Solving large nonlinear generalized eigenvalue problems from Density Functional Theory calculations in parallel

The quantum mechanical ground state of electrons is described by Density Functional Theory, which leads to large minimization problems. An efficient minimization method uses a self-consistent field (SCF) solution of large eigenvalue problems. The iterative Davidson algorithm is often used, and we pr...

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Bibliographic Details
Published in:Applied numerical mathematics 2001-04, Vol.37 (1), p.189-199
Main Authors: Bendtsen, Claus, Nielsen, Ole H., Hansen, Lars B.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Mathematics
Nonlinear algebraic and transcendental equations
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Numerical methods in mathematical programming, optimization and calculus of variations
Numerical methods in optimization and calculus of variations
Sciences and techniques of general use
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Summary:The quantum mechanical ground state of electrons is described by Density Functional Theory, which leads to large minimization problems. An efficient minimization method uses a self-consistent field (SCF) solution of large eigenvalue problems. The iterative Davidson algorithm is often used, and we propose a new algorithm of this kind which is well suited for the SCF method, since the accuracy of the eigensolution is gradually improved along with the outer SCF-iterations. Best efficiency is obtained for small-block-size iterations, and the algorithm is highly memory efficient. The implementation works well on both serial and parallel computers, and good scalability of the algorithm is obtained.
ISSN:0168-9274
1873-5460
DOI:10.1016/S0168-9274(00)00038-6