New Concept and Parallel Algorithms for Robust
Preconditioning in Large Scale Parallel Matrix Computation

Principal Investigator: Jun Zhang
Graduate Research Assistants: Yuan Hong
Graduate Research Assistants: Kai Wang (graduated with a Ph.D. in 2003)

Funding Sources: National Science Foundation
Funding Division: Advanced Computational Infrustrature and Reseach
Funding Program: Advanced Computational Research
Program Director: Xiaodong Zhang
Contract Number: ACI-0202934
Estimated Budget: $172,361
Duration: 06/01/2002 - 05/31/2005 (36 months)


Large sparse unstructured matrices arising from various computer simulation and modeling are commonly solved by preconditioned iterative methods. This research project will study and design robust high performance preconditioners for parallel solution of large sparse linear systems, based on a class of multistep successive sparse approximate inverse preconditioning techniques.

We will develop new concept and parallel algorithms of multistep successive preconditioning for enhancing the robustness of standard sparse approximate inverse preconditioning techniques, and generalize this concept to the context of other preconditioning techniques. Study will be conducted to show the advantages of such approach to enhance both preconditioning accuracy and factorization stability. We will build portable software packages to implement new preconditioning strategies for solving unstructured general sparse linear systems on high performance parallel computers.

The general purpose high performance preconditioned iterative solvers from this research project are expected to make significant impact in the field of applied scientific computing. Our experience and existing strength will ensure that the project be carried out fully as proposed. As U.S. industry is more and more relying on computer aided design and manufacturing, large scale computer simulation and modeling will be a vital component in new products research and development. The outcome of this research will benefit U.S. industry as well as scientific research community by providing more efficient kernel software for large scale computer simulations.

Technical Reports and Computer Software:
  1. MSP: a class of parallel multistep successive sparse approximate inverse preconditioning strategies, by Kai Wang and Jun Zhang. (January, 2002).
  2. A class of parallel multilevel sparse approximate inverse preconditionrs for sparse linear systems, by Kai Wang, Jun Zhang, and Chi Shen. (November, 2002).
  3. A comparative study on dynamic and static sparsity patterns in parallel sparse approximate inverse preconditioning, by Kai Wang, Sangbae Kim, and Jun Zhang. (November, 2002).
  4. SOFTWARE: Parallel multistep successive sparse approximate inverse preconditioning for solving general sparse linear systems (first version), by Kai Wang, and Jun Zhang. (May 20, 2003).

Conference, Workshop, and Seminar Presentations:

  1. A class of new parallel preconditioning strategies for solving large sparse linear systems, presented (by Jun Zhang) at the 2002 International Conference on Parallel and Distributed Processing techniques and Applications, Las Vegas, NV, June 24 - 27, 2002.
  2. Parallel multilevel sparse approximate inverse preconditioner for solving large sparse linear systems presented (by Kai Wang, Ph.D. student) at the SIAM 2002 Annual Meeting, Philadelphia, PA, July 8 - 12, 2002.
  3. Robust parallel matrix preconditioning through successive sparse approximate inverse, Kai Wang and Jun Zhang, presented (by Jun Zhang) at the 2nd International Workshop on Parallel Matrix Algorithms and Applications, Neuchhatatel, Switzerland, November 7 - 10, 2002.
  4. Robust parallel preconditioning techniques for solving general sparse linear systems, Kai Wang and Jun Zhang, presented (by Jun Zhang) at the 2002 International Symposium on Distributed Computing and Applications to Business, Engineering and Science, Wuxi, China, December 16 - 19, 2002.
  5. Global and localized parallel preconditioning techniques for large scale solid earth simulations, Kai Wang, Sangbae Kim, Jun Zhang, Kengo Nakajima, and Hiroshi Okuda, presented (by Jun Zhang) at the 2003 International Workshop on Parallel and Distributed Scientific and Engineering Computing with Applications, Nice, France, April 22-26, 2003.
  6. Parallel Multilevel Sparse Approximate Inverse Preconditioners in Large Sparse Matrix Computations, Kai Wang, Jun Zhang, and Chi Shen, presented (by Jun Zhang) at Supercomputing 2003 Igniting Innovation, Phoenix, AZ, November 17-20, 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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This page was created on Wednesday, July 17, 2002, by
Jun Zhang
Last modified on Wednesday, November 26, 2003.