEFIE for multiscale problems

A novel low-frequency fast multipole method based on the scaled plane wave expansion applied to the AEFIE is investigated in the work. A scale factor in the LF-FMM is dependent on the size of the boxes, and then each level has its own radiation and receiving pattern. Another important application is combing this method with adaptive Octree algorithm to solve multiscale problems, as changing the scaling factor can achieve the switching from low-frequency to high-frequency FMM freely and conveniently. A numerical example is given to demonstrate the accuracy and efficiency of the proposed method.