Publications

  1. H. Lee, Z. Chao, H. Cobb, Y. Liu, and D. Xie (corresponding author): A PNP Ion Channel Deep Learning Solver with Local Neural Network and Finite Element Input Data, arXiv:2401.17513, 31 Jan, 2024.
  2. H. Lee, Z. Chao, H. Cobb, Y. Liu, and D. Xie: A PNP Ion Channel Deep Learning Solver with Local Neural Network and Finite Element Input Data, submitted to Biophysical Journal, 2023.
  3. D. Xie and R. Dash: Ionic Flux Calculation by an Extended Goldman-Hodgkin-Katz Equation Accounting for Nonlinear Ion Channel Electrostatics, submitted to International Journal of Computer Mathematics, 2023.
  4. D. Xie: An Efficient Finite Element Solver for a Nonuniform Size-modified Poisson-Nernst-Planck Ion Channel Model, submitted, 2023.
  5. D. Xie and Z. Chao: A Poisson-Nernst-Planck Single Ion Channel Model and Its Effective Finite Element Solver, Vol. 481, Journal of Computational Physics, 2023. [PDF]
  6. D. Xie: An Efficient Finite Element Iterative Method for Solving a Nonuniform Size Modified Poisson-Boltzmann Ion Channel Model, Vol. 470, DOI 10.1016/j.jcp.2022.111556,  Journal of Computational Physics, 2022. [PDF]
  7. D. Xie and Z. Chao: A Poisson-Nernst-Planck Single Ion Channel Model and Its Effective Finite Element Solver, Preprint at SSRN on November 7, 2022: https://ssrn.com/abstract=4270098.
  8. D. Xie: An Extension of Goldman-Hodgkin-Katz Equations by Charges from Ionic Solution and Ion Channel Protein, arXiv:2208.11293 [q-bio.BM],  2022.
  9. Z. Chao, S. Gui, B. Lu, and D. Xie (corresponding author): Efficient Generation of Membrane and Solvent Tetrahedral Meshes for Finite Element Ion Channel Calculation,  International Journal of Numerical Analysis & Modeling, Vol. 19 (6), pages 885-904, 2022.
  10. H. Volkmer and D. Xie (corresponding author): Analytical solution of a nonlocal Poisson-Boltzmann equation with multiple charges in a spherical solute region surrounded by a water spherical shell, Physical Review E, Vol. 105, No. 1, 015305 (14), 2022.
  11. Z. Chao, S. Gui, B. Lu, and D. Xie (corresponding author): Efficient Generation of Membrane and Solvent Tetrahedral Meshes for Finite Element Ion Channel Calculation, arXiv:2201.05707 [math.NA], 2022.
  12. D. Xie: An Efficient Finite Element Iterative Method for Solving a Nonuniform Size Modified Poisson-Boltzmann Ion Channel Model, arXiv:2108.13616 [math.NA] , 2021.
  13. Z. Chao and D. Xie (corresponding author): An Improved Poisson-Nernst-Planck Ion Channel Model and Numerical Studies on Effects of Boundary Conditions,  Membrane Charges, and Bulk Concentrations, Vol. 42 (27), pages 1929–1943, Journal of Computational Chemistry, 2021.
  14. D. Xie and B. Lu: An  Effective Finite Element Iterative Solver for a Poisson-Nernst-Planck Ion Channel Model with Periodic Boundary Conditions, Vol. 42 (6), pages B1490–B1516, SIAM Journal on Scientific Computing, 2020. [PDF]
  15. D. Xie and Z. Chao: A Finite Element Iterative Solver for an Improved PNP Ion Channel Model by Neumann Boundary Condition and Membrane Surface Charge, Vol. 423,109915, Journal of Computational Physics, 2020. [PDF]
  16. D. Xie, S.H. Audi, and R.K. Dash: A Size Modified Poisson-Boltzmann Ion Channel Model in a Solvent of Multiple Ionic Species: Application to VDAC, Journal of Computational Chemistry, Vol 41 (3), pages 218-231, 2020. [PDF]
  17. Z. Chao, D. Xie (corresponding author), and A. H. Sameh: Preconditioners for nonsymmetric indefinite linear systems, Journal of Computational and Applied Mathematics, Vol. 367, pages 1 – 15, 2020. [PDF].
