1. D. Xie: New Solution Decomposition and Minimization Schemes for Poisson-Boltzmann Equation in Calculation of Biomolecular Electrostatics, accepted, Journal of Computational Physics, 2014.
2. D. Xie and J. Li: A New Analysis of Electrostatic Free Energy Minimization and Poisson-Boltzmann Equation for Protein in Ionic Solvent, accepted, Nonlinear Analysis: Real World Applications, 2014.
3. J. Li and D. Xie: A New Linear Poisson-Boltzmann Equation and Finite Element Solver by Solution Decomposition Approach, accepted, Communications in Mathematical Sciences, 2014.
4. J. Li and D. Xie: An Effective Minimization Protocol for Solving a Size-modified Poisson-Boltzmann Equation for Biomolecule in Ionic Solvent, submitted, 2014.
5. Xie, Y. Jiang, and L. R. Scott: Efficient algorithms for solving a nonlocal dielectric model for protein in ionic solvent, Vol. 38, pages B1267-1284, SIAM Journal on Scientific Computing, 2013.
6. D. Xie and H. Volkmer: A modified nonlocal continuum electrostatic model for protein in water and its analytical solutions for ionic Born models, Communications in Computational Physics, the special issue entitled “Modeling Electrostatics in Molecular Biology”, Vol. 13, No. 1, pages 174-194, 2013.
7. D. Xie, Y. Jiang, P. Brune, and L. R. Scott: A fast solver for a nonlocal dielectric continuum model, SIAM Journal on Scientific Computing, Vol. 34, No. 2, B107-B126, 2012.
8. D. Xie: An improved approximate Newton for implicit Runge-Kutta methods, Journal of Computational and Applied Mathematics, Vol. 235, No. 17, pages 5249-5258, 2011. [pdf]
9. D. Xie and L. R. Scott: A new boundary integral equation for molecular electrostatics with charges over whole space, BIT Numerical Mathematics, Vol. 51, No. 4, pages 1051-1071, 2011. [pdf]
10. D. Xie and M. G. Zarrouk: Convergence analysis of truncated incomplete Hessian Newton minimization method and application in biomolecular potential energy minimization, Computational Optimization and Applications, DOI 10.1007/s1058-009-9252-7, Vol. 48, No. 2, pages 213-232, 2011. [pdf]
11. D. Xie: A new boundary integral equation for computing biomolecular electrostatics, Proceedings of the 10th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2010, Madison, 24-26 May, 2010.
12. D. Xie: An effective sparse compressed natural preconditioner by biomolecular structure, to be submitted, 2010.
13. D. Xie and L. R. Scott: An analysis of parallel U-cycle method, Tech Report TR-2010-03, University of Chicago, April 20, 2010.
14. D. Xie: New parallel symmetric SOR preconditioners by multi-type partitioning, Journal of Computer Mathematics, Vol. 86, No. 2, pages 287-300, 2009. [pdf]
15. D. Xie, R. K. Dash, and D. A. Beard: An improved algorithm and its parallel implementation for solving a general blood-tissue transport and metabolism model, Journal of Computational Physics, Vol 228, No. 20, pages 7850-7861, 2009. [pdf]
16. 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 resonance energy transfer, Biophysical Chemistry, Vol. 144, pages 53-61, 2009.
17. D. Xie and Q. Ni: An incomplete Hessian Newton minimization method and its application in a chemical database problem, Computational Optimization and Applications, Vol. 44, No. 3, pages 467-485, 2009. [pdf]
18. 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. [pdf]
19. 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.
20. 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.
22. 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. [pdf]
23. D. Xie: Analysis of a class of parallel multigrid smoothers, BIT Numerical Mathematics, Vol. 44, pp.813-828, 2004. [pdf]
24. 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.) [pdf]
25. 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.
26. 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. [pdf]
27. 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. [pdf]
28. 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. [pdf]
30. D. Xie and T. Schlick: Visualization of chemical databases using the singular value decompositionand 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.
31. 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. [pdf]
32. 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. [pdf]
33. 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. [pdf]
35. 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. [pdf]
37. 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.
38. 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.
39. 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. Added to ScientificCommons in 2008.
40. D. Xie, The convergence of the non-linear multigrid methods for solving a kind of finite element equation, J. Comp. Math., 1, 1993, (in Chinese). [pdf]
41. D. Xie, On the essential assumptions of multigrid convergence proofs, J. Comp. Math., Supplementary Issue, pp. 158-164, 1992, (in Chinese).
42. D. Xie, On the essential assumption and convergence estimation of multigrid analysis, J. Hunan University, 17, pp. 103-112, 1990, (in Chinese).
43. D. Xie, A new multigrid iteration for solving interface problems with small media ratio, Comm. Appl. Math. Comput., 1, pp. 47-57, 1987, (in Chinese).
44. D. Xie, Analysis of the multigrid iterative algorithms, J. Hunan University, 13, pp. 231-237, 1986 (in Chinese).
Last modified August. 30, 2013