Solving large nonlinear generalized eigenvalue problems from Density Functional Theory calculations in parallel
Copyright policy )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 selfconsistent 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.
20 pages, 4 figures. Accepted for Applied Numerical Mathematics (Elsevier)
Numerical methods for eigenvalue problems for boundary value problems involving PDEs, self-consistent field, Condensed Matter - Materials Science, eigensolution, Completeness of eigenfunctions and eigenfunction expansions in context of PDEs, Materials Science (cond-mat.mtrl-sci), FOS: Physical sciences, Parallel numerical computation, Atomic physics, Numerical solution of nonlinear eigenvalue and eigenvector problems, iterative Davidson algorithm, large eigenvalue problems, quantum mechanical ground state of electrons, nonlinear matrix eigenproblem, parallel computation, density functional theory, PDEs in connection with quantum mechanics
Numerical methods for eigenvalue problems for boundary value problems involving PDEs, self-consistent field, Condensed Matter - Materials Science, eigensolution, Completeness of eigenfunctions and eigenfunction expansions in context of PDEs, Materials Science (cond-mat.mtrl-sci), FOS: Physical sciences, Parallel numerical computation, Atomic physics, Numerical solution of nonlinear eigenvalue and eigenvector problems, iterative Davidson algorithm, large eigenvalue problems, quantum mechanical ground state of electrons, nonlinear matrix eigenproblem, parallel computation, density functional theory, PDEs in connection with quantum mechanics
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