scikit-fem: A Python package for finite element assembly

Tom Gustafsson , Geordie Drummond Mcbain (1)

1 Memjet Australia Pty Ltd

Partial differential equations (PDEs)-such as the Navier-Stokes equations in fluid mechanics, the Maxwell equations in electromagnetism, and the Schrödinger equation in quantum mechanics-are the basic building blocks of modern physics and engineering. The finite element method (FEM) is a flexible computational technique for the discretization and solution of PDEs, especially in the case of complex spatial domains. Conceptually, the FEM transforms a time-independent (or temporally discretized) PDE into a system of linear equations Ax = b. scikit-fem is a lightweight Python library for the creation, or assembly, of the finite element matrix A and vector b. The user loads a computational mesh, picks suitable basis functions, and provides the PDE's weak formulation (Logg, Mardal, Wells, & others, 2012). This results in sparse matrices and vectors compatible with the SciPy (Virtanen et al., 2020) ecosystem.

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]; Modélisation et simulation; Analyse numérique [cs.NA]

Tom Gustafsson, Geordie Drummond Mcbain. scikit-fem: A Python package for finite element assembly. Journal of Open Source Software, 2020, 5 (52), pp.2369. ⟨10.21105/joss.02369⟩. ⟨hal-02919750⟩