The function mu_in_real_space

It is used to define a magnetic permeability depending of the time and all of the space direction \((r,\theta, z)\). If the permeability magnetic does not depend of the time and the azimuthal direction, this function is not used. We refer to the section Extension to magnetic permeability variable in time and azimuthal direction for more information on the formulation of the Maxwell equations in SFEMaNS.

This function defines a scalar function in the physical space for a number of angles, denoted nb_angles, on a number of nodes of the finite element mesh.

Inputs and outputs

The inputs of this function are the following:

1. H_mesh is the mesh where the magnetic field is approximated.
2. angles is the list of the angles where the penalty function is computed. These reals numbers are in the interval \([0,2\pi[\).
3. nb_angles is the number of angles considered. It is an interger.
4. nb is the label of the first node considered. It is an integer.
5. ne is the label of the last node considered. It is an integer.
6. time is the time at which this term is computed. It is a real number.

The output of this function is a real valued tabular vv with two columns of dimension (nb_angles,ne-nb+1).

Exemple

Here is an exemple where the following magnetic permeability is considered: \(\mu(r,\theta,z,t) = 1 + r^2 + |z|(1+\cos(t-\theta))\).

The corresponding code lines are written as follows.

DO i = 1, nb_angles
   DO n = 1, ne-nb+1
      r=H_mesh%rr(1,nb+n)
      theta=angles(i)
      z=H_mesh%rr(2,nb+n)
      vv(i,n)=1.d0 + r**2 + ABS(z)*(1.d0+COS(time-theta))
   END DO
END DO
RETURN

Remark: If the problem involves a magnetic perbeability with discontinuities, it is necessary to use a continuous magnetic permeabilty with a sharp gradient inthe regions where the discontinuities occur.

We refer to the sections Examples with manufactured solutions (see test 22, 23 and 29) and Examples on physical problems for more examples.