Project Principal Investigator: Eric S. Carlson (University of Alabama)
University of Kentucky Principal Investigator: Jun Zhang
University of Kentucky Graduate Research Assistants: Ning Kang, David A. Turner
DOE Lab Collaborators: Drs. Tony Drummond and Osni Margues.

Abstract:

The anisotropic diffusion equation is important to a variety of modeling applications. These applications include, among many others, diffusion through biological tissues, heat and mass transfer in microelectronics, and contaminant transport in ground water systems. Despite its importance and relative simplicity, only limited, proprietary capabilities exist for the numerical solution of this equation in heterogeneous systems.

The project team will develop a set of modules and perfect novel gridding techniques that will promote efficient numerical solutions to the anisotropic diffusion equation. The new modules will rely on the ACTS Toolkit, a set of high performance modules, developed by DOE and are available to the public. The team will develop tools that may be applied to composite (multiple region( systems of arbitrary shape through the use of an embedded domain framework, which means that regions will be immersed in structured grids without requiring contortion of the grids to accommodate the shapes.

The particular software package that has been used in our high performance diffusion solvers is the SUNDIALS package from the ACTS Toolkit Collection.

Pictures of the Research Team Activities:

Picture of the research team members and collaborators, on July 18, 2002, at the University of Kentucky.

Click here for a larger picture.

From left: David Turner, Tony Drummond, Jun Zhang, Eric Carlson, Osni Margues, Ning Kang, Haiwei Sun.

1. A fourth order compact difference scheme on face centered cubic grids with multigrid method for solving 2D convection diffusion equation, by Haiwei Sun, Ning Kang, Jun Zhang, and Eric S. Carlson. (April, 2002).
2. Performance of ILU preconditioning techniques in simulating anisotropic diffusion in the human brain, by Ning Kang, Jun Zhang, and Eric S. Carlson. (January 6, 2003).
3. Comparison of parallel preconditioners in anisotropic diffusion simulation with human brain DT-MRI data, by Ning Kang, Jun Zhang, and Eric S. Carlson. (June 24, 2003).
4. Second order accuracy of the 4-point hexagonal net grid finite difference scheme for solving the 2D Helmholtz equation, by Eric S. Carlson, Haiwei Sun, Duane H. Smith, and Jun Zhang. (July 23, 2003).
5. Third order accuracy of the 4-point hexagonal net grid finite difference scheme for solving the 2D Helmholtz equation, by Eric S. Carlson, Haiwei Sun, Duane H. Smith, and Jun Zhang. (July 25, 2003).
6. White matter fiber tractography via anisotropic diffusion simulation in the human brain, by Ning Kang, Jun Zhang, Eric S. Carlson, and Daniel Gembris. (July 27, 2004).

Technical Presentations at Conferences:

1. Performance of ILU preconditioning techniques in simulating anisotropic diffusion in human brain, (Ning Kang, Jun Zhang, Eric S. Carlson), presented (by Ning Kang) at the Sixth IMACS International Symposium on Iterative Methods in Scientific Computing, Denver, CO, March 27 - 30, 2003.
2. Performance of ILU preconditioning techniques in simulating anisotropic diffusion in the human brain, (Ning Kang, Jun Zhang, Eric S. Carlson), presented (by Ning Kang) at the Conference of ETNA Following the Flows of Numerical Analysis, Kent, OH, May 29-31, 2003.
3. , (Ning Kang, Jun Zhang, Eric S. Carlson), presented (by Jun Zhang) at the SIAM Conference on Life Science, Portland, Oregon, July 10-14, 2004.

• The DOE ACTS Collections;
• The Surgical Planning Laboratory, Harvard University;
• The Whole Brain Atlas, Harvard University;
• The Magnetic Resonance Imaging and Spectroscopy Center (MRISC), University of Kentucky;
• Section on Tissue Biophysics and Biomimetics (Peter J. Basser), National Institutes of Health;
• Computer Graphics Research, California Institute of Technology;
• Publications in Diffusion Tensor MRI;
• A few Diffusion Tensor MRI papers.
• DTI Track package at UNC.
• Brain Explorer - Introduction to Human Brain.
• The Human Brain: Dissection of the Real Brain.

This page is supported by the U.S. Department of Energy Office of Science. However, any opinions, findings, and conclusions or recommendations expressed in this documents are those of the author and do not necessarily reflect the views of the U.S. Department of Energy or U.S. Government.

Go back to Funded Research Projects page.