Error analysis for matrix factorizations using non-overlapped localizing basis functions

Xin Xu; Yuan Xu; Robert J. Adams

doi:10.1109/TAP.2010.2052546

Error analysis for matrix factorizations using non-overlapped localizing basis functions

Xin Xu, Yuan Xu, Robert J. Adams

Electrical and Computer Engineering

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

Local-global solution (LOGOS) modes provide a computationally efficient framework for developing error controllable, fast, direct solution methods for electromagnetic simulations. This communication provides an error control analysis for the non-overlapped localizing LOGOS factorization procedure. The error analysis indicates how to control the error in the factored representation of the system matrix. Numerical examples demonstrate that the proposed error control procedure provides factorizations with controllably small errors for a number of PEC scattering problems while maintaining the efficiency of the LOGOS factorization.

Original language	English
Article number	5484710
Pages (from-to)	3081-3086
Number of pages	6
Journal	IEEE Transactions on Antennas and Propagation
Volume	58
Issue number	9
DOIs	https://doi.org/10.1109/TAP.2010.2052546
State	Published - Sep 2010

Bibliographical note

Funding Information:
Manuscript received January 20, 2009; revised January 28, 2010; accepted February 24, 2010. Date of publication June 14, 2010; date of current version September 03, 2010. This work was supported in part by the Office of Naval Research (N00014-04-1-0485) and in part by the National Science Foundation (ECS-0547497).

Keywords

Electromagnetic scattering
error analysis
fast solvers

ASJC Scopus subject areas

Electrical and Electronic Engineering

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10.1109/TAP.2010.2052546

Cite this

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abstract = "Local-global solution (LOGOS) modes provide a computationally efficient framework for developing error controllable, fast, direct solution methods for electromagnetic simulations. This communication provides an error control analysis for the non-overlapped localizing LOGOS factorization procedure. The error analysis indicates how to control the error in the factored representation of the system matrix. Numerical examples demonstrate that the proposed error control procedure provides factorizations with controllably small errors for a number of PEC scattering problems while maintaining the efficiency of the LOGOS factorization.",

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note = "Funding Information: Manuscript received January 20, 2009; revised January 28, 2010; accepted February 24, 2010. Date of publication June 14, 2010; date of current version September 03, 2010. This work was supported in part by the Office of Naval Research (N00014-04-1-0485) and in part by the National Science Foundation (ECS-0547497).",

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AU - Xu, Yuan

AU - Adams, Robert J.

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N2 - Local-global solution (LOGOS) modes provide a computationally efficient framework for developing error controllable, fast, direct solution methods for electromagnetic simulations. This communication provides an error control analysis for the non-overlapped localizing LOGOS factorization procedure. The error analysis indicates how to control the error in the factored representation of the system matrix. Numerical examples demonstrate that the proposed error control procedure provides factorizations with controllably small errors for a number of PEC scattering problems while maintaining the efficiency of the LOGOS factorization.

AB - Local-global solution (LOGOS) modes provide a computationally efficient framework for developing error controllable, fast, direct solution methods for electromagnetic simulations. This communication provides an error control analysis for the non-overlapped localizing LOGOS factorization procedure. The error analysis indicates how to control the error in the factored representation of the system matrix. Numerical examples demonstrate that the proposed error control procedure provides factorizations with controllably small errors for a number of PEC scattering problems while maintaining the efficiency of the LOGOS factorization.

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KW - fast solvers

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Error analysis for matrix factorizations using non-overlapped localizing basis functions

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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