Hello,
I am trying to implement the common H-Formulation, used to model magnetic fields in superconductors, in MATLAB Partial Differential Equation Toolbox. I am starting as a 2-D Problem to understand to functionality.
The H-Formulation generally looks like
where H is the magnetic field, ρ is the material resistivity and μ the material permiability. To transform theis into the form
used in MATLAB Partial Differential Equation Toolbox for the 2-D case (only 
and 
) I get m = 0;
d = mu;
a = 0;
f = 0;
c = [0, 0, 0, 0;...
0, rho, -rho, 0;...
0, -rho, rho, 0;...
0, 0, 0, 0];
To model the H-Formulation I have to model the superconductor domain and the air around it. So I have two domains that are seperated by a shared interface. As far as my understanding on this shared interface a Neumann boundary of the form
is used. My problem is that with the equation for a Neumann boundary in Matlab Documentation given as
where c is the same as in the PDE formulation, I do not see how this represents the typical Neumann boundary condition.
Can someone explain to me how I can implement the correct Neumann boundary condition in such a PDE problem?
