The function H_B_quasi_static

It is used to define the basic states \(\bB_b\) and \(\bH_b\).

This function defines a time independent magnetic field for one given Fourier mode on all the nodes of the finite element mesh. We denote by H_mesh the finite element mesh used to approximate the magnetic field.

Inputs and outputs

The inputs of this function are the following:

1. char_h_b is a character of one letters. It is equal to B or H and allows to know which magnetic field is computed.
2. rr is a real valued tabular that contains two columns with dimensions (2,H_mesh%np). The tabular rr(1,:) contains the radial cylindrical coordinate of all the nodes of the finite element mesh H_mesh. Respectively, rr(2,:) contains the vertical coordinates of these nodes.
3. m is the Fourier mode \(m\) considered. It is an integer.

The output of this function is a real valued tabular vv of dimension (SIZE(rr,2),6).

Exemple

Here is an exemple where we set \(\bH_\text{b}= r\textbf{e}_\theta\) with \(\textbf{e}_\theta\) the unit vector in the azimuthal direction. Moreover, we assume that the Maxwell equations are approximated on one domain. The magnetic permeability of the domain is avaible via the data inputs%mu_H(1).

The corresponding code lines are written as follows.

IF (char_h_b=='B') THEN
   IF (TYPE==3.AND.m==0) THEN
      vv = inputs\%mu_H(1)*rr(1,:)
   ELSE
      vv = 0.d0
   END IF
ELSE
   IF (TYPE==3.AND.m==0) THEN
      vv = rr(1,:)
   ELSE
      vv = 0.d0
   END IF
END IF
RETURN

We refer to the section Examples on physical problems for more examples.