A segregated approach for modeling the electrochemistry in the 3-D microstructure of li-ion batteries and its acceleration using block preconditioners. (English) Zbl 07316873

Summary: 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.


68Qxx Theory of computing
15Axx Basic linear algebra
65Fxx Numerical linear algebra
Full Text: DOI


[1] Alnæs, MS; Blechta, J.; Hake, J.; Johansson, A.; Kehlet, B.; Logg, A.; Richardson, C.; Ring, J.; Rognes, ME; Wells, GN, The fenics project version 1.5, Arch. Numer. Softw. (2015)
[2] Amestoy, PR; Duff, IS; L’Excellent, JY; Koster, J.; Sørevik, T.; Manne, F.; Gebremedhin, AH; Moe, R., Mumps: a general purpose distributed memory sparse solver, Applied Parallel Computing. New Paradigms for HPC in Industry and Academia, 121-130 (2001), Berlin: Springer, Berlin
[3] Balay, S., Abhyankar, S., Adams, M.F., Brown, J., Brune, P., Buschelman, K., Dalcin, L., Eijkhout, V., Gropp, W.D., Kaushik, D., Knepley, M.G., May, D.A., McInnes, L.C., Mills, R.T., Munson, T., Rupp, K., Sanan, P., Smith, B.F., Zampini, S., Zhang, H., Zhang, H.: PETSc Web page (2018)
[4] Balay, S., Abhyankar, S., Adams, M.F., Brown, J., Brune, P., Buschelman, K., Dalcin, L., Eijkhout, V., Gropp, W.D., Kaushik, D., Knepley, M.G., McInnes, L.C., Rupp, K., Smith, B.F., Zampini, S., Zhang, H., Zhang, H.: PETSc users manual. Tech. Rep. ANL-95/11—Revision 3.8, Argonne National Laboratory (2017)
[5] Bunch, JR; Hopcroft, JE, Triangular factorization and inversion by fast matrix multiplication, Math. Comput., 28, 125, 231-236 (1974) · Zbl 0276.15006
[6] Chang, J.; Fabien, MS; Knepley, MG; Mills, RT, Comparative study of finite element methods using the Time-Accuracy-Size (TAS) spectrum analysis, SIAM J. Sci. Comput. (under revision), 40, 137-163 (2018) · Zbl 1417.65224
[7] Chang, J.; Karra, S.; Nakshatrala, KB, Large-scale optimization-based non-negative computational framework for diffusion equations: parallel implementation and performance studies, J. Sci. Comput., 70, 243-271 (2017) · Zbl 1359.65250
[8] Chang, J.; Nakshatrala, KB, Variational inequality approach to enforce the non-negative constraint for advection-diffusion equations, Comput. Methods Appl. Mech. Eng., 320, 287-334 (2017) · Zbl 1439.35153
[9] Chang, J.; Nakshatrala, KB; Knepley, MG; Johnsson, L., A performance spectrum for parallel computational frameworks that solve PDEs, Concurr. Comput. Pract. Exp., 30, e4401 (2018)
[10] Colclasure, AM; Dunlop, AR; Trask, SE; Polzin, BJ; Jansen, AN; Smith, K., Requirements for enabling extreme fast charging of high energy density Li-ion cells while avoiding lithium plating, J. Electrochem. Soc., 166, 8, A1412-A1424 (2019)
[11] Coppersmith, D.; Winograd, S., Matrix multiplication via arithmetic progressions, J. Symb. Comput., 9, 3, 251-280 (1990) · Zbl 0702.65046
[12] Dalcin, LD; Paz, RR; Kler, PA; Cosimo, A., Parallel distributed computing using Python, Adv. Water Resour., 34, 9, 1124-1139 (2011)
[13] Danner, T.; Singh, M.; Hein, S.; Kaiser, J.; Hahn, H.; Latz, A., Thick electrodes for li-ion batteries: a model based analysis, J. Power Sources, 334, 191-201 (2016)
[14] Dees, D.; Gunen, E.; Abraham, D.; Jansen, A.; Prakash, J., Electrochemical modeling of lithium-ion positive electrodes during hybrid pulse power characterization tests, J. Electrochem. Soc., 155, 8, A603-A613 (2008)
[15] Doyle, M.; Fuller, TF; Newman, J., Modeling of galvanostatic charge and discharge of the lithium/polymer/insertion cell, J. Electrochem. Soc., 140, 6, 1526-1533 (1993)
