A 1D multipoint auxiliary propagator (1D-MAP) for sourcing plane waves for FDTD

FDTD Discrete Planewave (FDTD-DPW) Formulation for a Perfectly Matched Source in TFSF Simulations

“…On the other hand, the IFA scheme [1] including the MND procedure [4] only utilize two neighboring points in each time-step. Since the MND technique ultimately amounts to modifying the grid spacing and/or the stability factor , it is conceptually concise to state that an improved IFA scheme effectively has somehow averaged out the four spatial points into two by finding the best operating and that result in a close approximation of the multipoint FDTD planewave (8)- (9).…”

“…A convenient and somewhat simpler alternative is to use an analytic expression for the fields at these points, as implemented in [9], [10], [19]. The user should be advised, however, that this introduces numerical artifacts directly into the source, and the level of these artifacts may be of concern depending on what one wants to draw from the simulation as a whole.…”

“…However, mixed and boundary source FDTD planewave equations may not be as compact. Also, care must be taken to make sure that the Huygens' surface source fields in the main grid are not populated using these hard-sourced fields in the -grid: in order to achieve proper TFSF field isolation one must use fields in the -grid that are actually iterated via (8)- (9).…”

“…We have recently reported on two techniques that improve upon both. In [9], [10] we introduced the 1D-multipoint auxiliary propagator (1D-MAP), which described an efficient perfectly matched FDTD planewave source in the time domain derived directly 0018-926X/$26.00 © 2010 IEEE from the dispersion equation for 2D problems, achieving machine level field isolation. Using the nature of numerical planewaves reported in [11], we reported on an optimized AFP (O-AFP) technique which maintains the accuracy but makes it much more efficient and extends its applicability to 3D [12], [13].…”