In open-region electromagnetic simulations, the computational domain has to be truncated by an absorbing boundary condition (ABC) to model the infinite space. The performance of ABC strongly affects the accuracy of overall numerical simulation.
For a class of advanced problems demanding high accuracy, such as in the modeling of medical detection devices, indoor wireless communication systems and remote sensing equipments, the received signal can be several orders of magnitude less than the transmitted signal. Furthermore, wide-band simulations require long running times for transients-based simulations, which increase the potential for instability. Therefore, accuracy and stability of absorbing boundary conditions are identified as critical in the design of numerical algorithms compatible with advanced applications.
In this work, theory of Concurrent Complementary Operators Method (C-COM) in both transient and frequency-domain numerical simulations is investigated. The C-COM is based on the basic premise of primary reflection cancellation. The C-COM applications to numerically derived ABCs in finite difference time-domain (FDTD) method, and to frequency domain ABCs in both finite difference frequency domain (FDFD) method and finite element method (FEM) method are developed.
Extensive numerical experiments are conducted showing dramatic increase in accuracy when the C-COM is applied in comparison to previous published techniques. Previous works that addressed the boundary instability arising from the application of the absorbing boundary condition used either the von Neumann analysis or the Gustafsson-Kreiss-Sundström (GKS) analysis. These earlier works, however, did not explain the inconsistencies that have been observed between the theoretical predictions and numerical experiments.
This study presents a new stability analysis applicable to boundary conditions. This new analysis, referred to as Coupled Stability Analysis (CSA), is based on the fundamental assumption that absorbing boundary conditions are not perfect, and therefore, generate waves that reflect back into the computational domain. It is found that this analysis yields results that are fully consistent with those obtained from numerical experiments. As an important consequence of this analysis, and contrary to earlier conjectures, we show that Higdon’s absorbing boundary condition of order 3 (and possibly, higher orders) to be unconditionally unstable.
Source: University of Maryland
Author: Wu, Xin