Sparse matrix factorization using overlapped localizing LOGOS modes on a shifted grid

Xin Xu; Robert J. Adams

doi:10.1109/TAP.2011.2180312

Sparse matrix factorization using overlapped localizing LOGOS modes on a shifted grid

Xin Xu, Robert J. Adams

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

15 Scopus citations

Abstract

Different types of local global solution (LOGOS) modes have been proposed to develop fast direct solvers for electromagnetic wave problems. While radiating LOGOS modes are suitable for high frequency problems, this paper focuses on the localizing LOGOS modes, which are suitable for low-to-mid frequency problems. Factorizations relying on non-overlapped, localizing LOGOS (NL-LOGOS) modes are provably error controllable, but fail to provide acceptable asymptotic computational efficiencies. Factorizations using overlapped, localizing LOGOS (OL-LOGOS) modes provide improved asymptotic computational performance, but have been observed to suffer from significant overhead and, in some cases, poorer error control. This paper describes a new procedure for obtaining the OL-LOGOS modes. It is observed that the asymptotic efficiency is similar to previously reported OL-LOGOS schemes while providing stable error control for standard problem formulations. The overhead associated with computing the OL-LOGOS modes is also reduced significantly.

Original language	English
Article number	6109325
Pages (from-to)	1414-1424
Number of pages	11
Journal	IEEE Transactions on Antennas and Propagation
Volume	60
Issue number	3
DOIs	https://doi.org/10.1109/TAP.2011.2180312
State	Published - Mar 2012

Bibliographical note

Funding Information:
Manuscript received October 27, 2010; revised August 10, 2011; accepted August 10, 2011. Date of publication December 20, 2011; date of current version March 02, 2012. This work was supported in part by the Office of Naval Research (N00014-04-1-0485) and the in part by National Science Foundation (ECS-0547497).

Funding

Manuscript received October 27, 2010; revised August 10, 2011; accepted August 10, 2011. Date of publication December 20, 2011; date of current version March 02, 2012. This work was supported in part by the Office of Naval Research (N00014-04-1-0485) and the in part by National Science Foundation (ECS-0547497).

Funders	Funder number
National Science Foundation (NSF)	ECS-0547497
Office of Naval Research	N00014-04-1-0485

Keywords

Fast direct solver
matrix decomposition
propagation
scattering

ASJC Scopus subject areas

Electrical and Electronic Engineering

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10.1109/TAP.2011.2180312

Cite this

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title = "Sparse matrix factorization using overlapped localizing LOGOS modes on a shifted grid",

abstract = "Different types of local global solution (LOGOS) modes have been proposed to develop fast direct solvers for electromagnetic wave problems. While radiating LOGOS modes are suitable for high frequency problems, this paper focuses on the localizing LOGOS modes, which are suitable for low-to-mid frequency problems. Factorizations relying on non-overlapped, localizing LOGOS (NL-LOGOS) modes are provably error controllable, but fail to provide acceptable asymptotic computational efficiencies. Factorizations using overlapped, localizing LOGOS (OL-LOGOS) modes provide improved asymptotic computational performance, but have been observed to suffer from significant overhead and, in some cases, poorer error control. This paper describes a new procedure for obtaining the OL-LOGOS modes. It is observed that the asymptotic efficiency is similar to previously reported OL-LOGOS schemes while providing stable error control for standard problem formulations. The overhead associated with computing the OL-LOGOS modes is also reduced significantly.",

keywords = "Fast direct solver, matrix decomposition, propagation, scattering",

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note = "Funding Information: Manuscript received October 27, 2010; revised August 10, 2011; accepted August 10, 2011. Date of publication December 20, 2011; date of current version March 02, 2012. This work was supported in part by the Office of Naval Research (N00014-04-1-0485) and the in part by National Science Foundation (ECS-0547497).",

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PY - 2012/3

Y1 - 2012/3

N2 - Different types of local global solution (LOGOS) modes have been proposed to develop fast direct solvers for electromagnetic wave problems. While radiating LOGOS modes are suitable for high frequency problems, this paper focuses on the localizing LOGOS modes, which are suitable for low-to-mid frequency problems. Factorizations relying on non-overlapped, localizing LOGOS (NL-LOGOS) modes are provably error controllable, but fail to provide acceptable asymptotic computational efficiencies. Factorizations using overlapped, localizing LOGOS (OL-LOGOS) modes provide improved asymptotic computational performance, but have been observed to suffer from significant overhead and, in some cases, poorer error control. This paper describes a new procedure for obtaining the OL-LOGOS modes. It is observed that the asymptotic efficiency is similar to previously reported OL-LOGOS schemes while providing stable error control for standard problem formulations. The overhead associated with computing the OL-LOGOS modes is also reduced significantly.

AB - Different types of local global solution (LOGOS) modes have been proposed to develop fast direct solvers for electromagnetic wave problems. While radiating LOGOS modes are suitable for high frequency problems, this paper focuses on the localizing LOGOS modes, which are suitable for low-to-mid frequency problems. Factorizations relying on non-overlapped, localizing LOGOS (NL-LOGOS) modes are provably error controllable, but fail to provide acceptable asymptotic computational efficiencies. Factorizations using overlapped, localizing LOGOS (OL-LOGOS) modes provide improved asymptotic computational performance, but have been observed to suffer from significant overhead and, in some cases, poorer error control. This paper describes a new procedure for obtaining the OL-LOGOS modes. It is observed that the asymptotic efficiency is similar to previously reported OL-LOGOS schemes while providing stable error control for standard problem formulations. The overhead associated with computing the OL-LOGOS modes is also reduced significantly.

KW - Fast direct solver

KW - matrix decomposition

KW - propagation

KW - scattering

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Sparse matrix factorization using overlapped localizing LOGOS modes on a shifted grid

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