VECTOR ONE-WAY ABSORBING BOUNDARY-CONDITIONS FOR FEM APPLICATIONS

In this paper a derivation is presented which leads to a new and gener al class of vector absorbing boundary conditions (ABC's) for use with the finite element method (FEM). The derivation is based on a vector o ne-way wave equation and a polynomial approximation of the vector radi cal. It is shown that wide-angle absorbing boundary conditions, as pro posed in [13] for optimal absorption of out-going waves, can be obtain ed in vector form. Vector plane waves are used to evaluate the accurac y and the reflection performance of these boundary conditions in a wid e 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 sec ond-order. A possible formulation is described which not only yields a third-order accuracy with first-order derivatives, but also retains t he symmetry of the FEM matrix.