High-order finite element method for atomic structure calculations

We introduce featom, a general purpose Fortran library which implements finite element methods for solving the radial Schrödinger, Dirac, and Kohn–Sham equations. This allows a systematic control over the convergence by increasing the polynomial order of the elements. By using a novel squared Hamiltonian approach the spurious states of the solutions to the Dirac equations are avoided. Varying quadratures have been used to mantain high accuracy (10^-6 a.u) at low computational costs for heavy elements. The formulation is robust and able to accuracy and precision of the state of the art (dftatom) while being significantly faster. The featom library is designed to be used as a modular component and integrates with libraries which provide general potentials, while a series of meshes are also implemented. We follow best practices for Fortran codebases including testing guidelines, a reproducible build system with the fortran packaging manager with a well defined API which allows extensions and language bindings. For reproduciblity within and with our tooling is guranteed by the workflow used to generate the reference runs in a programmatic manner.