[16] Doyle, M.; Newman, J., The use of mathematical modeling in the design of lithium/polymer battery systems, Electrochim. Acta, 40, 13, 2191-2196 (1995)
[17] Du, W.; Xue, N.; Shyy, W.; Martins, JRRA, A surrogate-based multi-scale model for mass transport and electrochemical kinetics in lithium-ion battery electrodes, J. Electrochem. Soc., 161, 8, E3086-E3096 (2014)
[18] Falgout, R.D., Yang, U.M.: HYPRE: a library of high performance preconditioners. In: International Conference on Computational Science. Springer, pp 632-641 (2002) · Zbl 1056.65046
[19] García, RE; Chiang, YM; Craig Carter, W.; Limthongkul, P.; Bishop, CM, Microstructural modeling and design of rechargeable lithium-ion batteries, J. Electrochem. Soc., 152, 1, A255-A263 (2005)
[20] Goldin, GM; Colclasure, AM; Wiedemann, AH; Kee, RJ, Three-dimensional particle-resolved models of li-ion batteries to assist the evaluation of empirical parameters in one-dimensional models, Electrochim. Acta, 64, 118-129 (2012)
[21] Hein, S.; Latz, A., Influence of local lithium metal deposition in 3d microstructures on local and global behavior of lithium-ion batteries, Electrochim. Acta, 201, 354-365 (2016)
[22] Henson, VE; Yang, UM, Boomeramg: a parallel algebraic multigrid solver and preconditioner, Appl. Numer. Math., 41, 1, 155-177 (2002) · Zbl 0995.65128
[23] Higa, K.; Wu, SL; Parkinson, DY; Fu, Y.; Ferreira, S.; Battaglia, V.; Srinivasan, V., Comparing macroscale and microscale simulations of porous battery electrodes, J. Electrochem. Soc., 164, 11, E3473-E3488 (2017)
[24] Holzer, L.; Münch, B.; Iwanschitz, B.; Cantoni, M.; Hocker, T.; Graule, T., Quantitative relationships between composition, particle size, triple phase boundary length and surface area in nickel-cermet anodes for solid oxide fuel cells, J. Power Sources, 196, 17, 7076-7089 (2011)
[25] Hutzenlaub, T.; Thiele, S.; Paust, N.; Spotnitz, R.; Zengerle, R.; Walchshofer, C., Three-dimensional electrochemical Li-ion battery modelling featuring a focused ion-beam/scanning electron microscopy based three-phase reconstruction of a LiCOO2 cathode, Electrochim. Acta, 115, 131-139 (2014)
[26] Joshaghani, MS; Chang, J.; Nakshatrala, KB; Knepley, MG, Composable block solvers for the four-field double porosity/permeability model, J. Comput. Phys., 386, 428-466 (2019)
[27] Kashkooli, AG; Farhad, S.; Lee, DU; Feng, K.; Litster, S.; Babu, SK; Zhu, L.; Chen, Z., Multiscale modeling of lithium-ion battery electrodes based on nano-scale X-ray computed tomography, J. Power Sources, 307, 496-509 (2016)
[28] Kim, GH; Smith, K.; Lee, KJ; Santhanagopalan, S.; Pesaran, A., Multi-domain modeling of lithium-ion batteries encompassing multi-physics in varied length scales, J. Electrochem. Soc., 158, 8, A955-A969 (2011)
[29] Logg, A.; Mardal, KA; Wells, GN, Automated Solution of Differential Equations by the Finite Element Method (2012), Berlin: Springer, Berlin · Zbl 1247.65105
[30] Malavé, V.; Berger, J.; Zhu, H.; Kee, RJ, A computational model of the mechanical behavior within reconstructed LixCoO2 Li-ion battery cathode particles, Electrochim. Acta, 130, 707-717 (2014)
[31] Mapakshi, NK; Chang, J.; Nakshatrala, KB, A scalable variational inequality approach for flow through porous media models with pressure-dependent viscosity, J. Comput. Phys., 359, 137-163 (2018) · Zbl 1383.76342
[32] Mistry, AN; Smith, K.; Mukherjee, PP, Secondary-phase stochastics in lithium-ion battery electrodes, ACS Appl. Mater. Interfaces, 10, 7, 6317-6326 (2018)
