Infinite Element Domain for Whitney AV solver

Numerical methods and mathematical models of Elmer
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modelman75
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Infinite Element Domain for Whitney AV solver

Post by modelman75 »

For a magnetodynamics harmonic problem, is it possible to employ an infinite element domain at the outer boundary? I have run into an issue with assigning an outer boundary condition that results in fields reasonably close to what is expected from a boundary at infinity.

For example, consider the simple case of a 3-D wire. Because a wire with a circular cross-section has an analytic solution, the inductance obtained from the whitney solver was compared with analytic solutions. For the Elmer solutions, inductance was obtained as the distance of the outer boundary from the wire was varied. Boundary conditions considered include an open boundary (no explicitly assigned conditions) and the magnetic vector potential normal to the boundary forced to zero (zero magnetic flux density in the direction of the wire).

What boundary conditions would be best for a magnetodynamics harmonic problem of this type?
raback
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Re: Infinite Element Domain for Whitney AV solver

Post by raback »

Hi

You cannot enforce the vector potential in the normal direction. The reason is that the vector potential is spanned by the basis functions defined on the edges. And on the boundary all edges are by construction tangential. So you can only set the tangential component to zero, "AV {e} = 0". At some stage we looked at ways to emulate the spherical far-field condition of the nodal Poisson equation but there really is no easy way to do it. I would argue that the situation is not as dim as it would be if we would set the nodal potential field to zero. I'm happy to hear if there would be a better way to set this.

-Peter
modelman75
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Re: Infinite Element Domain for Whitney AV solver

Post by modelman75 »

Peter, Thank you very much for the clear explanation. I should have realized the constraint imposed by the edge elements. A-V solvers are new to me. My past experience is mostly with E-V solvers.
ftrillaudp
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Re: Infinite Element Domain for Whitney AV solver

Post by ftrillaudp »

Dear Peter and modelman75,

Looking for such item in Elmerfem, I have stumbled upon this post.

I am using for time to time the FE solver GetDP. They implement there a shell transformation that blows up some elements of the mesh sending the boundary at A = 0 father away that it appears in the actual mesh.

In the manual of GetDP (https://getdp.info/), one of the function to be used in the Jacobian method is "VolSphShell" in 3D (Volume Jacobian with spherical shell transformation, for n-D regions in n-D geometries, n = 2 or 3.), for instance if one has a sphere as air. It is found in the chapter 5.5 of the reference manual.

I do not know how it is exactly implemented but it allows to reduce the mesh size while having the boundary far enough to avoid disrupting the field.

Sure it would be a nice feature to have at hand!

Best regards,

Frederic
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