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Iterative diagonalization in augmented plane wave based methods in electronic structure calculations. (English) Zbl 1183.82003

Summary: Due to the increased computer power and advanced algorithms, quantum mechanical calculations based on density functional theory are more and more widely used to solve real materials science problems. In this context large nonlinear generalized eigenvalue problems must be solved repeatedly to calculate the electronic ground state of a solid or molecule. Due to the nonlinear nature of this problem, an iterative solution of the eigenvalue problem can be more efficient provided it does not disturb the convergence of the self-consistent-field problem. The blocked Davidson method is one of the widely used and efficient schemes for that purpose, but its performance depends critically on the preconditioning, i.e. the procedure to improve the search space for an accurate solution. For more diagonally dominated problems, which appear typically for plane wave based pseudopotential calculations, the inverse of the diagonal of \((H - ES)\) is used. However, for the more efficient “augmented plane wave + local-orbitals” basis set this preconditioning is not sufficient due to large off-diagonal terms caused by the local orbitals. We propose a new preconditioner based on the inverse of \((H - \lambda S)\) and demonstrate its efficiency for real applications using both, a sequential and a parallel implementation of this algorithm into our WIEN2k code.

MSC:

82B10 Quantum equilibrium statistical mechanics (general)
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65F10 Iterative numerical methods for linear systems
65Z05 Applications to the sciences

Software:

WIEN2k
PDFBibTeX XMLCite
Full Text: DOI

References:

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