In ultra-low temperature cryogenics, such as dilution refrigeration, the primary challenge for power delivery is managing heat loss. While superconducting wires offer a zero-resistance approach for delivering power, they also act as parasitic thermal links. This project develops a C++ simulation to quantify and minimize these parasitic thermal links in a composite wire consisting of Niobium-Titanium (NbTi) and Copper (Cu). 

Because material properties at cryogenic scales vary by orders of magnitude, an implicit Crank-Nicolson method is used to solve the heat equation. This accounts for the temperature-dependent evolution of material properties across discrete nodes. To address the numerical challenges of numerical stiffness caused by sharp material interfaces (where NbTi meets the Copper), Jacobian-based smoothing functions are implemented. This ensures the simulation converges on a stable steady-state solution without typical numerical oscillations.

The final testing suite allows for the visualization of power-removal requirements at each refrigeration stage. By iterating on the placement of heat anchors and the volumetric ratio of NbTi to Copper, this tool provides a path to optimize lead assemblies and reduce the cooling power required to maintain base temperatures in complex cryogenic systems.