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Absorbing

Description​

Applies an absorbing boundary condition to selected surfaces of the electromagnetic model.

An absorbing boundary condition approximates an open electromagnetic domain by reducing reflections of outgoing waves at the boundaries of the computational region.

Construction​

abc = Absorbing()abc = Absorbing(boundary)

abc = Absorbing()

abc = Absorbing() Creates an absorbing boundary condition without assigning it to any mesh boundary. The boundary can be specified later using the boundary property.

abc = Absorbing(boundary)

abc = Absorbing(boundary) Creates an absorbing boundary condition and assigns it to the mesh surfaces identified by boundary.

Constructor Inputs​

NameTypeRequiredDefaultDescription

boundary

int | list[int]

Optional

None

Mesh boundary IDs identifying the surfaces where the absorbing boundary condition is applied. Each boundary ID may correspond to multiple triangular surface elements of the mesh.

Properties​

boundary

Type int | list[int]Access read/write

Mesh boundary IDs identifying the surfaces where the absorbing boundary condition is applied.

Examples​

Apply an absorbing boundary condition

Create a Absorbing boundary condition (ABC).

Mathematical Definition​

The first-order absorbing boundary condition approximates an open electromagnetic domain by imposing an outgoing-wave condition on the selected boundary surfaces:

n^×(∇×E)+jk0 n^×(n^×E)=0.(1)\vu{n}\times\left(\curl\vb{E}\right) + j k_0\,\vu{n}\times\left(\vu{n}\times\vb{E}\right) = \vb{0}. \tag{1}

Here, E\vb{E} is the complex electric field, n^\vu{n} is the outward unit normal vector, jj is the imaginary unit, and k0=ωμ0ε0k_0 = \omega\sqrt{\mu_0\varepsilon_0} is the free-space wavenumber.

This first-order approximation reduces reflections from outgoing electromagnetic waves but does not eliminate them completely. Its accuracy depends on factors such as the direction of wave propagation relative to the boundary.

The formulation assumes a relative permeability of μr=1\mu_r = 1.

Notes​

An absorbing boundary condition is an approximation of an open electromagnetic domain. Some reflection may remain, particularly when electromagnetic waves reach the boundary at oblique angles.

The absorbing boundary should be placed at a suitable distance from the structure being analyzed to reduce its influence on the computed electromagnetic response.