Switched boundary condition techniques in FDTD
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AbstractThe Finite-Difference Time-Domain (FDTD) method is a numerical technique that is used to analyze complex electromagnetic problems. The memory requirement and time duration of a given FDTD simulation are critical issues that are consistently addressed in research. Absorbing Boundary Conditions (ABCs) attempt to solve these issues by effectively extending the simulation domain to infinity. Current widely used boundary conditions like the Perfectly Matched Layer (PML) have high absorption characteristics however the memory and time required to use and implement this method is relatively high. A new boundary class is proposed that takes advantage of the time domain properties of FDTD to construct an ABC with low memory requirement and comparatively high absorption. This method involves a switched impedance that upconverts waves incident on the boundary to high frequency. This high frequency energy can then be removed from the simulation using the inherent attenuation properties of numerical dispersion in FDTD. A hybrid ABC is developed integrating the Switched Boundary Condition (XBC) with existing classical Mur and PML boundaries. The new XBC class is validated against existing ABCs over a set of test simulations giving an overall performance evaluation of each boundary. The switched boundary implementations are found to offer complete absorption, however, this is only valid in specific FDTD cases. A hybrid, 1st order, switched Mur boundary is designed giving a general boundary solution with improved absorption over standard Mur and 4-layer PML in all simulation cases.
Bibliography: p. 120-123