Error control for the 3D FIPWA in complex media

The fast inhomogeneous plane wave algorithm (FIPWA) was developed as an alternative to the fast multipole method (FMM). One advantage FIPWA claims over FMM is extension to layered media problems while scaling as O(N log N) in processing time and O(N) in memory. However, to the best of our knowledge, error control has been limited to lossless media problems. The paper explores the nature of the error control in lossy and active media and proposes control mechanisms for 3D problems by exploiting the integral representation of the 3D Green´s function. The error for 3D FIPWA in complex media is shown to be controllable. The desired accuracy can be achieved only for large buffers in lossy media, but, in active media, the error is controllable with the excess bandwidth formula when used with an effective group size. Thus, it is believed that the 2D FIPWA offers an alternative approach to controlling the error in the 3D Green´s function.