  18. H. Volkmer and D. Xie (corresponding author):  Study of Local and Nonlocal Poisson-Boltzmann Equations for Linear and Nonlinear Models with Spherical Symmetry, Journal of Computational and Applied Mathematics, Vol. 362, pages 653-662, 2019. [PDF].
  19. J. Li, J. Ying, and D. Xie: On the analysis and application of an ion size-modified Poisson-Boltzmann equation, Nonlinear Analysis: Real World Applications, Vol 47, pages 188–203, 2019.
  20. X. Zhang, R.K. Dash, A.V. Clough, D. Xie, E.R. Jacobs, and S.H. Audi: Integrated computational model of lung tissue bioenergetics, Frontiers in Physiology, published on March 8, Vol 10, pages 191, 2019. https://doi.org/10.3389/fphys.2019.00191
  21. D. Xie and Y. Jiang: Nonlocal Poisson-Fermi double layer models: Effects of nonuniform ion sizes on double layer structure, Vol. 97, No. 5, 052610, Physical Review E, 2018. [PDF].
  22. J. Ying and D. Xie: A Hybrid Solver of Size Modified Poisson-Boltzmann Equation by Domain Decomposition, Finite Element, and Finite Difference, Applied Mathematical Modelling, Vol. 58, pages 166–180,  2018. 
  23. J. Ying and D. Xie:  An accelerated nonlocal Poisson-Boltzmann equation solver for electrostatics of biomolecule, International Journal for Numerical Methods in Biomedical Engineering, Vol. 34 (11), e3129, 2018.
  24. H. Volkmer and D. Xie (corresponding author):  Series solutions of local and nonlocal dielectric test models for a solute ball with multiple point charges in an ionic solvent, Communications in Information and Systems, Vol. 18, No. 4, pages 251–268, 2018.
  25.  D. Xie: New Finite Element Iterative Methods for Solving a Nonuniform Ionic Size Modified Poisson-Boltzmann Equation, International Journal of Numerical Analysis & Modeling, Vol. 14, No. 4-5, pages 688–711, 2017. [PDF]
  26. Yang Xie, J. Ying, and D. Xie (corresponding author):  SMPBS: Web server for computing biomolecular electrostatics using finite element solvers of size modified Poisson-Boltzmann equation, Journal of Computational Chemistry, Vol. 38, No. 8, pages 541-552, 2017. [PDF] Web server URL: smpbs.math.uwm.edu
  27. J. Liu, D. Xie, and B. Eisenberg: Poisson-Fermi formulation of nonlocal electrostatics in electrolyte solutions, Molecular Based Mathematical Biology, Vol. 5, No. 1, pages 116–124, 2017. Open Access. 
  28. H. Volkmer and D. Xie (corresponding author): Study of Local and Nonlocal Poisson-Boltzmann Equations for Linear and Nonlinear Models with Spherical Symmetry, submitted, Journal of Computational and Applied Mathematics, 2017.
  29. D. Xie, J. Liu, and B. Eisenberg: Nonlocal Poisson-Fermi Model for Ionic Solvent,  Physical Review E, Vol. 94, page 012114, 2016. [PDF]
  30. D. Xie, J. Liu, B. Eisenberg, L. R. Scott: A Nonlocal Poisson-Fermi Model for Ionic Solvent,  arXiv:1603.05597  [physics.chem-ph], 2016.
