**Recent Publications**

*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, *

*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.
*

*11. **D. Xie: A new boundary integral
equation for computing biomolecular electrostatics,
Proceedings of the 10 ^{th} 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. *

*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. *

*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. *

*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. *

*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.*

*21. **D. Xie: A
new block parallel SOR method and its analysis, SIAM J. Sci. Comput., Vol. 27, No. 5, pp.
1513-1533, 2006. *

*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. *

*23. **D. Xie: Analysis
of a class of parallel multigrid smoothers,
BIT Numerical Mathematics, Vol. 44, pp.813-828, 2004. *

*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.) *

*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. *

*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. *

*29. **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. *

*30. **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. *

*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. *

*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. *

*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. *

*34. **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. *

*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. *

*36. **D. Xie, New
nonlinear multigrid analysis, Proceedings of
1995 Copper Mountain Conference on Multigrid Methods,
NASA Conference Publication 3339, 1996. *[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). *

*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*