MIKA: a multigrid-based program package for electronic structure calculations

TL;DR

The paper introduces MIKA, a multigrid-based computational package for solving Kohn-Sham equations efficiently in electronic structure calculations, utilizing a specialized multigrid solver that is optimized for parallel architectures and various geometries.

Contribution

MIKA presents a novel multigrid algorithm for electronic structure calculations, employing the Rayleigh quotient multigrid method for efficient, parallelizable solutions of the Schrödinger equation.

Findings

Effective multigrid solver for electronic structure calculations.

Successful application to systems with nonlocal pseudopotentials and jellium models.

Demonstrated efficiency in calculating positron states in solids.

Abstract

A general real-space multigrid algorithm MIKA (Multigrid Instead of the K-spAce) for the self-consistent solution of the Kohn-Sham equations appearing in the state-of-the-art electronic-structure calculations is described. The most important part of the method is the multigrid solver for the Schr\"odinger equation. Our choice is the Rayleigh quotient multigrid method (RQMG), which applies directly to the minimization of the Rayleigh quotient on the finest level. Very coarse correction grids can be used, because there is in principle no need to represent the states on the coarse levels. The RQMG method is generalized for the simultaneous solution of all the states of the system using a penalty functional to keep the states orthogonal. Special care has been taken to optimize the iterations towards the self-consistency and to run the code in parallel computer architectures. The scheme has been implemented in multiple geometries. We show examples from electronic structure calculations employing nonlocal pseudopotentials and/or the jellium model. The RQMG solver is also applied for the calculation of positron states in solids.