Numerical implementation of second- and third-order conformal absorbing boundary conditions for the vector-wave equation

A rigorous implementation, in an edge-based finite-element formulation of second- and third-order conformal absorbing boundary conditions (ABCs) is presented for the solution of three-dimensional (3-D) scattering problems when the boundary S terminating the mesh is the surface of a parallelepiped. A special treatment is provided for the singularities (edges) of S. A systematic numerical study is carried out that compares the performances of these ABCs with those of the standard zero-order ABC, as well as of a more simple, though less rigorous, implementation of the second-order ABC. When S is separated from the scatterer by only one or two layers of elements, the numerical results that are presented demonstrate the good level of numerical accuracy achieved when the second- and third-order ABCs are employed and the singularities of S are appropriately dealt with.