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Fast iterative interior eigensolver for millions of atoms. (English) Zbl 1251.82061
Summary: We show that a combination of the generalized Davidson method and harmonic Ritz values (called harmonic Davidson) is well-suited for solving large interior eigenvalue problems using a plane wave basis. The algorithm enables us to calculate impurity and band edge states for systems of 100,000 atoms in about one day on 32 cores. We demonstrate the capabilities of the method by calculating the electronic states of a large GaAs quantum dot embedded in an AlAs matrix.

MSC:
82D37 Statistical mechanical studies of semiconductors
82-08 Computational methods (statistical mechanics) (MSC2010)
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65Y05 Parallel numerical computation
Software:
BLOPEX; JDQR; JDQZ; ONETEP; SIESTA
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