Three Dimensional Pseudospectral Self -Consistent Field Approximation
Chow, Wing Fai
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https://hdl.handle.net/2142/81615
Description
Title
Three Dimensional Pseudospectral Self -Consistent Field Approximation
Author(s)
Chow, Wing Fai
Issue Date
2003
Doctoral Committee Chair(s)
Kerkhoven, Thomas
Department of Study
Computer Science
Discipline
Computer Science
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Computer Science
Language
eng
Abstract
For the eigenvalue problem, a novel variant of Davidson's method, or spectrally localized Arnoldi's method, is used. The full-size problem is projected onto Krylov subspaces of limited size with an explicitly orthogonalized basis. The smaller-size projected problem is solved using LAPACK library functions and then the solution is transformed back to the original space. In Arnoldi's method, vectors in the selected range of the energy spectrum are amplified by a specially designed energy range selector, which amounts to tempered inverse iteration. The starting vectors for Arnoldi are enriched with new randomized components in order to decrease the iteration number and to reduce the chance of missing eigenvectors. The linear systems in the Krylov space generation are solved by a spectrally preconditioned conjugate gradient (CG) method. The energy range selector contains two parameters, which let us select a limited range in the eigenvalue spectrum. With the greatly improved adaptive algorithm for controlling the parameters and the more flexible adjustable subspace size, the solver has become highly efficient, robust and accurate.
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