Striving for the improvement of the energy density of LIBs and for the minimization of their charging time thanks to design, is not new. Up to date, experimental works conducted on laser-perforated electrodes showed engaging results, while technologies relying on additive manufacturing have only been tested in a few academic studies to improve the performance of LIB cells . At the same time, the burst of recent researches on the parametric and topology optimization of such battery cells have allowed to hope for the numerical conception of new battery architectures, outperforming the standard planar geometry. Studies on the parametric optimization of LIB cells have created a substantial literature, and the first works on their topology optimization have appeared recently. The homogenized model of Doyle, Fuller and Newman~\cite{d1} (DFN) - serves as the foundation for numerous academic and industrial softwares~\cite{d2} used to simulate the operation of lithium-ion batteries during charging and discharging. Studying a battery cell $\Omega = \Omega_{\rm anode}\cup\Omega_{\rm separator}\cup\Omega_{\rm cathode}$ subject to a constant current discharge, our goal is to optimize each electrode interface by minimizing a shape dependent objective function. We propose here an implementation of the so-called pseudo-3D (P3D) version of the DFN model, which combines finite-element and finite-difference methods using the FreeFem and C++ languages. Coupled with the application of geometric optimization tools to the electrode interfaces, this implementation allows us to compute a shape gradient through the adjoint method and to apply a gradient flow algorithm to minimize a performance function under geometric constraints. We impose for instance in this minimization process the non-mixing constraint between the anodic domain and the cathodic domain. These computations represent a first step towards a complete geometric and topological optimization of the battery cell, including the optimization of the porous microstructure within each electrode.