Including PML-based absorbing boundary conditions in the MLFMA

In this letter, the multilevel fast multipole algorithm is extended to the use of complex coordinates. These complex coordinates appear, e.g., when extracting the S-parameters of an electromagnetic crystal device terminated by perfectly matched layer based absorbing boundary conditions with the multiple scattering technique. The coordinates of the centers of the boxes on the different levels in the multilevel multipole algorithm are chosen so that they follow the path according to which the coordinates of the cylinders´ centers become complex. Therefore, a new real coordinate is introduced along this path. The boxes are first constructed based on this real coordinate and after that the corresponding complex coordinates are calculated. The described scheme is applied to the analysis of a multiplexer-demultiplexer device.