Julia for Charge Transport in Condensed Matter

Charge transport and reactions in electrochemical and semiconductor devices are described by systems of nonlinear PDEs for the electric field and the diffusive and convective movement of charged particles.
A finite volume discretization approach turns these into a system of nonlinear algebraic equations. The Julia package VoronoiFVM.jl provides an infrastructure or this discretization approach and uses forward mode AD to set up the sparse Jacobi matrices for the solution with Newton's method.

In the talk we give a short introduction into the application case and provide some simulation examples highlighting the capabilities of Julia and the VoronoiFVM.jl package. In addition we give an overview on a number of Julia packages for meshing, sparse matrix handling and visualization which have grown around the package and are now part of the Meta package PDELib.jl.

[1] J.Fuhrmann & contributors: https://github.com/j-fu/VoronoiFVM.jl

[2] D. Abdel, P. Vágner, J. Fuhrmann, and P. Farrell, “Modelling charge transport in perovskite solar cells: Potential-based and limiting ion vacancy depletion,” Preprint 2780, 2020. URL: http://www.wias-berlin.de/preprint/2780/wias_preprints_2780.pdf.

[3] V. Miloš, P. Vágner, D. Budáč, M. Carda, M. Paidar, J. Fuhrmann, and K. Bouzek, “Generalized Poisson-Nernst-Planck-based physical model of O2 | LSM | YSZ electrode,” Preprint 2797, 2020. URL: http://www.wias-berlin.de/preprint/2797/wias_preprints_2797.pdf.

[4] B. Gaudeul and J. Fuhrmann, “Entropy and convergence analysis for two finite volume schemes for a Nernst-Planck-Poisson system with ion volume constraints.” 2021. URL: http://www.wias-berlin.de/preprint/2811/wias_preprints_2811.pdf.

[5] D. Abdel, J. Fuhrmann, and P. Farrell, “Assessing the quality of the excess chemical potential flux scheme for degenerate semiconductor device simulation,” Opt. Quant. Electr, vol. 41, no. 53, p. 163, 2021.

[6] C. Cancès, C. Chainais-Hillairet, J. Fuhrmann, and B. Gaudeul, “A numerical-analysis-focused comparison of several finite volume schemes for a unipolar degenerate drift-diffusion model,” IMA Journal of Numerical Analysis, vol. 41, no. 1, pp. 271–314, 2021.

[7] P. Vágner, C. Guhlke, V. Miloš, R. Müller, and J. Fuhrmann, “A continuum model for yttria-stabilized zirconia incorporating triple phase boundary, lattice structure and immobile oxide ions,” Journal of Solid State Electrochemistry, vol. 23, pp. 2907–2926, 2019.