Performance of ILU preconditioning techniques in simulating anisotropic diffusion in the human brain

Ning Kang; Jun Zhang; Eric S. Carlson

doi:10.1016/j.future.2003.07.014

Performance of ILU preconditioning techniques in simulating anisotropic diffusion in the human brain

Ning Kang, Jun Zhang, Eric S. Carlson

Computer Science

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

6 Scopus citations

Abstract

We conduct simulations for the unsteady state anisotropic diffusion process in the human brain by discretizing the governing diffusion equation on a face-centered cubic grid and adopting a high performance differential-algebraic equation solver, IDA, to deal with the resulting large-scale system of DAEs. Incomplete LU preconditioning techniques are used with the GMRES method to accelerate the convergence rate of the iterative solution. We then investigate and compare the efficiency and effectiveness of a number of ILU preconditioners, and find out that the ILUT with a dual dropping strategy gives the best overall performance when it is provided with the optimum choices of the fill-in parameter and the threshold dropping tolerance.

Original language	English
Pages (from-to)	687-698
Number of pages	12
Journal	Future Generation Computer Systems
Volume	20
Issue number	4
DOIs	https://doi.org/10.1016/j.future.2003.07.014
State	Published - May 3 2004

Bibliographical note

Funding Information:
This study was funded by the US Department of Energy Office of Science under the project “Development of a High Performance Anisotropic Diffusion Equation Solver Using the ACTS Toolkit” (DE-FG02-02ER45961). The first two authors would also like to acknowledge DOE’s support of their attending the ACTS Workshop, organized by Drs. Tony Drummond and Osni Marques, at the Lawrence Berkeley National Laboratory, in September 2002. We would also like to thank Dr. Daniel Gembris, at the Institute for Medicine, Jülich Research Center, Jülich, Germany, for providing the diffusion tensor data set. The research work of Ning Kang was supported by the US Department of Energy Office of Science under grant DE-FG02-02ER45961. The research work of Jun Zhang was supported in part by the US National Science Foundation under grants CCR-9988165, CCR-0092532, and ACR-0202934, in part by the US Department of Energy Office of Science under grant DE-FG02-02ER45961, in part by the Kentucky Science and Engineering Foundation under grant KSEF-02-264-RED-002, in part by the Japan Research Organization for Information Science and Technology (RIST), and in part by the University of Kentucky Research Committee. The research work of Eric S. Carlson was supported by the US Department of Energy Office of Science under grant DE-FG02-02ER45961.

Keywords

Anisotropic diffusion
DT-MRI
FCC grid
Preconditioning

ASJC Scopus subject areas

Software
Hardware and Architecture
Computer Networks and Communications

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10.1016/j.future.2003.07.014

Cite this

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title = "Performance of ILU preconditioning techniques in simulating anisotropic diffusion in the human brain",

abstract = "We conduct simulations for the unsteady state anisotropic diffusion process in the human brain by discretizing the governing diffusion equation on a face-centered cubic grid and adopting a high performance differential-algebraic equation solver, IDA, to deal with the resulting large-scale system of DAEs. Incomplete LU preconditioning techniques are used with the GMRES method to accelerate the convergence rate of the iterative solution. We then investigate and compare the efficiency and effectiveness of a number of ILU preconditioners, and find out that the ILUT with a dual dropping strategy gives the best overall performance when it is provided with the optimum choices of the fill-in parameter and the threshold dropping tolerance.",

keywords = "Anisotropic diffusion, DT-MRI, FCC grid, Preconditioning",

author = "Ning Kang and Jun Zhang and Carlson, {Eric S.}",

note = "Funding Information: This study was funded by the US Department of Energy Office of Science under the project “Development of a High Performance Anisotropic Diffusion Equation Solver Using the ACTS Toolkit” (DE-FG02-02ER45961). The first two authors would also like to acknowledge DOE{\textquoteright}s support of their attending the ACTS Workshop, organized by Drs. Tony Drummond and Osni Marques, at the Lawrence Berkeley National Laboratory, in September 2002. We would also like to thank Dr. Daniel Gembris, at the Institute for Medicine, J{\"u}lich Research Center, J{\"u}lich, Germany, for providing the diffusion tensor data set. The research work of Ning Kang was supported by the US Department of Energy Office of Science under grant DE-FG02-02ER45961. The research work of Jun Zhang was supported in part by the US National Science Foundation under grants CCR-9988165, CCR-0092532, and ACR-0202934, in part by the US Department of Energy Office of Science under grant DE-FG02-02ER45961, in part by the Kentucky Science and Engineering Foundation under grant KSEF-02-264-RED-002, in part by the Japan Research Organization for Information Science and Technology (RIST), and in part by the University of Kentucky Research Committee. The research work of Eric S. Carlson was supported by the US Department of Energy Office of Science under grant DE-FG02-02ER45961.",

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N2 - We conduct simulations for the unsteady state anisotropic diffusion process in the human brain by discretizing the governing diffusion equation on a face-centered cubic grid and adopting a high performance differential-algebraic equation solver, IDA, to deal with the resulting large-scale system of DAEs. Incomplete LU preconditioning techniques are used with the GMRES method to accelerate the convergence rate of the iterative solution. We then investigate and compare the efficiency and effectiveness of a number of ILU preconditioners, and find out that the ILUT with a dual dropping strategy gives the best overall performance when it is provided with the optimum choices of the fill-in parameter and the threshold dropping tolerance.

AB - We conduct simulations for the unsteady state anisotropic diffusion process in the human brain by discretizing the governing diffusion equation on a face-centered cubic grid and adopting a high performance differential-algebraic equation solver, IDA, to deal with the resulting large-scale system of DAEs. Incomplete LU preconditioning techniques are used with the GMRES method to accelerate the convergence rate of the iterative solution. We then investigate and compare the efficiency and effectiveness of a number of ILU preconditioners, and find out that the ILUT with a dual dropping strategy gives the best overall performance when it is provided with the optimum choices of the fill-in parameter and the threshold dropping tolerance.

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KW - FCC grid

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Performance of ILU preconditioning techniques in simulating anisotropic diffusion in the human brain

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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