Numerical absorbing boundary conditions for the scalar and vector wave equations

Electromagnetic field computation may be carried out conveniently by using the finite element method (FEM), When solving open region problems using this technique, it becomes necessary to enclose the scatterer with an outer boundary upon which an absorbing boundary condition (ABC) is applied; analytically-derived ABC's have been used extensively for this purpose, Recently, numerical absorbing boundary conditions (NABC's) have been proposed as alternatives to analytical ABC's, For the two-dimensional (2-D) Helmholtz equation, it has been demonstrated analytically that these NABC's become equivalent to many of the existing analytical ABC's in the limit as the cell size tends to zero, In addition, the numerical efficiency of these NABC's has been evaluated by using as an indicator the reflection coefficient for plane and cylindrical waves incident upon an arbitrary boundary. In this paper, we have extended this procedure to the study of NABC's, derived herein, for the three-dimensional (3-D) scalar and vector wave equations from the point of view of their numerical implementation in node- and edge-based FEM formulations, respectively.