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

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

2002-05-02

arxiv.org/abs/cond-mat/0205056v1

Int. J. Quantum Chem. 91, 171 (2003)

Physics

Condensed Matter

To appear in a special issue of Int J. Quant. Chem. devoted to the conference proceedings of 9th International Conference on t

Scientific paper

10.1002/qua.10397

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.

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