My primary research interest is in large scale parallel and scientific computation, in particular, in developing algorithms and software packages for large scale computer simulation of physical processes on high performance computers. Research topics have been focused on designing robust iterative methods for solving general sparse linear systems and on developing fast and high accuracy methods for computer simulations. Recent application emphasis is placed on exploiting computational science technologies in data mining and information retrieval, bioinformatics, and nanotechnology. I have published more than 60 research papers in refereed professional journals in scientific computing and computational sciences. I am associate editor or on the editorial board of three professional journals in computing science and simulation. My research has been funded by NSF, DOE, and other research agencies with current total grants in force exceeding $1 M. For the past few years, I have established a research group in the Laboratory for High Performance Scientific Computing and Computer Simulation (the HiPSCCS Lab) at the University of Kentucky. The HiPSCCS Lab, currently supports 2 postdocs and 8 Ph.D. students, is one of the world's largest research laboratories of its kind. The following is a list of research interest that I have been pursuing during the past few years and will continue to develop and expand for the next few years.
Iterative solution of large sparse linear systems is central to many scientific and engineering computations. My latest research work concerns the development of robust multilevel and multigrid preconditioning techniques for solving such systems on high performance computers. A total of three previous and current projects have been funded by NSF to develop new high performance preconditioning techniques for robust and scalable solution of some large scale realistic linear systems. We are the world's leading research laboratory in this important research area.
Proposals have been submitted to DOE to conduct more application specific research in developing multiscale and multigrid computer simulation techniques.
In recent years I have developed several efficient multigrid methods and acceleration techniques to solve convection diffusion equation and the incompressible Navier-Stokes equation. An NSF funded research project studies the use of high order compact discretization methods and develops a novel nonstandard multigrid solution method to solve convection dominated problems with application to the numerical simulation of laminar diffusion flames. This research project employs both numerical and symbolic computation techniques.
We have submitted a follow-up research project to study bioheat transfer in biological bodies subjected to fires. This idea is to use our laminar diffusion flame modeling code to simulate the reaction of biological bodies under active fires, to study the skin burns caused by such an exposure, and to develop technologies to protect human beings from accidental disasters such as wild fires and house fires. Such computer simulation based studies will be very important in protecting firefighters from dangerous environments and in evacuating people from burning environments in cases of nature disasters. This will be a joint study with a few researchers at several schools.
In collaboration with Dr. E. Carlson of the University of Alabama, and funded by DOE, we have started a research work to develop high performance solvers for anisotropic problems with applications to nerve fiber tracking in human brains. The idea is to make use of the Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) technology to in vivo track the nerve fiber bundles in human brains. This study is very important in medical applications when a brain surgeon has to determine how to remove a cancer from a patient's brain and not to damage any important nerve fiber. It is also important to study the nerve system connectivity between different parts of the brain to determine if any brain disease is related to the disconnection of certain nerve fibers. For example, we are preparing a proposal for using the DT-MRI technology to study the Alzheimer's disease at the University of Kentucky, in collaboration with the UK Alzheimer's Disease Research Center. Due to the obvious nature of the studying subjects (human beings), such studies have to be conducted in vivo, i.e., without harming the subjects. The computer based DT-MRI technology provides the most promising direction in this area.
For applications, we are using our fiber tracking algorithms to reconstruct certain white matter fiber tracts to detect the minor changes between Alzheimer's disease patients and healthy control subjects. Our hope is to find some quantitative measure of certain white matter fiber tracts that are affected by Alzheimer's disease in its very early stage, before the typical symptoms of patients become apparent and can be detected by conventional means. The early detection or prediction of Alzheimer's disease can be very important, as the patients can be put on certain therapies to delay the onset of Alzheimer's disease.
A research project has been under way, joint with Dr. F. Yang of the Department of Chemical & Materials Engineering at UK, to use computer techniques in the modeling and simulation of nanotechnology. Currently, we are studying the surface evolution of the crystalline tubes and the growth stability of the nanotubes. Research proposals have been submitted to NSF to seek funding for expended collaborative research in this area, involving a research team with several other faculty members at UK and at other universities.
For the past two years, in collaboration with Dr. C. Lu of the Electrical & Computer Engineering at UK, we have developed some high quality preconditioning techniques in use with the multilevel fast multipole algorithm to conduct large scale computer simulations in computational electromagnetics. Our techniques are new and research results have been accepted for publication in leading journals in computational sciences. We also submitted an NSF proposal to seek funding to develop the next generation electromagnetics simulators, promising great advances in applicability, scalability, and reliability. Not such full scale study has been done by other researchers, to the best of our knowledge.
I have been working on developing new memory efficient algorithms for web and textual document retrieval using latent semantic indexing method. The new algorithms exploit wavelet techniques and document clustering algorithms in traditional latent semantic indexing method to make it more practically useful in real time online document retrieval. The salient features of the new algorithms are memory efficient and low preprocessing cost. A research project in information retrieval has been funded by the University of Kentucky Research Committee. Two related proposals have been submitted to NSF and Kentucky Science \& Engineering Foundation to study fast and accurate web document retrieval techniques for digital libraries.
I will also start a project to design effective and intelligent scientific computing recommendation system for linear system solvers, through mining sparse matrices and extracting matrix features. The goal of this project is to build an intelligent recommendation system that is useful for application scientists and engineers to make intelligent choice of suitable solvers for realistic sparse matrix problems. A one year NSF exploratory research project is expected to start in early 2003 to explore this untested new research idea.
In the near future (next five to ten years), I plan to focus my research effort on the following three areas: