@article{abee6f4e29b14fd68be81b4db6ce2613,
title = "Vector One-Way Wave Absorbing Boundary Conditions for FEM Applications",
abstract = "In this paper a derivation is presented which leads to a new and general class of vector absorbing boundary conditions (ABC's) for use with the finite element method (FEM). The derivation is based on a vector one-way wave equation and a polynomial approximation of the vector radical. It is shown that wide-angle absorbing boundary conditions, as proposed in [13] for optimal absorption of out-going waves, can be obtained in vector form. Vector plane waves are used to evaluate the accuracy and the reflection performance of these boundary conditions in a wide range of incidence angles. The implementation of the vector ABC's in a FEM formulation is also provided to show how up to the fifth-order absorbing accuracy can be achieved with derivatives only up to the second-order. A possible formulation is described which not only yields a third-order accuracy with first-order derivatives, but also retains the symmetry of the FEM matrix.",
author = "Weimin Sun and Constantine Balanis",
note = "Funding Information: With the continued advance of finite element and finite difference techniques for modeling electromagnetic scattering and radiation problems, the use of absorbing boundary conditions for truncating unbounded space has become an important technique. The space truncation by an ABC not only limits the number of unknowns to a manageable size, but also preserves the sparsity of the resulting matrix. The research in the area of absorbing boundary conditions is extensive. Much of the research originated in the applied mathematics and computational physics, and recently adapted in the electromagnetics community. There are two basic types of absorbing boundary conditions which are used in the EM community. One is based on differential operators which can annihilate the low-order terms of the Wilcox far-field expansion [I]-[9]. The other is based on symbolic polynomial approximation of an one-way wave operator [lo]-[ 151. The former type of ABC{\textquoteright}s is exclusively used in the frequency domain, notably with a finite element method. The latter type of ABC{\textquoteright}s is widely used in the time-domain with a finite difference method. The ABC{\textquoteright}s derived from the Wilcox far-field expansion are a natural extension of the Sommerfeld radiation condition. They provide a physical insight into how the low-order mode contributions are eliminated by the boundary operators, and a systematic way to achieve arbitrarily high-order boundary conditions. But this type of ABC renders high accuracy only when the boundary is consistent with the wave front. In most applications, there exists no fixed phase center, so a circular or spherical boundary is preferred. Secondly, this type of ABC does not possess the feature of wide-angle absorption, and is complicated for higher orders. The ABC{\textquoteright}s derived from a one-way wave equation have several merits. They can be designed to allow efficient absorption over much wider incidence angles, and be implemented up to a desirable order of accuracy without complication. However, the one-way wave type of ABC{\textquoteright}s was primarily developed from a two-dimensional scalar wave Manuscript received April 26, 1993; revised December 29, 1993. This work was supported by the Advanced Helicopter Electromagnetics (AHE) Program and NASA under Grant NAG-1-1082. The authors are with the Telecommunications Research Center, Arizona State University, Tempe, AZ 85287-7206 USA. IEEE Log Number 9402828.",
year = "1994",
month = jun,
doi = "10.1109/8.301715",
language = "English (US)",
volume = "42",
pages = "872--878",
journal = "IEEE Transactions on Antennas and Propagation",
issn = "0018-926X",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "6",
}