Current Density Computation Method

It is possible to set an environment variable in SimLab to change the method for the computation of the current density for Magnetic AC 3D and Magnetic Transient 3D solutions with solid conductors.

Available methods for the current density computation

We want to compute the current density in solid conductors with the electric conduction model.

1. The first approach computes from the result of the electric scalar potential formulation, , with σ the electric conductivity. This formulation used nodal final elements to compute the electric scalar potential V. But this formulation does not strongly respect the conservation of the current.
   
   

   

   
   
2. The second approach computes the source current density with the least square method. The source current density uses facet finite element. This formulation respects the conservation of the current density. However, the source current density is not unique with the least square method.
   
   

   

   
   
3. In the third approach, the value of is corrected by the curl of an arbitrary electric vector potential to have a unique current density. The first step of this third approach is the same as the second approach, computing the source current density with the least square method. The second step of finding an electric vector potential , such that the current density is . The electric vector potential is computed with edge finite element. This formulation respects the conservation of the current density and has a unique solution for the current density .
   
   

   

   
   

Environment variable setting

If the environment variable is not set, the current density is computed with the first approach:

It is possible to change the computation method by defining the environment variable: SL_FLUX_J0_COMPUTATION.