Principal Investigator: Jun Zhang
Graduate Research Assistants: Li Wang, Jeonghwa Lee, ShuTing Xu, Chi Shen

Abstract:

This career development proposal integrates a research project and an education plan in the area of high performance scientific computing. We will develop a class of robust scalable preconditioning techniques for solving large sparse linear systems on high performance computers, which use multilevel recursive incomplete LU factorization preconditioning techniques to achieve high degree of robustness. The concepts of recursive preconditioning and dynamic preconditioning will be investigated. The resulting software packages can be used by researchers and engineers as kernel software in large scale numerical simulations and computations. An important component of this research project is to customize the designed general linear system solvers for a few specific scientific, engineering and industrial applications to maximize computational efficiency. Collaborations with researchers and engineers in application areas will be developed during the course of the research project. High performance scientific computing graduate courses will be developed and a student research and training laboratory will be developed at the University of Kentucky.

The high performance preconditioning techniques obtained in this research project will make significant impact on large scale scientific and engineering computations. The results of this research will advance iterative techniques to a new level of robustness by utilizing recursive and dynamic preconditioning strategies. Graduate students will be trained to gain expertise in state-of-the-art high performance scientific computing techniques. Collaborations with engineering and industrial researchers promote high performance scientific computing techniques and practices in applications environments and provide invaluable opportunity for students to gain practical experience. The outcome of this research will benefit U.S. industry as well as scientific research community by providing robust linear system software and skilled researchers and engineers for large scale numerical simulations. Industries that will be impacted include aerospace engineering, semiconductor, car and airplane manufacturing, reservoir simulation, combustion, ocean/climate modeling, pollution tracking, nuclear reaction simulation, and many more.

1. A two step combined stable preconditioning strategy for incomplete factorization of CFD matrices, by Li Wang and Jun Zhang. (February, 2002).
2. Incomplete LU preconditioning for large scale dense complex linear systems from electromagnetic wave scattering problems, by Jeonghwa Lee, Jun Zhang, and Cai-Cheng Lu. (April, 2002).
3. Distribued block independent set algorithms and parallel multilevel ILU preconditioners, by Chi Shen, Jun Zhang, and Kai Wang. (October 20, 2002).
4. Sparse inverse preconditioning of multilevel fast multipole algorithm for hybrid integral equations in electromagnetics, by Jeonghwa Lee, Jun Zhang, and Cai-Cheng Lu. (December 13, 2002).
5. A fully parallel block independent set algorithm for distributed sparse matrices, by Chi Shen, and Jun Zhang. (January 15, 2003).

Technical Presentations at Conferences and Seminars:

1. Robust preconditioning techniques for electromagnetics, (Jeonghwa Lee, Jun Zhang, Cai-Cheng Lu), presented (by Jeonghwa Lee, Ph.D. student) in the Department of Mathematics, Chonnam National University, Kwangju, South Korea, December 24, 2002.
2. Preconditioning techniques for large dense matrices from electromagnetic wave scattering simulation, (Cai-Cheng Lu, Jeonghwa Lee, and Jun Zhang), presented (by Jun Zhang) at the 2003 SIAM Conference on Computational Science & Engineering, San Diego, CA, February 10 - 13, 2003.
3. Robust preconditioning techniques for electromagnetic wave scattering problems, (Jeonghwa Lee, Jun Zhang, and Cai-Cheng Lu), presented (by Stephen Gedney) at the 19th Annual Review of Progress in Applied Computational Electromagnetics, Naval Post Graduate School, Monterey, CA, March 24 - 28, 2003.
4. Parallel multilevel block ILU preconditioning techniques for large sparse linear systems, (Chi Shen, Jun Zhang, and Kai Wang), presented (by Chi Shen) at the Sixth IMACS International Symposium on Iterative Methods in Scientific Computing, Denver, CO, March 27 - 30, 2003.
5. Incomplete LU preconditioning for large scale dense complex linear systems, (Jeonghwa Lee, Jun Zhang, and Cai-Cheng Lu), presented (by Jeonghwa Lee) at the Sixth IMACS International Symposium on Iterative Methods in Scientific Computing, Denver, CO, March 27 - 30, 2003.
6. Preconditioning techniques for solving combined integral equations in electromagnetics, (Jeonghwa Lee, Jun Zhang, and Cai-Cheng Lu), presented (by Jeonghwa Lee) at the 17th Annual Eastern Kentucky University Symposium in Mathematical, Statistical, & Computer Sciences, Richmond, KY, April 4, 2003.
7. Parallel multilevel block ILU preconditioning techniques for large sparse linear systems, (Chi Shen, Jun Zhang, and Kai Wang), presented (by Jun Zhang) at the 17th International Parallel & Distributed Processing Symposium, Nice, France, April 22 - 26, 2003.

This page is supported by the U.S. National Science Foundation. 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. National Science Foundation.

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