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

Ning Kang

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

Jun Zhang
Eric S. Carlson

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.