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Title: An Implementation and Evaluation of the AMLS Method for SparseEigenvalue Problems

Abstract

We describe an efficient implementation and present aperformance study of an algebraic multilevel sub-structuring (AMLS)method for sparse eigenvalue problems. We assess the time and memoryrequirements associated with the key steps of the algorithm, and compareitwith the shift-and-invert Lanczos algorithm in computational cost. Oureigenvalue problems come from two very different application areas: theaccelerator cavity design and the normal mode vibrational analysis of thepolyethylene particles. We show that the AMLS method, when implementedcarefully, is very competitive with the traditional method in broadapplication areas, especially when large numbers of eigenvalues aresought.

Authors:
; ; ;
Publication Date:
Research Org.:
Ernest Orlando Lawrence Berkeley NationalLaboratory, Berkeley, CA (US)
Sponsoring Org.:
USDOE Director. Office of Science. Advanced ScientificComputing Research
OSTI Identifier:
929006
Report Number(s):
LBNL-57438
R&D Project: KS1210; BnR: KJ0101010; TRN: US0804069
DOE Contract Number:  
DE-AC02-05CH11231
Resource Type:
Journal Article
Resource Relation:
Journal Name: ACM Transactions on Mathematical Software; Journal Volume: 34; Journal Issue: 4; Related Information: Journal Publication Date: 09/19/2007
Country of Publication:
United States
Language:
English
Subject:
99; ACCELERATORS; ALGORITHMS; DESIGN; EIGENVALUES; EVALUATION; IMPLEMENTATION; PERFORMANCE; POLYETHYLENES; multilevel substructuring method sparse eigenvalueproblems

Citation Formats

Gao, Weiguo, Li, Xiaoye S., Yang, Chao, and Bai, Zhaojun. An Implementation and Evaluation of the AMLS Method for SparseEigenvalue Problems. United States: N. p., 2006. Web.
Gao, Weiguo, Li, Xiaoye S., Yang, Chao, & Bai, Zhaojun. An Implementation and Evaluation of the AMLS Method for SparseEigenvalue Problems. United States.
Gao, Weiguo, Li, Xiaoye S., Yang, Chao, and Bai, Zhaojun. Tue . "An Implementation and Evaluation of the AMLS Method for SparseEigenvalue Problems". United States. doi:. https://www.osti.gov/servlets/purl/929006.
@article{osti_929006,
title = {An Implementation and Evaluation of the AMLS Method for SparseEigenvalue Problems},
author = {Gao, Weiguo and Li, Xiaoye S. and Yang, Chao and Bai, Zhaojun},
abstractNote = {We describe an efficient implementation and present aperformance study of an algebraic multilevel sub-structuring (AMLS)method for sparse eigenvalue problems. We assess the time and memoryrequirements associated with the key steps of the algorithm, and compareitwith the shift-and-invert Lanczos algorithm in computational cost. Oureigenvalue problems come from two very different application areas: theaccelerator cavity design and the normal mode vibrational analysis of thepolyethylene particles. We show that the AMLS method, when implementedcarefully, is very competitive with the traditional method in broadapplication areas, especially when large numbers of eigenvalues aresought.},
doi = {},
journal = {ACM Transactions on Mathematical Software},
number = 4,
volume = 34,
place = {United States},
year = {Tue Feb 14 00:00:00 EST 2006},
month = {Tue Feb 14 00:00:00 EST 2006}
}