EM Module: Generalized reflection and scattering problems

[moosebuild]

Imported from idaholab/elk#3 by @cticenhour at May 30, 2018 12:10PM MST

Mentioned merge requests:

• Maxwells electric field vector interface conditions (!14)
• Fill in all documentation stubs (!44)

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Rationale

Antenna problems will require a more general reflection and scattering model than has been created so far (in JinSlab1D). This should be included in Elk.

Description

This will require a rework of the boundary and interface conditions currently developed for 1-D, as well as test benchmarks. Resources for this would include mostly Jin texts:

1. The Finite Element Method in Electromagnetics, 3rd Edition
2. Theory and Computation of Electromagnetic Fields
3. Finite Element Analysis of Antennas and Arrays

Impact

New capability for future antenna problems.

[moosebuild]

Imported from idaholab/elk#3 by @cticenhour at May 23, 2019 10:33AM MST

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Additionally, the more general interface conditions derived naturally from Maxwell's (as shown in Introduction to Electrodynamics, 3rd Edition by David Griffiths in Section 7.3, pg 333), could/should be more useful than those in Jin's texts, which could be considered more specific. I need to explore this difference more.

Maxwells general conditions between two materials (1 and 2) are:

1. eps_1 E_1_perpendicular - eps_2 E_2_perpendicular = sigma_f
2. E_1_parallel - E_2_parallel = 0
3. B_1_perpendicular - B_2_perpendicular = 0
4. (1 / _mu_1) B_1_parallel - (1 / _mu_2) B_2_parallel = K_f x normal

where:

5. eps is the material permittivity
6. mu is the material magnetic permeability
7. sigma_f is the free charge on the interface
8. K_f is the free current on the interface

(7) and (8) are zero on a dielectric interface, but non-zero for conductors.