Infinite Element Domain is not Working in 2D domain

Posted 16.04.2025, 04:10 GMT-4 Electromagnetics, Mesh, Modeling Workflow Version 6.0 2 Replies

Poonam Chand

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Hello everyone,

I am simulating a simple long conductor in COMSOL 2D in a magnetic field (mf) to observe its inductance value. However, its inductance values do not converge as I increase the domain size. I used the parametric sweep option. (Please see attached File_1)

Then, I tried to add the infinite element domain to find the inductance value, but it is still not working (File_2)

Finally, inductance value convergences when I perform the exact simulation in the 2D-axisymmetric domain (File_3). Most of the avaialble tutorial on COMSOL focuses on 2D axi-symmetric simulation.

In summary, 2D = not convergence, 2D axisymmetric = converges.

Please help me solve this issue for the 2D domain. Note that I am not asking about the values but about the convergence of inductance values.

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2 Replies Last Post 17.04.2025, 07:43 GMT-4

Magnus Olsson COMSOL Employee

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Posted: 2 days ago

Updated: 2 days ago

Hi,

The difference here is that the axisymmetric model describes a ring-shaped coil with finite wire radius/thickness and that has a well-defined and finite inductance. However, the planar 2D model describes a straight, infinitely long, out-of-plane conductor and that configuration does not have a finite inductance, not even per unit length. You can convince yourself by starting with an ideal coaxial cable, see for example: https://en.wikipedia.org/wiki/Coaxial_cable In the article you can see that the inductance per unit length scales as the natural logarithm of the ratio of the outer (screen ) radius to the radius of the center conductor. The formula is for conductors with surface currents (small skin depth) but the formula for a uniform (DC) current density has the same properties.

Now, let the outer radius approach infinity and you have the single conductor in an infinite space. However, the inductance formula will then diverge as log(inf)=inf. The same thing happens if you let the inner radius approach zero. As a matter of fact even the inductance of a ring-shaped coil diverges when the wire radius approaches zero.

Thus:

A single, infinitely long straight conductor does not have a finite inductance per unit length.
A closed loop coil with an infinitely thin conductor cross-section does not have a finite inductance either.

In finite element models, these two (analytical) results often confuse people as they result in computed inductances that depend on the model's geometrical size for (1) and on the element size for (2).

Note that, in the planar 2D model, when you leave the outer Magnetic Insulation boundaries at finite distance, you have a coax-like model as the constraint on the magnetic vector potential (nxA=0) results in "reaction surface currents" flowing in the opposite direction of the applied coil current and perfectly balancing that. The equation of continuity states that div(J)=0 and this is implicit in Maxwell's equations (take the divergence of Maxwell-Ampère's Law). Thus all current loops are closed and there is no such thing as an infinitely long straight current-carrying conductor.

It may be worth noting that transmission lines always have a forward and a return current path and thus have a finite inductance per unit length provided that the conductors have finite cross section areas and a finite separation distance.

Best regards,

-------------------
Magnus

Hi, The difference here is that the axisymmetric model describes a ring-shaped coil with finite wire radius/thickness and that has a well-defined and finite inductance. However, the planar 2D model describes a straight, infinitely long, out-of-plane conductor and that configuration does not have a finite inductance, not even per unit length. You can convince yourself by starting with an ideal coaxial cable, see for example: https://en.wikipedia.org/wiki/Coaxial_cable In the article you can see that the inductance per unit length scales as the natural logarithm of the ratio of the outer (screen ) radius to the radius of the center conductor. The formula is for conductors with surface currents (small skin depth) but the formula for a uniform (DC) current density has the same properties. Now, let the outer radius approach infinity and you have the single conductor in an infinite space. However, the inductance formula will then diverge as log(inf)=inf. The same thing happens if you let the inner radius approach zero. As a matter of fact even the inductance of a ring-shaped coil diverges when the wire radius approaches zero. Thus: 1. A single, infinitely long straight conductor does not have a finite inductance per unit length. 2. A closed loop coil with an infinitely thin conductor cross-section does not have a finite inductance either. In finite element models, these two (analytical) results often confuse people as they result in computed inductances that depend on the model's geometrical size for (1) and on the element size for (2). Note that, in the planar 2D model, when you leave the outer Magnetic Insulation boundaries at finite distance, you have a coax-like model as the constraint on the magnetic vector potential (nxA=0) results in "reaction surface currents" flowing in the opposite direction of the applied coil current and perfectly balancing that. The equation of continuity states that div(J)=0 and this is implicit in Maxwell's equations (take the divergence of Maxwell-Ampère's Law). Thus all current loops are closed and there is no such thing as an infinitely long straight current-carrying conductor. It may be worth noting that transmission lines always have a forward and a return current path and thus have a finite inductance per unit length provided that the conductors have finite cross section areas and a finite separation distance. Best regards,

Poonam Chand

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Posted: 1 day ago

Updated: 1 day ago

Thanks a lot, Magnus Olsson, for your valuable reply.

The transmission lines concept is really useful in my simulation, where I modelled the return current path for the conductor.

Next, I want to speed up my simulation by performing half-symmetry conditions in my model. However, I am unable to model the return path.

Which boundary condition can I use for 2D simulation (not 2D Axi-symmetric) in the Magnetic field interface? I have tried all different boundary conditions like PMC, Symmetry plane, but I still have not found any correct solution. i.e. inductance value is not converging.

Please see the attached PNG file for more clarification.

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