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

Thomas Roy, Nicholas W. Brady, Giovanna Bucci, Nicholas R. Cross, Victoria M. Ehlinger, Tiras Y. Lin, Hanyu Li, Marcus A. Worsley

TL;DR

This work addresses the challenge of solving large, tightly coupled nonlinear systems arising from fully implicit pseudo-4D DFN battery models in three-dimensional geometries. It introduces block-structured preconditioners that combine algebraic multigrid for electrode-level operators with localized solvers for particle diffusion, enabling scalable Newton–Krylov solutions on hundreds of millions of degrees of freedom. The authors demonstrate robust weak and strong scaling across diverse geometries, including homogeneous, heterogeneous, flattened jelly-roll, and TPMS-based electrodes, highlighting the tradeoffs between block Jacobi and block Gauss–Seidel preconditioners. The approach substantially extends the practical capability of high-fidelity 3D battery simulations on large HPC resources, with implications for design, optimization, and understanding of complex electrode architectures.

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.

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

TL;DR

This work addresses the challenge of solving large, tightly coupled nonlinear systems arising from fully implicit pseudo-4D DFN battery models in three-dimensional geometries. It introduces block-structured preconditioners that combine algebraic multigrid for electrode-level operators with localized solvers for particle diffusion, enabling scalable Newton–Krylov solutions on hundreds of millions of degrees of freedom. The authors demonstrate robust weak and strong scaling across diverse geometries, including homogeneous, heterogeneous, flattened jelly-roll, and TPMS-based electrodes, highlighting the tradeoffs between block Jacobi and block Gauss–Seidel preconditioners. The approach substantially extends the practical capability of high-fidelity 3D battery simulations on large HPC resources, with implications for design, optimization, and understanding of complex electrode architectures.

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.
Paper Structure (24 sections, 52 equations, 11 figures, 8 tables)

This paper contains 24 sections, 52 equations, 11 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Governing equations
  3. Lithium diffusion in active particles
  4. Electrolyte transport
  5. Charge conservation
  6. Interfacial kinetics
  7. Boundary and initial conditions
  8. Discretization
  9. Spatial discretization of the particle equation
  10. Spatial discretization for the electrode-level equations
  11. Temporal discretization
  12. Implementation details
  13. Solution strategy
  14. Linear system structure
  15. Preconditioning
  16. ...and 9 more sections

Figures (11)

  • Figure 1: Schematic of the pseudo-4D DFN battery model with 3D electrodes and 1D spherical particles.
  • Figure 1: Sparsity pattern of the linearized system matrix for a P3D case with a $3 \times 3$ quadrilateral mesh for the electrode-level domain and 3 points in the particle direction.
  • Figure 1: Diagram of the simulation domain for Cases I and II.
  • Figure 2: Spatially varying material properties for Case II.
  • Figure 3: Diagrams of the simulation domain of a flattened jelly roll for Case III. The diagrams are not to scale (note the dimensions in (a)). The curvature in (b) is for illustrative purposes only and is not considered in the simulations.
  • ...and 6 more figures

Theorems & Definitions (1)

  • Remark 3.1