Sparse inverse preconditioning of multilevel fast multipole algorithm for hybrid integral equations in electromagnetics

Jeonghwa Lee; Jun Zhang; Cai Cheng Lu

doi:10.1109/TAP.2004.834084

Sparse inverse preconditioning of multilevel fast multipole algorithm for hybrid integral equations in electromagnetics

Jeonghwa Lee, Jun Zhang, Cai Cheng Lu

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

153 Scopus citations

Abstract

In computational electromagnetics, the multilevel fast multipole algorithm (MLFMA) is used to reduce the computational complexity of the matrix vector product operations. In iteratively solving the dense linear systems arising from discretized hybrid integral equations, the sparse approximate inverse (SAI) preconditioning technique is employed to accelerate the convergence rate of the Krylov iterations. We show that a good quality SAI preconditioner can be constructed by using the near part matrix numerically generated in the MLFMA. The main purpose of this study is to show that this class of the SAI preconditioners are effective with the MLFMA and can reduce the number of Krylov iterations substantially. Our experimental results indicate that the SAI preconditioned MLFMA maintains the computational complexity of the MLFMA, but converges a lot faster, thus effectively reduces the overall simulation time.

Original language	English
Pages (from-to)	2277-2287
Number of pages	11
Journal	IEEE Transactions on Antennas and Propagation
Volume	52
Issue number	9
DOIs	https://doi.org/10.1109/TAP.2004.834084
State	Published - Sep 2004

Bibliographical note

Funding Information:
Dr. Lu is a recipient of the 2000 Young Investigator Award from the Office of Naval Research and a CAREER Award from the National Science Foundation.

Funding Information:
Manuscript received December 11, 2002; revised July 28, 2003. The work of J. Lee was supported in part by the U.S. National Science Foundation (NSF) under Grant CCR-0092532. The work of J. Zhang was supported in part by the U.S. National Science Foundation (NSF) under Grants CCR-9988165, CCR-0092532, and ACR-0202934, in part by the U.S. Department of Energy Office of Science under Grant DE-FG02-02ER45961, in part by the Japanese Research Organization for Information Science & Technology (RIST), and in part by the University of Kentucky Research Committee. The work of C.-C. Lu was supported in part by the U.S. National Science Foundation under Grant ECS-0093692 and in part by the U.S. Office of Naval Research under Grant N00014-00-1-0605.

Funding

Dr. Lu is a recipient of the 2000 Young Investigator Award from the Office of Naval Research and a CAREER Award from the National Science Foundation. Manuscript received December 11, 2002; revised July 28, 2003. The work of J. Lee was supported in part by the U.S. National Science Foundation (NSF) under Grant CCR-0092532. The work of J. Zhang was supported in part by the U.S. National Science Foundation (NSF) under Grants CCR-9988165, CCR-0092532, and ACR-0202934, in part by the U.S. Department of Energy Office of Science under Grant DE-FG02-02ER45961, in part by the Japanese Research Organization for Information Science & Technology (RIST), and in part by the University of Kentucky Research Committee. The work of C.-C. Lu was supported in part by the U.S. National Science Foundation under Grant ECS-0093692 and in part by the U.S. Office of Naval Research under Grant N00014-00-1-0605.

Funders	Funder number
Japanese Research Organization for Information Science & Technology
RIST
U.S. Department of Energy Office of Basic Science	DE-FG02-02ER45961
U.S. National Science Foundation (NSF)
U.S. Office of Naval Research	N00014-00-1-0605
University of Kentucky Research Committee	ECS-0093692
National Science Foundation (NSF)	CCR-0092532, ACR-0202934, CCR-9988165
Office of Naval Research

ASJC Scopus subject areas

Electrical and Electronic Engineering

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10.1109/TAP.2004.834084

Cite this

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title = "Sparse inverse preconditioning of multilevel fast multipole algorithm for hybrid integral equations in electromagnetics",

abstract = "In computational electromagnetics, the multilevel fast multipole algorithm (MLFMA) is used to reduce the computational complexity of the matrix vector product operations. In iteratively solving the dense linear systems arising from discretized hybrid integral equations, the sparse approximate inverse (SAI) preconditioning technique is employed to accelerate the convergence rate of the Krylov iterations. We show that a good quality SAI preconditioner can be constructed by using the near part matrix numerically generated in the MLFMA. The main purpose of this study is to show that this class of the SAI preconditioners are effective with the MLFMA and can reduce the number of Krylov iterations substantially. Our experimental results indicate that the SAI preconditioned MLFMA maintains the computational complexity of the MLFMA, but converges a lot faster, thus effectively reduces the overall simulation time.",

author = "Jeonghwa Lee and Jun Zhang and Lu, {Cai Cheng}",

note = "Funding Information: Dr. Lu is a recipient of the 2000 Young Investigator Award from the Office of Naval Research and a CAREER Award from the National Science Foundation. Funding Information: Manuscript received December 11, 2002; revised July 28, 2003. The work of J. Lee was supported in part by the U.S. National Science Foundation (NSF) under Grant CCR-0092532. The work of J. Zhang was supported in part by the U.S. National Science Foundation (NSF) under Grants CCR-9988165, CCR-0092532, and ACR-0202934, in part by the U.S. Department of Energy Office of Science under Grant DE-FG02-02ER45961, in part by the Japanese Research Organization for Information Science & Technology (RIST), and in part by the University of Kentucky Research Committee. The work of C.-C. Lu was supported in part by the U.S. National Science Foundation under Grant ECS-0093692 and in part by the U.S. Office of Naval Research under Grant N00014-00-1-0605.",

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N2 - In computational electromagnetics, the multilevel fast multipole algorithm (MLFMA) is used to reduce the computational complexity of the matrix vector product operations. In iteratively solving the dense linear systems arising from discretized hybrid integral equations, the sparse approximate inverse (SAI) preconditioning technique is employed to accelerate the convergence rate of the Krylov iterations. We show that a good quality SAI preconditioner can be constructed by using the near part matrix numerically generated in the MLFMA. The main purpose of this study is to show that this class of the SAI preconditioners are effective with the MLFMA and can reduce the number of Krylov iterations substantially. Our experimental results indicate that the SAI preconditioned MLFMA maintains the computational complexity of the MLFMA, but converges a lot faster, thus effectively reduces the overall simulation time.

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Sparse inverse preconditioning of multilevel fast multipole algorithm for hybrid integral equations in electromagnetics

Abstract

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