A theoretical study of numerical absorbing boundary conditions

Electromagnetic field computation involving inhomogeneous, arbitrarily-shaped objects may be carried out conveniently by using partial differential equation techniques, e.g., the finite element method (FEM). When solving open region problems using these techniques, it becomes necessary to enclose the scatterer with an outer boundary on which an absorbing boundary condition (ABC) is applied, and analytically-derived ABCs, e.g., the Bayliss-Gunzburger-Turkel and Engquist-Majda boundary conditions have been used extensively for this purpose. Numerical absorbing boundary conditions (NABCs) have been proposed as alternatives to analytical ABCs, and they are based upon a numerically-derived relationship that links the values of the field at the boundary nodes to those at the neighboring nodes. In the paper the authors demonstrate, analytically, that these NABCs become equivalent to many of the existing analytical ABCs in the limit as the cell size tends to zero. In addition, one can evaluate the numerical efficiency of these NABCs by using as an indicator the reflection coefficient for plane and cylindrical waves incident upon an arbitrary boundary