Accuracy of local absorbing boundary conditions for use with the vector Helmholtz equation

Frequency-domain procedures for 3-D electromagnetic scattering that are based on the vector Helmholtz differential equation must incorporate some form of radiation boundary condition to truncate the computational domain. Recently, a family of local absorbing boundary conditions has been developed for the 3-D vector case based on a general outward-propagating field. The authors present the error obtained using the 3-D vector absorbing boundary conditions as a function of boundary location and harmonic number. All the local boundary conditions degrade in accuracy as the harmonic index increases or as the radius of the boundary decreases. The error in the second-order condition is a significant improvement over that of the first-order condition and has been observed to be approximately the same for a given harmonic number as the second-order Bayliss-Turkel condition for the scalar problem. These results suggest that the second-order condition be used within numerical implementations.<>