An algebraic sub-structuring method for large-scale eigenvaluecalculation

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We examine sub-structuring methods for solving large-scalegeneralized eigenvalue problems from a purely algebraic point of view. Weuse the term "algebraic sub-structuring" to refer to the process ofapplying matrix reordering and partitioning algorithms to divide a largesparse matrix into smaller submatrices from which a subset of spectralcomponents are extracted and combined to provide approximate solutions tothe original problem. We are interested in the question of which spectralcomponentsone should extract from each sub-structure in order to producean approximate solution to the original problem with a desired level ofaccuracy. Error estimate for the approximation to the small esteigen pairis developed. The estimate leads ... continued below

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Yang, C.; Gao, W.; Bai, Z.; Li, X.; Lee, L.; Husbands, P. et al. May 26, 2004.

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We examine sub-structuring methods for solving large-scalegeneralized eigenvalue problems from a purely algebraic point of view. Weuse the term "algebraic sub-structuring" to refer to the process ofapplying matrix reordering and partitioning algorithms to divide a largesparse matrix into smaller submatrices from which a subset of spectralcomponents are extracted and combined to provide approximate solutions tothe original problem. We are interested in the question of which spectralcomponentsone should extract from each sub-structure in order to producean approximate solution to the original problem with a desired level ofaccuracy. Error estimate for the approximation to the small esteigen pairis developed. The estimate leads to a simple heuristic for choosingspectral components (modes) from each sub-structure. The effectiveness ofsuch a heuristic is demonstrated with numerical examples. We show thatalgebraic sub-structuring can be effectively used to solve a generalizedeigenvalue problem arising from the simulation of an acceleratorstructure. One interesting characteristic of this application is that thestiffness matrix produced by a hierarchical vector finite elements schemecontains a null space of large dimension. We present an efficient schemeto deflate this null space in the algebraic sub-structuringprocess.

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  • Journal Name: Society for Industrial and Applied Mathematics: Journal onMatrix Analysis and Applications; Journal Volume: 27; Journal Issue: 3; Related Information: Journal Publication Date: 2005

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  • Report No.: LBNL--55050
  • Grant Number: DE-AC02-05CH11231
  • Office of Scientific & Technical Information Report Number: 918549
  • Archival Resource Key: ark:/67531/metadc877515

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  • May 26, 2004

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  • Sept. 22, 2016, 2:13 a.m.

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  • Sept. 29, 2016, 1:37 p.m.

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Yang, C.; Gao, W.; Bai, Z.; Li, X.; Lee, L.; Husbands, P. et al. An algebraic sub-structuring method for large-scale eigenvaluecalculation, article, May 26, 2004; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc877515/: accessed August 23, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.