**Recent Publications**

*1.
**J.
Ying and D. Xie: A New Finite Element and Finite Difference
Hybrid Method for Computing Electrostatics of Ionic Solvated Biomolecule,
Journal of Computational Physics, Vol. 298, pages 636-651, 2015. [pdf]*

*2.
**L.
R. Scott, Y. Jiang, and D. Xie:* *Comparison
of a nonlocal dielectric model with a discontinuous model, **University of Chicago Technical Report **TR-2015-06**, 2015.*

*3.
**D.
Xie and J. Ying: *** A
New Box Iterative Method for a Class of Nonlinear Interface Problems with
Application in Solving Poisson-Boltzmann Equation**,

*4.
**H.
Volkmer, J. Yang, and D. Xie: Analytical Solutions of Two Nonlocal Poisson Dielectric Test Models
with Spherical Solute Region Containing Multiple Point Charges, submitted,
2015.*

*5.
**J.
Ying and D. Xie: A Hybrid Solver of Size
Modified Poisson-Boltzmann Equation by Domain Decomposition, Finite Element,
and Finite Difference, submitted, 2015.*

*6.
**L.
R. Scott and D. Xie: Analysis of a
Nonlocal Poisson-Boltzmann Equation, submitted, 2015.*

*7.
**D.
Xie and J. Li: A New
Analysis of Electrostatic Free Energy Minimization and Poisson-Boltzmann
Equation for Protein in Ionic Solvent, Nonlinear Analysis: Real World
Applications, Vol. 21, pages 185-196, 2015. [pdf]*

*8.
**J.
Li and D. Xie: An Effective Minimization
Protocol for Solving a Size-modified Poisson-Boltzmann Equation for Biomolecule
in Ionic Solvent,*

*9.
**J.
Li and D. Xie:* *A New Linear Poisson-Boltzmann
Equation and Finite Element Solver by Solution Decomposition Approach**, Communications in Mathematical
Sciences, Vol. 13, No. 2, pages 315-325, 2015. [pdf]*

*10. **D. Xie and Y. Jiang: A Nonlocal Modified Poisson-Boltzmann
Equation and Finite Element Solver for Computing Electrostatics of Biomolecules,
submitted, 2014. *

*11. **D. Xie: New
Solution Decomposition and Minimization Schemes for Poisson-Boltzmann Equation
in Calculation of Biomolecular Electrostatics, Journal of Computational
Physics, Vol. 275, pages 294-309, 2014. [pdf] *

*12. **Y. Jiang, J. Ying, and D. Xie: A
Poisson-Boltzmann Equation Test Model for Protein in Spherical Solute Region
and its Applications, Molecular Based Mathematical Biology, Vol. 2, pages
86-97, 2014. Open Access. [pdf]*

*13. **D. Xie, Y. Jiang, and L. R. Scott:
**Efficient algorithms
for solving a nonlocal dielectric model for protein in ionic solvent**,
Vol. 35, No. 6, pages B1267-1284, **SIAM Journal on Scientific Computing, 2013*.
*[pdf]*

*14. **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. [pdf]*

*15. **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. [pdf]*

*16. **D. Xie: An improved
approximate Newton for implicit Runge-Kutta methods,
*

*17. **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]*

*18. **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.
*

*19. **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.*

*20. ** D. Xie:
An effective sparse compressed natural preconditioner
by biomolecular structure, to be submitted, 2010.*

*21. **D. Xie and L. R. Scott: An analysis of parallel U-cycle method,
Tech Report TR-2010-03,
University of Chicago, April 20, 2010.*

*22. **D. Xie: New
parallel symmetric SOR preconditioners by multi-type
partitioning, Journal of Computer Mathematics, Vol. 86, No. 2, pages
287-300, 2009. *

*23. **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. *

*24. **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. *

*25. **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. *

*26. **D. Xie and S. Zhou: A new minimization
protocol for solving nonlinear Poisson-Boltzmann mortar finite element equation,
BIT Numerical Mathematics, Vol. 47, pages 853-871, 2007. *

*27. **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.*

*28. **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.*

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

*30. **J. Xie, P. Butko,
and D. Xie: Molecular dynamics
simulations of the cytolytic toxin Cyt1A in solution,
IEEE Trans. Nanobioscience, Vol. 4, No. 3, pages
235-240, 2005. *

*31. **D. Xie: Analysis
of a class of parallel multigrid smoothers,
BIT Numerical Mathematics, Vol. 44, pages813-828, 2004. *

*32. **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, pages
64-70, 2004. (Proceedings of the International Symposium on Computational and
Information Sciences. Shanghai, China, December 16-18, 2004.) *

*33. **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.*

*34. **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), pages 81-97, 2003. *[pdf]

*35. **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, pages 161-185, 2003. *

*36. **D. Xie and T. Schlick:
A
more lenient stopping rule for line search algorithms, Optimization
Methods and Software, Vol. 17, No. 4, pages 683-700, 2002. *

*37. **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. 7, No. 3, page 577-590, 2000. *

*38. **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, pages
267-286, 2000. *

*39. **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, pages 167-177, 2000. *

*40. **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, pages 31-55,
2000. *

*41. **D. Xie and T. Schlick:
Efficient
implementation of the truncated-Newton algorithm for large-scale chemistry
applications, SIAM J. Opt., Vol. 10, pages 132-154, 1999. *

*42. **D. Xie and L. Adams: New
Parallel SOR Method by Domain Partitioning, SIAM J. on Scientific
Computing, Vol. 20, No. 6, pages 2261-2281, 1999. *

*43. **D. Xie and T. Schlick:
Remark on
Algorithm 702---The Updated Truncated Newton Minimization Package, ACM
Trans. on Math. Software, Vol. 25, No. 1, pages 108-122, 1999. *

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

*45. **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.*

*46. **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.*

*47. **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.*

*48. **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). *

*49. **D. Xie, On the essential assumptions of multigrid
convergence proofs, J. Comp. Math., Supplementary
Issue, pages 158-164, 1992, (in Chinese).*

*50. **D. Xie, On the essential assumption and convergence estimation of multigrid analysis, J. Hunan University, 17, pages
103-112, 1990, (in Chinese).*

*51. **D. Xie, A new multigrid iteration for solving interface problems with small media ratio, Comm. Appl.
Math. Comput., 1, pages
47-57, 1987, (in Chinese).*

*52. **D. Xie, Analysis of the multigrid iterative
algorithms, J. Hunan University, 13, pages 231-237, 1986 (in Chinese).*

*Last modified September 1, 2015*