A general class of vector absorbing boundary conditions for FEM applications

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. Wide-angle absorbing boundary conditions, as proposed in Halpern and Trefethen (1988) for optimal absorption of outward waves, can be obtained in vector forms and their implementation in a FEM formulation can achieve the fifth-order absorbing accuracy with derivatives only up to the second order.<>