  31. D. Xie and Y. Jiang: A Nonlocal Modified Poisson-Boltzmann Equation and Finite Element Solver for Computing Electrostatics of Biomolecules, Journal of Computational Physics, Vol. 322, pages 1-20, 2016. [pdf]
  32. D. Xie, H. Volkmer, and J. Ying: Analytical Solutions of Two Nonlocal Poisson Dielectric Test Models with Spherical Solute Region Containing Multiple Point Charges, Physical Review E, Vol. 93, page 043304, 2016. [PDF]
  33. D. Xie and J. Ying: A New Box Iterative Method for a Class of Nonlinear Interface Problems with Application in Solving Poisson-Boltzmann Equation, Journal of Computational and Applied Mathematics, Vol. 307, pages 319-334, 2016. [pdf]
  34. L. R. Scott and D. Xie: Analysis of a Nonlocal Poisson-Boltzmann Equation, University of Chicago Technical Report TR-2016-01, 2016.
  35. J. Ying and D. Xie (corresponding author): 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]
  36. Y. Jiang, Y. Xie, J. Ying, D. Xie (corresponding author), and Z. Yu: SDPBS web server for calculation of electrostatics of ionic solvated biomolecules, Molecular Based Mathematical Biology, Vol. 3, pages 179-196, 2015. Web server URL: sdpbs.math.uwm.edu
  37. 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.
  38. J. Ying and D. Xie: A Hybrid Solver of Size Modified Poisson-Boltzmann Equation by Domain Decomposition, Finite Element, and Finite Difference, arXiv: 1610.06173 [Math.NA], 2016.
  39. 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]
  40. J. Li and D. Xie (corresponding author): An Effective Minimization Protocol for Solving a Size-modified Poisson-Boltzmann Equation for Biomolecule in Ionic Solvent, International Journal of Numerical Analysis & Modeling, Vol. 12, No. 2, pages 286-301, 2015. [pdf]
  41. J. Li and D. Xie (corresponding author): 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]
  42. 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]
  43. Y. Jiang, J. Ying, and D. Xie (corresponding author): 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]
  44. 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]
  45. 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]
  46. 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]
  47. 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]
  48. 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]
  49. 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]
  50. 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.
  51. D. Xie and L. R. Scott: An analysis of parallel U-cycle method, Tech Report TR-2010-03, University of Chicago, April 2010.
  52. D. Xie: New parallel symmetric SOR preconditioners by multi-type partitioning, International Journal of Computer Mathematics, Vol. 86, No. 2, pages 287-300, 2009. [pdf]
  53. 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]
  54. 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. 
  55. 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]
  56. 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. [pdf]
  57. 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.
  58. 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.
  59. D. Xie: A new block parallel SOR method and its analysis, SIAM J. Sci. Comput., Vol. 27, No. 5,pages 1513-1533, 2006. [pdf]
  60. J. Xie, P. Butko, and D. Xie (corresponding author): Molecular dynamics simulations of the cytolytic toxin Cyt1A in solution, IEEE Trans. Nanobioscience, Vol. 4, No. 3, pages 235-240, 2005. [pdf]
  61. D. Xie: Analysis of a class of parallel multigrid smoothers, BIT Numerical Mathematics, Vol. 44, pages813-828, 2004. [pdf]
  62. 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.) [pdf]
  63. 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.
  64. 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]
  65. 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. [pdf]
  66. 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. [pdf]
  67. 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. [pdf]
  68. 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, pages 267-286, 2000. 
  69. 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. [pdf]
  70. L. R. Scott and D. Xie (corresponding author): 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. [pdf]
  71. 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. [pdf]
  72. 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. [pdf]
  73. 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. [pdf]
  74. D. Xie, New nonlinear multigrid analysis, Proceedings of 1995 Copper Mountain Conference on Multigrid Methods, NASA Conference Publication 3339, 1996. [pdf]
  75. 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.
  76. 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.
  77. 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.
  78. 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]
  79. D. Xie, On the essential assumptions of multigrid convergence proofs, J. Comp. Math., Supplementary Issue, pages 158-164, 1992, (in Chinese).
  80. D. Xie, On the essential assumption and convergence estimation of multigrid analysis, J. Hunan University, 17, pages 103-112, 1990, (in Chinese).
  81. 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).
  82. D. Xie, Analysis of the multigrid iterative algorithms, J. Hunan University, 13, pages 231-237, 1986 (in Chinese).

Last modified December 2, 2023