# Joint dynamics and efficient initialization techniques for potentials and currents in the P2D battery model

## TL;DR

This paper introduces a new method to improve the efficiency of solving battery models by using a better initial guess for calculations.

## Contribution

The novel contribution is an analytically derived linear solution for initializing boundary conditions in the P2D battery model.

## Key findings

- The proposed initialization method enhances convergence speed in solving the P2D model.
- The approach is computationally efficient and straightforward to implement.
- Using the new method improves the overall performance of the P2D battery model.

## Abstract

Solving the physics-based pseudo-two-dimensional (P2D) models involves using iterative methods, such as the Newton or the shooting method to solve a boundary condition problem. To use these iterative methods effectively, it is imperative to transform the boundary condition problem into an initial condition problem. This, in turn, necessitates initializing certain parameters, often done by providing guess values. The choice of these initial guess values can significantly impact convergence speed. This study proposes an analytically derived linear solution for initializing these conditions as an approximate guess. The proposed approach is not only computationally efficient, enhancing convergence speed and overall performance of the P2D model, but also straightforward to implement, making it a practical solution.