Scalable Preconditioners for the Pseudo-4D DFN Lithium-ion Battery Model

TL;DR

This paper introduces scalable block-structured preconditioners for the pseudo-4D DFN lithium-ion battery model, enabling efficient simulation of complex geometries with hundreds of millions of degrees of freedom on parallel hardware.

Contribution

It presents novel multigrid-based preconditioning strategies tailored for the coupled nonlinear systems in the pseudo-4D DFN model, improving scalability and solver robustness.

Findings

Achieved efficient convergence across various geometries.

Enabled large-scale simulations with hundreds of millions of degrees of freedom.

Demonstrated strong parallel scalability of the proposed methods.

Abstract

The pseudo-4D Doyle-Fuller-Newman (DFN) model enables predictive simulation of lithium-ion batteries with three-dimensional electrode architectures and particle-scale diffusion, extending the standard pseudo-2D (P2D) formulation to fully resolve cell geometry. This leads to large, nonlinear systems with strong coupling across multiple physical scales, posing significant challenges for scalable numerical solution. We introduce block-structured preconditioning strategies that exploit the mathematical properties of the coupled system, employing multigrid techniques for electrode-level operators and localized solvers for particle-scale diffusion. Comprehensive scalability studies are performed across a range of geometries, including homogeneous and heterogeneous cubic cells, flattened jelly-roll configurations, and triply periodic minimal surface electrodes, to assess solver robustness and parallel scalability. The proposed methods consistently deliver efficient convergence and enable the solution of battery models with hundreds of millions of degrees of freedom on large-scale parallel hardware.