Performance of ILU Preconditioning Techniques in
Simulating Anisotropic Diffusion in the Human Brain

Ning Kang, Jun Zhang
Laboratory for High Performance Scientific Computing and Computer Simulation
Department of Computer Science
University of Kentucky
773 Anderson Hall
Lexington, KY 40506-0046, USA

Eric S. Carlson
Department of Chemical Engineering
University of Alabama
P. O. Box 870203
Tuscaloosa, AL 35487-0203, USA


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.

Key words: anisotropic diffusion simulation, diffusion tensor imaging, face-centered cubic grid, differential-algebraic equation, preconditioning techniques

Mathematics Subject Classification:

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This paper has been accepted for publication in Future Generation Computer Systems in June 2003.

Technical Report No. 364-03, Department of Computer Science, University of Kentucky, Lexington, KY, 2003.

This research was supported in part by the U.S. National Science Foundation under the grant 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 Kentucky Science and Engineering Foundation under grant KSEF-02-264-RED-002, in part by the Japanese Research Organization for Information Science & Technology, and in part by the University of Kentucky Research Committee.