I am trying to verify the Biot savart law for a circular current loop with three different models.

**2D-axi**-> here I can provide the already compiled mesh

**3D-full**-> The data file is too lare to upload it here. So I included the hdf file of Salome where the mesh must be compiled and exported to unv. Via elmergrid the native elmer mesh file can be generated. If there is any issue by doing so please let me know.

**3D-halve**-> like the 3D-full case the meshdata is too large.

see: Because of the limited number of attachments,

**the figures I name below are included in the subfolders of Biot-Savart.zip respectively.**

The analytic solution is given by:

$mu0=4*pi*1.0e-7 ! permeability of vacuum

$r=0.01 !Radius of current loop in meter

$h=0 !height along centerline in meter

$I=1.1 !excitation current in A

$B=(mu0*I*r^2)/(2*(r^2+h^2)^(3/2))!analytical solution of magnetic field along the centerline

See also BiotSavart_cir.png I have 5 Questions about my implementations and would be very happy If someone could help me in answering them:

**Questions according the 3D-halve simulation.**

My solver does converge, but the distribution of the B-Field does not coincide with my expectations (see Output3D-halve.PNG).

1. How can I fix this problem?

I believe I am messing up the BC for this model.

For example, when I implement:

AV {e} = 0

Is this equivalent to setting the three vector potentials equal to zero (please see below)

AV {e} 1=0

AV {e} 2=0

AV {e} 3=0

**Questions According the 2D-axi simulation**

I use the Saveline solver to post process the data. Here I recognize that my included range-distance from 0 to 0.04 is processed at the end of a bunch of data along the whole geometrical edge in the model. Now I manually delete all provided entities except for my defined range (see Fig BiotSavart-cir2DaxisCutData.png). The output of the raw data can be seen in Fig. BiotSavart-cir_2Daxis_RawData.png

2. How can I save only the data as I specify it in the sif?

3. How do I know which solver is used if no solver (i.e. Linear System Solver = Iterative) is explicit inserted in Procedure = "MagnetoDynamics" "MagnetoDynamicsCalcFields"? When is it important to specify the solver and when can I skip the information?

4. Now I calculate the field only at one point by defining h=0 explicit in the model and generating it in the savescalar model. Is there a way to include this as a variable containing different heights and exporting the point data equally to the saveline-solver points? In the figures I did this with octave, but I am curious if this is possible also within the procedure of elmer?

**Questions for the 3D-full model:**

5. When I use the saveline solver and 100 entities I get the distribution as depicted in Fig. BiotSavart-cir3D-full_100Datapoints.png when I save only 20 datapoints the results do not show this behavior as depicted in Fig. BiotSavart-cir3D-full_20Datapoints.png

How can I solve this issue?

I would be very tankful if anybody could help me!

Best regards,

Felix