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Using SfePy for solving Kohn-Sham equations
Authors: Robert Cimrman, Jiří Vackář, Matyáš Novák
Keywords: DFT, electronic structure, FEM, Python
We describe the open source finite element package SfePy (Simple Finite Elements in Python, http://sfepy.org) and its application to ab-initio calculations of electronic states within the density-functional theory (DFT) framework. The base package is quite general - it has been successfully employed, for example, for finite element multiscale models in biomechanics (bones, muscle tissue with blood perfusion), acoustics (computation of acoustic transmission coefficients across an interface of arbitrary microstructure geometry, acoustic band gaps), etc. Its implementation in Python allows fast exploration of various ideas and fast and efficient implementation, thanks to many numerical tools and libraries available within open source packages, most notably Numpy and SciPy. Here we discuss relevance and convenience of using finite-element method in Python for electronic structure calculations.
The aim of the present application is to be able to understand and predict material properties from first principles quantum mechanical calculations. In the contribution we describe our computer implementation of a new robust ab-initio real-space code based on (i) density functional theory [1, 2], (ii) finite element method  and (iii) environment-reflecting pseudopotentials . This approach brings a new quality to solving Kohn-Sham equations, calculating electronic states, total energy, Hellmann-Feynman forces and material properties (stiffness, electric and magnetic properties, etc.) particularly for non-crystalline, non-periodic structures .
The main asset of the above approach is an efficient combination of excellent convergence control of standard, universal basis used in industrially proved finite-element method, high precision of ab-initio pseudopotentials, and applicability to non-periodic structures without supercells and without the restriction of electrical neutrality. In the contribution we present also numerical examples illustrating the outputs of the method.
The work was supported by the Grant Agency of the Czech Republic, project P108/11/0853.
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 J. Vackář, O. Čertík, R. Cimrman, M. Novák, O. Šipr, J. Plešek: Finite Element Method in Density Functional Theory Electronic Structure Calculations. Chapter 12 in "Advances in the Theory of Quantum Systems in Chemistry and Physics", eds. P.E.Hoggan, E.J.Brändas, J.Maruani, P.Piecuch, G.Delgado-Barrio, in series: Progress in Theoretical Chemistry and Physics, Vol. 22, Springer 2011, pp. 199-217