## 3D Magnetic Vector Potential

General discussion about Elmer
juliuspiso
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Joined: 07 Feb 2018, 13:42
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### 3D Magnetic Vector Potential

Hi!
I am working on a project which requires the calculation of the mutual inductance between two coils (one arbitrarily shaped coil to be tested and a circular probe coil (which can be moved to different positions)). My idea was to use the MagnetoDynamicsCalcFields solver to calculate the magnetic vector potential of the arbitrarily shaped coil only and do some further calculations with the computed field in a python script. I attached the main mathematical formulation of the way I plan to calculate the mutual inductance below. I_1 is the current flowing through the arbitrary coil, A is the calculated magnetic vector potential, Gamma_2 is the path following the shape of the circular probe coil (which I can move in the python script), t is the tangent vector of this path. I already wrote the python script to do this calculation based on the node/vector data provided by the ElmerPost file of the mgdyn_torus example (which I only wanted to slightly modify to support my coil designs). But by reading the Keyword section of "Model 15: Computation of Magnetic Fields in 3D" of the Elmer Models Manual I realized that neither the WhitneyAVSolver nor the MagnetoDynamicsCalcFields are using the magnetic vector potential. Instead they use the scalar magnetic potential. So my question is: Is there any way to calculate the magnetic vector potential (3D) produced by a coil using one of the solvers provided by Elmer?
Kind regards,
Julius
Attachments
mutual_inductance.jpg

raback
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### Re: 3D Magnetic Vector Potential

Hi,

The WhitneyAVSolver is using vector potential. It is just solved using Hcurl conforming elements. So instead of the vector potential having three components sitting in every node we have the degree of freedom as the amplitude of an vector oriented along element edges (for lowest order). Hence you cannot save the vector potential on the nodes. If you interpolate them to nodes you're bound to introduce some interpolation errors. Hence it would make most sense to compute that integral within Elmer where you have access to the edge basis functions.

-Peter

juliuspiso
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Joined: 07 Feb 2018, 13:42
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### Re: 3D Magnetic Vector Potential

Hi!
Thank you very much for your fast reply! Indeed, your solution seems to be the least error prone way to do that kind of calculation. However I think I'll need to learn a lot more about Elmer to actually do this calculation using the solver. Yesterday I realized that I completely ignored the first steps of the derivation of the formula I attached in my first message: the derivation started with the double integral of the magnetic flux density over the area of the coil - which the mgdyn_torus test already supplies.

As the precision requirements of my test run are not too strict - because the calculation is mainly intended to show changes in the inductive coupling between the coils depending on their relative position than to calculate the absolute value of it - I think for now I will work with the double integral of the B-field inside python. But I definitely want to improve the accuracy in the future using your suggestions.
Kind regards,
Julius

Alma J. Taylor
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Joined: 02 Apr 2019, 12:25
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### Re: 3D Magnetic Vector Potential

A 3-dimensional magnetic vector potential is a formulation for electromagnetic devices containing a permanent magnet is presented. This method is based on developing models for first and second order tetrahedral type elements. The magnetic circuit of an electrical device containing a samarium-cobalt permanent magnet is used to verify the two models is an example. Various finite element techniques based on the magnetic vector potential for the solution of three-dimensional magnetostatic problems are presented. A lack of gauging results in an ill-conditioned system if nodal finite elements are used for the approximation of the vector potential.