Premium
MIKA: Multigrid‐based program package for electronic structure calculations
Author(s) -
Torsti T.,
Heiskanen M.,
Puska M. J.,
Nieminen R. M.
Publication year - 2002
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.10397
Subject(s) - multigrid method , solver , mathematics , fock space , computer science , consistency (knowledge bases) , space (punctuation) , computational science , mathematical optimization , physics , mathematical analysis , quantum mechanics , partial differential equation , geometry , operating system
A general real‐space multigrid‐based program package 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 Schrödinger equation. Our choice is the Rayleigh quotient multigrid method (RQMG), which applies directly to the minimization of the Rayleigh quotient on the finest level. 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 toward the self‐consistency and 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. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2003