An algebraic sub-structuring method for large-scale eigenvaluecalculation
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.
- Research Organization:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Sponsoring Organization:
- USDOE Director. Office of Science.
- DOE Contract Number:
- DE-AC02-05CH11231
- OSTI ID:
- 918549
- Report Number(s):
- LBNL-55050; R&D Project: KS1210; BnR: KJ0101010; TRN: US0805405
- Journal Information:
- Society for Industrial and Applied Mathematics: Journal onMatrix Analysis and Applications, Vol. 27, Issue 3; Related Information: Journal Publication Date: 2005
- Country of Publication:
- United States
- Language:
- English
Similar Records
Algebraic Sub-Structuring for Electromagnetic Applications
Deflation as a method of variance reduction for estimating the trace of a matrix inverse