atl_eqn_maxwell_module Module

Module to describe the Maxwell equation system for electrodynamics.

This implements the equation system for electric-magnetic fields of the following form Change of (electric) displacement field $D = \epsilon E$: $$\partial_t D = \nabla \times \frac{B}{\mu} - J$$

Change of magnetic field $B$: $$\partial_t B = - \nabla \times \frac{D}{\epsilon}$$

Nonexistence of magnetic monopoles: $$\nabla \cdot B = 0$$

Sources of electric field: $$\nabla \cdot D = \rho$$

Where $\rho$ is the spatial charge density and $J = \sigma E$ the free The magnetic permeability $\mu$, the electric permittivity $\epsilon$ and the conductivity $\sigma$ need to be provided as variables in a material table. See tem_variable_module for details on the definition of variables. In their simplest form they may just be scalars. Thus, a typical definition for the Maxwell equation system takes the following form:

  equation = {
    name = 'maxwell',
    material = {
      permeability = 1.0,
      permittivity = 1.0,
      conductivity = 0.0
    }
  }

There are various variants of the Maxwell equations available in Ateles:

• maxwell
• maxwell_2d
• maxwelldivcorr

For the divergence correction conductivity is not available. Instead the parameters gam and chi have to be provided for the divergence correction.