The function grad_mu_bar_in_fourier_space

It is used to define the gradient in the radial and vertical direction of the function mu_bar_in_fourier_space. We remind that mu_bar_in_fourier_space is either a magnetic permeability \(\mu(r,z)\) or a stabilization term \(\overline{\mu}(r,z)\) when the magnetic permeability depends of the time or the azimuthal direction \(\theta\). 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 gradient in the radial and vertical direction for one given gauss point of the finite element mesh.

Inputs and outputs

The inputs of this function are the following:

1. pts is real valued tabular of dimension two. pts(1) is the radial cylindrical coordinate of the gauss point considered. pts(2) is the vertical cylindrical coordinate of the gauss point considered.
2. pts_id is the label of the domain that contains the gauss point considered.

The output of this function is a real valued tabular vv of dimension two.

Exemple

Here is an exemple where we consider the magnetic permeability \(\mu(r,z)=1 + r z^2\).

The corresponding code lines are written as follows.

vv(1)=pts(2)**2
vv(1)=2.d0*pts(1)*pts(2)
RETURN

We refer to the sections Examples with manufactured solutions (see tests 17, 18, 22, 23 or 29) and Examples on physical problems for more examples.