Vector one-way wave absorbing boundary conditions for FEM applications

In the paper a derivation is presented which leads to a new and general class of vector absorbing boundary conditions (ABCs) 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 Halpern and Trefethen (1988) 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 ABCs 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