Absorbing Boundary Condition¶

You generally apply this condition to the outer boundary of the computational domain. It absorbs radiation that comes from within. This prevents reflections and simulates an enclosure in infinite free space. The boundary must be far enough from the radiating or scattering object. Then you can assume that waves that reach the boundary from within the computational domain are incident normally. In this case the electric field satisfies the following relation [1]:

\[ \hat{\mathbf{n}} \times \left(\frac{1}{\mu} \nabla \times \tilde{\mathbf{E}}\right) = j \frac{\omega}{Z} \hat{\mathbf{n}} \times \left(\tilde{\mathbf{E}} \times \hat{\mathbf{n}}\right), \]

where \(\hat{\mathbf{n}}\) is the unit vector normal to the boundary, \(\omega\) is the angular frequency, and \(Z = \sqrt{\mu/(\varepsilon - j\sigma/\omega)}\) is the impedance with \(\mu\), \(\varepsilon\), and \(\sigma\) being the permeability, permittivity, and conductivity of the material adjacent to the boundary.

To create an AbsorbingBoundaryCondition, give a name and the boundary Marker:

condition = AbsorbingBoundaryCondition(
    name = "My Absorbing Boundary Condition",
    marker = my_marker,
)

References¶

[1] J.-M. Jin, "The finite element method in electromagnetics", 3^rd edition, Wiley, 2014 (Chapter 9.2)