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oai:www.ideals.illinois.edu:2142/81615 2023-07-11 col_2142_5131 col_2142_10761 com_2142_5130 com_2142_10755 com_2142_234

Kerkhoven, Thomas Chow, Wing Fai 2015-09-25T20:19:32Z 2015-09-25T20:19:32Z 10000-01-01 2003 2003 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. Made available in DSpace on 2015-09-25T20:19:32Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3086035.pdf: 4072373 bytes, checksum: 1ab6d97b4b91529ea42b57e3a326f2f5 (MD5) Previous issue date: 2003 Embargo set by: Seth Robbins for item 82896 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 94 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2003. http://hdl.handle.net/2142/81615 (MiAaPQ)AAI3086035 eng Computer Science Three Dimensional Pseudospectral Self -Consistent Field Approximation text Computer Science Computer Science University of Illinois at Urbana-Champaign Dissertation Ph.D.