Rig orous, auxiliary variable-based implementation of a second-order ABC for the vector FEM

The finite element method (FEM) is commonly used for electromagnetic radiation and scattering analysis. When an infinite, free space exterior domain needs to be incorporated into the method, a radiation boundary condition must be enforced. An approach which has received considerable attention, is to employ approximate conditions, known as absorbing boundary conditions (ABCs), that preserve the sparsity of the original FEM system upon discretization. In the case of time-harmonic analysis based on the vector wave equation in three dimensions, the symmetric, spherical Bayliss-Turkel-type ABCs of first- and second-orders are well-established. The second-order version is expected to be more accurate, however when using the standard curl-conforming approach to FEM discretization, an implementation difficulty is encountered, relating to successive derivatives being required of the nonconforming field components. This issue is addressed here by introducing a scheme where the nonconforming first-order derivatives are projected onto a suitably conforming auxiliary field, of which another derivative can then be taken instead. Additional computational costs are minimal and the scheme retains the symmetry of the standard formulation. Numerical results demonstrate the superior performance of the rigorously implemented second-order ABC over its first-order counterpart.