An Implementation and Evaluation of the AMLS Method for SparseEigenvalue Problems

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

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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:: Gao, Weiguo; Li, Xiaoye S.; Yang, Chao; Bai, Zhaojun

Publication Date:: Tue Feb 14 00:00:00 EST 2006

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.

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                    Gao, Weiguo, Li, Xiaoye S., Yang, Chao, & Bai, Zhaojun. An Implementation and Evaluation of the AMLS Method for SparseEigenvalue Problems.  United States.

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                    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.

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@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}

}

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