# getDP model of a helicoidal symmetric power cable
This getDP model is an implementation answer of the question _"how to solve a helicoidal symmetric, time-harmonic eddy current boundary value problem (BVP)?"_ In a nutshell: Here, a special coordinate transformation is used to transform a 3D BVP into an equivalent 2D BVP, which is then solved by the finite element method (based on a $\mathbf{H}-\phi$ formulation using proper manipulated cohomology basis fuctions). This is demonstrated for a cable with 13 conductors, carrying each the same total current of $\sqrt{2}/13$ Amperes at frequency $50$ Hz. The resulting magnetic field $\mathbf{H}$ and current density $\mathbf{J}$ are plotted in the _physical_ coordinate system $(x,y,z)$ as well as in the helicoidal coordinate system $(u,v,w)$.
The model had been developed by Julien Dular (University of Liege) and Albert Piwonski (Technische Universität Berlin).
Here you can find further information about the model and ansatz:
-[IEEE Transactions on Magnetics paper version](https://ieeexplore.ieee.org/document/10006756)
-[arXiv paper version](https://arxiv.org/abs/2301.03370)
This directory contains:
- getDP solver file: helicoidal_power_cable.pro (extensively documented and close to the paper notation as possible)
→ open this file using Gmsh
- Gmsh mesh file: helicoidal_power_cable.msh
I.e., the .msh file was not generated using a .geo scripting file, but using the [Julia API for Gmsh](https://gmsh.info/). This is because the calculation of the conductors' cross-sections was performed in Julia as well. Also, the .pro file may not look like a _typical_ getDP .pro file, since [Julia's string interpolation functions](https://docs.julialang.org/en/v1/manual/strings/#string-interpolation) were used extensively to create it automatically.
