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.
Mathematics Subject Classification:
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.