Further improvements to lumped element geometry processing

[sebastiangrimberg]

A follow-up to #246, which removes the integration of the port area to calculate the geometry of uniform and coaxial lumped elements. This step was susceptible to discretization error, in particular for coaxial lumped ports with circular boundaries. These geometric properties can now be calculated directly using the element bounding box/sphere.

This change mandates rebaselining the coaxial regression tests. For the coaxial cable with inner and outer diameters of 1.6383 and 5.461 mm, respectively, the impedance per square for the 50 Ohm coaxial lumped port should be 260.9 Ohm/sq (R = Rs * ln(R_o/R_i) / 2π). The values computed by Palace and used internally for the impedance BC are:

• main: 261.8 Ohm/sq
• This PR: 260.9 Ohm/sq

Thus, this PR corrects a previous geometry processing accuracy issue which showed up for coarsely meshed curves. Looking at the port V and I time histories, it looks like the errors were on the order of 1% for this example.

[hughcars]

The points here, are they from the geometry or refinements of the interpolant? Basically, are they guaranteed to be on the geometry for any interpolating basis function.

[sebastiangrimberg]

This isn't new code, but is the general "MFEM way" of extracting the nodes of a high-order curved element. I believe they will be on the geometry given the basis, but it probably depends on the basis and the conversion from the basis for the original mesh vs. the basis for high-order nodes in MFEM (I am fairly certain there is an interpolation step to convert the Gmsh equispaced basis to MFEM H1).

[hughcars]

What happens for an L shaped bracket of a port? I.e. an incompletely wrapping shell similar to the ones which triggered #89. This would give the sum of the two lengths rather than twice it.

[sebastiangrimberg]

My understanding is the geometry in #89 was not L-shaped but was the entire shell of the rectangular prism (4 quad surfaces, not 2). But I do suppose an L-shaped port could also be valid and indeed would not be addressed by this. Maybe we have to fall back to the area calculation but that seems like a weird use case.

[hughcars]

From what I remember working on that issue (it was a while ago), the geometry was that L shape, which was what threw me off in debugging it, as I had assumed everything would be planar for lumped. That was the reason I stuck with the area calculation as opposed to pulling directly off the bounding box, then only if planar checked that it was a rectangle.

[sebastiangrimberg]

Yep. To address this concern and also support #89, we'll take the following approach:

• Add a check for bounding_box.planar, like we do for coaxial lumped elements, and remove the second branch if the if/else which makes this 4-sided assumption.
• For the case of Unclear Degenerate coordinates error #89, each side can be a separate element for a multielement lumped port, as:

  "LumpedPort": [{
    "Index": 1,
    "Elements": [{
      "Attributes": [<attribute 1>],
      "Direction": "-Y"
    },
    {
      "Attributes": [<attribute 2>],
      "Direction": "+Y"
    },
    ...
  ]
  

This will give the correct behavior for the impedance BC, with each planar rectangular element adding in parallel much like a usual multielement lumped port.

I've added this in e4366f7 and claified the requirement in the docs in
8d24299.