Link to the Journal paper: Editor’s Choice-Perspective/J. Electrochem. Soc.
Link to the extended version: extended/arXiv article
- Model 1. Primary Current Distribution
The code and document provided under this section involve solving Laplace’s equation with primary current distribution as shown in the schematic below:
This seeming simple linear problem is challenging to solve numerically due to the change in the boundary condition type from Dirichlet to Neumann at x=0.5, y=0 in the domain shown above. Using conformal mapping technique, it is possible to obtain analytical solution for this problem. Numerical solution based on finite element method is found to be converging very slowly to the analytical solution, particularly close to the singularity. The code for the analytical solution using conformal mapping can be downloaded from below. This code can be opened and run only in Maple platform. A PDF document showing the code along with the solution procedure can also be downloaded from below. Additional details on this model can be found in the arXiv version (link provided below) of the perspective article from our group on numerical challenges in moving to multiscale battery models which is currently being reviewed for publication in the Journal of Electrochemical Society.
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- Conformal Mapping : Maple Code (PDF)
- Finite Element Method (FEM) : Maple Code (PDF)
Note: The FEM Maple code is only for demonstration purpose, and has not been optimized for numerical efficiency. In the future, codes in MATLAB and other environments will be posted.