[33] Newman, J.; Thomas-Alyea, KE, Electrochemical Systems (2004), Hoboken: Wiley-Interscience, Hoboken
[34] Newman, J.; Tiedemann, W., Porous-electrode theory with battery applications, AIChE J., 21, 1, 25-41 (1975)
[35] Newman, JS; Tobias, CW, Theoretical analysis of current distribution in porous electrodes, J. Electrochem. Soc., 109, 12, 1183-1191 (1962)
[36] Plett, GL, Battery Management Systems, Volume I: Battery Modeling (2015), Norwood: Artech House Publishers, Norwood
[37] Qianqian, F., Boas, D.A.: Tetrahedral mesh generation from volumetric binary and grayscale images. In: 2009 IEEE International Symposium on Biomedical Imaging: From Nano to Macro, pp. 1142-1145 (2009). doi:10.1109/ISBI.2009.5193259
[38] Roberts, SA; Mendoza, H.; Brunini, VE; Trembacki, BL; Noble, DR; Grillet, AM, Insights into lithium-ion battery degradation and safety mechanisms from mesoscale simulations using experimentally reconstructed mesostructures, J. Electrochem. Energy Convers. Storage, 13, 3, 031005-1 (2016)
[39] Saad, Y.; Schultz, MH, GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Stat. Comput., 7, 3, 856-869 (1986) · Zbl 0599.65018
[40] Smith, K.; Wang, CY, Power and thermal characterization of a lithium-ion battery pack for hybrid-electric vehicles, J. Power Sources, 160, 1, 662-673 (2006)
[41] Smith, K.A., Rahn, C.D., Wang, C.: Model-based electrochemical estimation of lithium-ion batteries. In: 2008 IEEE International Conference on Control Applications, pp. 714-719 (2008). doi:10.1109/CCA.2008.4629589
[42] Smith, KA; Rahn, CD; Wang, CY, Control oriented 1d electrochemical model of lithium ion battery, Energy Convers. Manag., 48, 9, 2565-2578 (2007)
[43] Stephenson, DE; Hartman, EM; Harb, JN; Wheeler, DR, Modeling of particle-particle interactions in porous cathodes for lithium-ion batteries, J. Electrochem. Soc., 154, 12, A1146-A1155 (2007)
[44] Strassen, V., Gaussian elimination is not optimal, Numer. Math., 13, 4, 354-356 (1969) · Zbl 0185.40101
[45] Trefethen, L.N., Bau, D., for Industrial, S., Mathematics, A.: Numerical linear algebra. Society for Industrial and Applied Mathematics, Philadelphia (1997)
[46] Usseglio-Viretta, FLE; Colclasure, A.; Mistry, AN; Claver, KPY; Pouraghajan, F.; Finegan, DP; Heenan, TMM; Abraham, D.; Mukherjee, PP; Wheeler, D.; Shearing, P.; Cooper, SJ; Smith, K., Resolving the discrepancy in tortuosity factor estimation for li-ion battery electrodes through micro-macro modeling and experiment, J. Electrochem. Soc., 165, 14, A3403-A3426 (2018)
[47] Usseglio-Viretta, FLE; Smith, K., Quantitative microstructure characterization of a NMC electrode, ECS Trans., 77, 11, 1095-1118 (2017)
[48] Wiedemann, AH; Goldin, GM; Barnett, SA; Zhu, H.; Kee, RJ, Effects of three-dimensional cathode microstructure on the performance of lithium-ion battery cathodes, Electrochim. Acta, 88, 580-588 (2013)
[49] Yan, B.; Lim, C.; Yin, L.; Zhu, L., Three dimensional simulation of galvanostatic discharge of LiCoO2 cathode based on X-ray nano-CT images, J. Electrochem. Soc., 159, 10, A1604-A1614 (2012)
[50] Zielke, L.; Hutzenlaub, T.; Wheeler, DR; Chao, CW; Manke, I.; Hilger, A.; Paust, N.; Zengerle, R.; Thiele, S., Three-phase multiscale modeling of a LiCoO2 cathode: combining the advantages of FIB-SEM imaging and X-ray tomography, Adv. Energy Mater., 5, 5, 1401612 (2015)
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