Recent Publications

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1. D. Xie and M. G. Zarrouk: Convergence Analysis of Truncated Incomplete Hessian Newton Minimization Method and Application in Biomolecular Potential Energy Minimization, Submitted, 2008.
2. D. Xie: New parallel symmetric SOR preconditioners by multi-type partitioning, Journal of Computer Mathematics, accepted, 2008.
3. D. Xie, R. K. Dash, and D. A. Beard: An Efficient Parallel Algorithm for a General Blood-Tissue Transport and Metabolism Model Governed by a System of Nonlinear Hyperbolic Equations, Submitted, 2008.
4. D. Xie and Q. Ni: An incomplete Hessian Newton minimization method and its application in a chemical database problem, Computational Optimization and Applications, accepted, 2007, published online: Jan. 12, 2008.
5. D. Xie and S. Zhou: A new minimization protocol for solving nonlinear Poisson-Boltzmann mortar finite element equation, BIT Numerical Mathematics, Vol. 47, pp. 853-871, 2007.
6. D. Xie: New parallel symmetric SOR preconditioners by multi-type partitioning, Proceedings of the International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2007, Chicago, 20-23 June, 2007, pages 418-428.
7. X. Li, K. J. Nevels1, Z. Gryczynski, I. Gryczynski, M. Pusztai-Carey, D. Xie, and P. Butko: A molecular dynamics model of Bt toxin Cyt1A and its validation by fluorescence resonance energy transfe, Submitted, 2007.
8. D. Xie: An effective sparse compressed natural preconditioner by biomolecular structure, Submitted, 2007.
9. X. Li, K. J. Nevels, D. Xie, and P. Butko: Molecular Dynamics Simulations of the Bt Toxin Cyt1A in Solution, Proceeding of 15th Conference on Current Trends in Computational Chemistry, Jackson, Mississippi, Nov. 3-4, 2006, pages 232-234.
10. D. Xie: A new block parallel SOR method and its analysis, SIAM J. Sci. Comput., Vol. 27, No. 5, pp. 1513-1533, 2006.
11. J. Xie, P. Butko, and D. Xie: Molecular dynamics simulations of the cytolytic toxin Cyt1A in solution, IEEE Trans. Nanobioscience, Vol. 4, No. 3, pp. 235-240, 2005.
12. D. Xie: Analysis of a class of parallel multigrid smoothers, BIT Numerical Mathematics, Vol. 44, pp.813-828, 2004.
13. D. Xie: An effective sparse compressed preconditioner for large scale biomolecular simulations, Lecture Notes in Computer Science, Vol. 3314, Edited by J. Zhang etc., Springer-Verlag, pp. 64-70, 2004. (Proceedings of the International Symposium on Computational and Information Sciences. Shanghai, China, December 16-18, 2004.)
14. D. Xie: New block parallel SOR methods by multi-type partitions, Proceedings of International Conference on Parallel Processing Workshop, Montreal, Canada, August 15-18, 2004, IEEE Computer Society Press.
15. D. Xie: Visualization of large chemical databases with application to drug design, one chapter of Numerical Linear Algebra and Optimization, edited by Y. Yuan, Science Press (Beijing/New York), pp. 81-97, 2003.

16. D. Xie, S. B. Singh, E. M. Fluder, and T. Schlick: Principal component analysis combined with truncated-Newton minimization for dimensionality reduction of chemical databases, Mathematical Programming, Vol. 95, No. 1, pp. 161-185, 2003.
17. D. Xie and T. Schlick: A more lenient stopping rule for line search algorithms, Optimization Methods and Software, Vol. 17, No. 4, pp. 683-700, 2002.
18. D. Xie, L. R. Scott, and T. Schlick: Analysis of the SHAKE-SOR algorithm for constrained molecular dynamics simulations, Methods and Applications of Analysis, Vol. 3, pp. 577-590, 2000.
19. D. Xie and T. Schlick: Visualization of chemical databases using the singular value decomposition and truncated-Newton minimization, Optimization in Computational Chemistry and Molecular Biology: Local and Global Approaches, C. A. Floudas and P. M. Pardalos, Editors, Nonconvex Optimization and Its Applications, Kluwer Academic Publishers, Vol. 40, pp. 267-286, 2000.
20. D. Xie, A. Tropsha, and T. Schlick: An efficient projection protocol for chemical databases: the singular value decomposition combined with truncated-Newton minimization, Journal of Chemical Information and Computer Sciences, Vol. 40, pp. 167-177, 2000.
21. L. R. Scott and D. Xie: Parallel Linear Stationary Iterative Methods, Parallel Solution of Partial Differential Equations, P. Bjorstad and M. Luskin, Editors, IMA Volumes in Mathematics and Its Applications, Springer-Verlag, Vol. 120, pp. 31-55, 2000.
22. D. Xie and T. Schlick: Efficient implementation of the truncated-Newton algorithm for large-scale chemistry applications, SIAM J. Opt., Vol. 10, pp. 132-154, 1999.
23. D. Xie and L. Adams: New Parallel SOR Method by Domain Partitioning, SIAM J. on Scientific Computing, Vol. 20, No. 6, pp. 2261-2281, 1999.
24. D. Xie and T. Schlick: Remark on Algorithm 702---The Updated Truncated Newton Minimization Package, ACM Trans. on Math. Software, Vol. 25, No. 1, pp. 108-122, 1999.
25. D. Xie, New nonlinear multigrid analysis, Proceedings of 1995 Copper Mountain Conference on Multigrid Methods, NASA Conference Publication 3339, 1996.
26. D. Xie, New parallel iterative methods, new nonlinear multigrid analysis, and application in computational chemistry, Research report UH/MD 208, Ph.D. thesis, University of Houston, 1995.

27. B. Bagheri, A. Ilin, J. A. McCammon, L. R. Scott, and D. Xie: Parallel algorithms for biomolecular modeling, Proceedings of the Workshop on Algorithms for Macromolecular Modeling, pages 77-82, Lawrence, KA, September 1994.
28. L. R. Scott, B. Bagheri, A. Ilin, and D. Xie: Parallel solution of elliptic boundary value problems, Proceedings of the Third International Workshop on Computational Electronics, Portland, OR, May 1994.
29. D. Xie, The convergence of the non-linear multigrid methods for solving a kind of finite element equation, J. Comp. Math., 1, 1993.
30. D. Xie, On the essential assumptions of multigrid convergence proofs, J. Comp. Math., Supplementary Issue, pp. 158-164, 1992.
31. D. Xie, On the essential assumption and convergence estimation of multigrid analysis, J. Hunan University, 17, pp. 103-112, 1990.
32. D. Xie, A new multigrid iteration for solving interface problems with small media ratio, Comm. Appl. Math. Comput., 1, pp. 47-57, 1987.
33. D. Xie, Analysis of the multigrid iterative algorithms, J. Hunan University, 13, pp. 231-237, 1986.