A fast solver for the pseudo-two-dimensional model of lithium-ion batteries

The pseudo-two-dimensional (P2D) model is a complex mathematical model that can capture the electrochemical processes in Li-ion batteries. However, the model also brings a heavy computational burden. Many simplifications to the model have been introduced in the literature to reduce the complexity. We present a method for fast computation of the P2D model which can be used when simplifications are not accurate enough. By rearranging the calculations, we reduce the complexity of the linear algebra problem. We also employ automatic differentiation, using an open source package JAX for robustness, while also allowing easy implementation of changes to coefficient expressions. The method alleviates the computational bottleneck in P2D models without compromising accuracy.