Battery performance is strongly correlated with electrode microstructure. Electrode materials for lithium-ion batteries have complex microstructure geometries that require millions of degrees of freedom to solve the electrochemical system at the microstructure scale. A fast-iterative solver with an appropriate preconditioner is then required to simulate large representative volume in a reasonable time. In this work, a finite element electrochemical model is developed to resolve the concentration and potential within the electrode active materials and the electrolyte domains at the microstructure scale, with an emphasis on numerical stability and scaling performances. The block Gauss-Seidel (BGS) numerical method is implemented because the system of equations within the electrodes is coupled only through the nonlinear Butler–Volmer equation, which governs the electrochemical reaction at the interface between the domains. The best solution strategy found in this work consists of splitting the system into two blocks—one for the concentration and one for the potential field—and then performing block generalized minimal residual preconditioned with algebraic multigrid, using the FEniCS and the Portable, Extensible Toolkit for Scientific Computation libraries. Significant improvements in terms of time to solution (six times faster) and memory usage (halving) are achieved compared with the MUltifrontal Massively Parallel sparse direct Solver. Additionally, BGS experiences decent strong parallel scaling within the electrode domains. Last, the system of equations is modified to specifically address numerical instability induced by electrolyte depletion, which is particularly valuable for simulating fast-charge scenarios relevant for automotive application.

电池性能与电极的微观结构密切相关。锂离子电池的电极材料具有复杂的微观结构几何形状，需要数百万个自由度才能在微观结构规模上解决电化学系统。然后需要具有适当预处理器的快速迭代求解器，以在合理的时间内模拟较大的代表体积。在这项工作中，建立了有限元电化学模型，以解决微观结构尺度上电极活性材料和电解质域内的浓度和电势，并着重于数值稳定性和尺度性能。实施块高斯-赛德尔（BGS）数值方法是因为电极内的方程组仅通过非线性Butler-Volmer方程耦合，它决定着区域之间界面上的电化学反应。这项工作中发现的最佳解决方案策略包括：将系统分为两个模块-一个用于浓度，一个用于势场-然后使用FEniCS和Portable，Extensible Toolkit对模块进行通用代数多重网格预处理的最小残差预处理。科学计算库。与MUltifrontal Massive Parallelly稀疏直接求解器相比，在求解时间（加快六倍）和内存使用（减半）方面有了显着的改进。另外，BGS在电极域内经历了不错的强并行缩放。最后，对方程组进行了修改，以专门解决电解质耗尽引起的数值不稳定性，