I would like to calculate the mutual inductance between a control line and a flux loop in a quantum chip design, which requires the use of superconducting materials.

In the past I have been using other materials to calculate values of the mutual inductance because I did not believe this would make a significant difference in the values achieved, but I know think otherwise. I have tried to remedy this by creating a material with near 0 (10^(-10)) value for the relative permeability, since a true superconductor would have a value of 0 here, but Maxwell doesn't seem to be able to simulate something with a relative permeability of 0, and a large value for the conductivity (it starts throwing errors around 10^12). A relative permeability of 0 would give a magnetic susceptibility value of -1, but I have not been able to find a location that I can specific the chi value. The built in material 'perfect conductor' does not have the parameters that a true superconductor has, and also Maxwell does not allow conduction paths to be made out of this material. I'm mostly curious about a way that I can confidently represent the true mutual inductance of my chip and get around the restrictions maxwell has put on the material settings.

I also have the issue of the problem region I am solving over. Since I have a current entering and exiting the chip, I am only able to make the problem region flush with two of the sides, and then extend some distance on the others. I'm not sure what effect the problem region has with the values, but they seem to fluctuate significantly as I adjust the size of the region that I am solving over. But this still restricts me to have a gap of 0 on two of the sides, which seems like it is causing issues. What is the proper way to create a problem region to give me accurate results.

Summary: How do I accurately represent a superconductor in Maxwell for mutual inductance calculations and what is the proper way to create the problem region to solve over?