3.3.2   MUR with superabsorption

The MUR with superabsorption (MUR) absorbing boundary condition (ABC) allows for specifying only one parameter, which is effective permittivity of the medium in which the wave propagates. This parameter is used by the software to calculate the correct phase velocity of the wave. Incorrect assumption of the effective permittivity increases the level of spurious reflections from the ABC. The MUR ABC assumes traveling wave conditions.

The general remarks regarding the practical use of MUR ABC should be made at this point:

·        The MUR ABC penetrates towards the circuit (from the plane where it is formally defined into the meshed area) for two FDTD cells. This should be taken into account when placing other elements i.e. NTF (Near-To-Far transformation surfaces), to avoid their overlapping and simulation inaccuracies. That means that the NTF box  must be placed not less than 3 FDTD cells from the superabsorbing plane.

·        The user should also be aware that the MUR ABC should be placed at sufficient distance from the radiating element so that the radiation fields dominate there. When the absorbing boundary is placed in the area of high density of the close (inductive) fields of the antenna, it can significantly change its radiation patterns and cause computational errors or even algorithm instabilities. The minimum distance depends on application but typically at least half-wavelength is recommended since the MUR ABC assumes traveling wave conditions.

·        The MUR ABC can be used when transformation of near fields to far fields in homogeneous medium other than air is of interest (e.g. in biomedical applications). The region between the NTF surface and absorbing boundaries must be homogeneous but may be filled with a medium of arbitrary permittivity ε_r, permeability μ_r, conductivity s, and magnetic loss s_M. It is then required to ensure that effective permittivity of all absorbing boundaries of MUR ABC type is set to: Permittivity (effective) = ε_rμ_r

·        For the MUR ABC the angle of wave incidence should be taken into account when calculating the effective permittivity parameter.

·        The MUR ABC is more flexible in case of possible applications than PML ABC. It can be applied practically in any case and its implementation takes into account the conformal cells. Thus it is a standard choice in the case of termination of arbitrarily shaped transmission lines. As shown in various examples of the User Guide 3D and User Guide V2D, it can also be quite effective in antenna problems.