Compact second-order accurate transparent boundary condition for the Helmholtz equation

The well-known Engquist-Majdat absorbing boundary condition for the wave equation is an essential component in the finite-difference time-domain (FD-TD) method. We present the frequency-domain version of this algorithm applied to the Helmholtz equation. While the time-domain implementation of the one way equation is only first-order accurate in step size, in frequency-domain realization we are able to keep every finite-difference operator accurate to the second power of the grid spacing for both the edge and corner points. For the performance analysis, we derive the plane wave reflection coefficient as function of the incident angle.