DTE AICCOMAS 2025

Battery Modeling Through Bulk-Surface PDEs

  • Frittelli, Massimo (University of Salento)
  • Sgura, Ivonne (University of Salento)
  • Quarta, Maria Grazia (University of Salento)
  • Madzvamuse, Anotida (University of British Columbia)
  • Bozzini, Benedetto (Politecnico di Milano)

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We present a novel Bulk-Surface Reaction-Diffusion System (BSRDS) for the simulation of electrodeposition processes taking place in batteries, called BSDIB model [1]. As the name suggests, the model is composed of two surface PDEs that model metal growth on the electrodes, coupled with two bulk PDEs that model concentrations in the electrolyte. The BSDIB model extends the so-called DIB model previously introduced in [2], where the bulk PDEs were not present and the electrolyte concentrations were assumed to be spatially uniform for simplicity. Our numerical simulations, carried out via the Bulk-Surface Virtual Element Method [3] and the Matrix-Oriented Finite Element Method [4] are backed up experimentally through lab tests. Artificial intelligence techniques based on Convolutional Neural Networks (CNNs) recently allowed to classify the morphological classes of asymptotic-in-time solutions (Turing patterns) of the DIB model [5]. As a work-in-progress, CNNs allow to prove that the novel BSDIB model can exhibit more morphological classes, compared to the previous DIB model. REFERENCES [1] Bozzini, B. et al. (2013) Spatio-temporal organization in alloy electrodeposition: a morphochemical mathematical model and its experimental validation. J Solid State Electrochem, 17, 467-479. [2] Frittelli, M. et al. (2024) Turing patterns in a 3D morpho-chemical bulk-surface reaction-diffusion system for battery modeling. Mathematics in Engineering, 6(2), 363-393. [3] Frittelli, M. et al. (2023) The Bulk-Surface Virtual Element Method for Reaction-Diffusion PDEs: Analysis and Applications. Communications in Computational Physics, 33(3), 733-763. [4] Frittelli, M. & Sgura, I. (2024) Matrix-oriented FEM formulation for reaction-diffusion PDEs on a large class of 2D domains. Applied Numerical Mathematics, 200, 286-308. [5] Sgura, I. et al. (2023) Deep-learning based parameter identification enables rationalization of battery material evolution in complex electrochemical systems. J Computat Sci, 66, 101900.