Christophe, thank's a lot for your answer and link for article! I am not so good in mathematic, but will try to understand. −(∇ξh,A′h) part looking strange, due to it similar Galerkin { [ sigma[] * Dof{d v}, {a} ] for A-v formulation. Then we get eqution including Galerkin {sigma[] * Dof{d v}, {a}} and Galerkin {Dof{ξh}, {a}} (v-scalar electrodynamic potential, ξh - uncnown introduced in Ampere equation (13) in article). Will the ξh distort the solution for the scalar electrodynamic potential? Is it necessary to take into account the ξh when calculating the electric field strength on a par with the scalar dynamic potential? Judging by the solution, ξh does not affect the scalar electrodynamic potential and it does not need to be taken into account when calculating the electric field strength. I get solution for ξh same as for v (multipilled on sigma value). If I understood correctly, ξh is entered in order to the number of equations corresponded to the number of variables, because adding the requirement div A = 0, leads to the fact that the equations become more than the variables and we can't get unique solution. The only question is why this additive does not affect the resulting solution for A and v? The component (∇ ξh,A'h) may not be equal to zero, if so, then it must distort the Ampere law.

Hello Dear Sirs!

Unfortunately, I have not found any forums where people discuss the use of the gmsh/getdp software package, so I decide to write here. If there are forums where I can communicate with experienced users of this product, please send me link.

There is a question about using gmsh/getdp for modeling problems related to the electromagnetic field (eddy current nondestructive testing of ferromagnetic products). Based on magstadyn_av_js0_3d.pro the problem was described(the exciting coil and the conducting object located in it). A-v formulation was used. The problem is solved presumably correctly, but there is a question that I could not answer.

The question concerns the last integral in the Equation section for Coulomb calibration, namely Galerkin { [ Dof{d xi}, {a} ] ; In Domain ; Jacobian Vol ; Integration II ; }.

Please tell me what is the meaning of this integral?
I tried to change the basis functions to d{xi} or to d{v} (Galerkin { [ Dof{d xi}, {d xi} ] ;...), the problem stops being solved correctly.
If I understand correctly in the case of using Coulomb calibration, the requirement div(A)=0 is added. After integrating by xi and applying Green's formula, we get the integral of (div(xi*a) – a* d xi). If homogeneous Dirichlet boundary conditions are given for xi, then a* d xi remains. Where does Dof{d xi}, {a} come from?