Publication


    Data assimilation and uncertainty quantification

  1. Archibald R., Bao F., Tu X., "A direct filter method for parameter estimation", J. Comput. Phys. accepted (2019) Link to the published verion .

  2. Tao X., Tu X., Wu H., "A new development in magnetic particle tracking technology and its application in a sheared dense granular flow", Rev. Sci. Instrum. 90(6): 065116 (2019) Link to the published verion .

  3. de Leeuw B., Dubinkina S., Frank J., Steyer A., Tu X., Van Vleck E.,"Projected Shadowing-based Data Assimilation", SIAM J. Appl. Dyn. Syst., 17: 2446-2477 (2018) Link to the published verion .

  4. Lu F., Tu X., Chorin A., "Accounting for model error from unresolved scales in Ensemble Kalman Filters by stochastic parameterization", Mon. Wea. Rev., 145: 3709-3723 (2017) Link to the published verion .

  5. Su C., Tu X., "Sequential implicit sampling methods for Bayesian inverse problems", SIAM/ASA J. Uncertain. Quantif., 5: 519-539 (2017) Link to the published verion .

  6. Gao X., Wang Y., OVerton N., Zupanski M., Tu X., "Data-assimilated computational fluid dynamics modeling of convection-diffusion-reaction problems",J. Comput. Sci.,21: 38-59 (2017) Link to the published verion .

  7. Chorin A., Lu F., Miller R., Morzfeld M., Tu X.,"Sampling, feasibility, and priors in data assimilation", Discrtet Contin. Dyn. Syst., 36: 4227-4246 (2016) Link to the published verion .

  8. Gao X., Wang Y., Overton N.,Zupanski M., Tu X., "Properties of a Modified Ensemble Kalman Filter Algorithm for Combustion Application", AIAA 2016-3484(2016) Link to the published verion .

  9. Gao X.,Wang Y.,Overton N., May I.,Tu X., "Data assimilated computational fluid dynamics algorithm for combustion", AIAA 2016-1810(2016) Link to the published verion .

  10. Morzfeld M.,Tu X.,Wilkening J., Chorin A., "Parameter estimation by implicit sampling", Commun. Appl. Math. Comput. Sci., 10: 205-225 (2015) Link to the published verion .

  11. Lu F.,Morzfeld M., Tu X.,Chorin A., "Limitations of polynomial chaos ex- pansions in the Bayesian solution of inverse problems", J. Comput. Phys., 282:138 -147 (2015) Link to the published verion .

  12. Chorin A., Morzfeld M., Tu X., "A survey of implicit particle filters for data assimilation", "State Space Models--Application in Economics and Finance", Springer series "Statistics and Econometrics for Finance", Volume 1, 63-88 (2013) Full text in pdf. Link to the published verion .

  13. Chorin A., Morzfeld M., Tu X., "Implicit Sampling, with Application to Data Assimilation", Chin. Ann. Math. Ser. B, 34: 89-98 (2013). Full text in pdf. Link to the published verion .

  14. Chorin A. and Tu X., "Interpolation and Iteration for Nonlinear Filters", M2AN Math. Model. Numer. Anal. 46: 535-543 (2012) Full text in pdf.

  15. Morzfeld M., Tu X., Atkins E., and Chorin A., "A Random Map Implementation of Implicit filters", J. Comput. Phys. 231: 2049-2066 (2012) Full text in pdf. Link to the published verion.

  16. Chorin A., Morzfeld M., and Tu X., "Implicit Particle Filters for Data Assimilation", Commun. Appl. Math. Comput. Sci. 5: 221-240 (2010) Full text in pdf. Link to the published verion.

  17. Chorin A. and Tu X., "Implicit Sampling for Particle Filters", P.N.A.S. 106: 17249-17254 (2009) Link to the published version.

    Numerical P.D.E. and scientific computing

  18. Tu X., Zhang J. "BDDC algorithms for advection-diffusion problems with HDG discretizations", Comput. Math. Appl. 101:74 -106(2021). Link to the published verion .

  19. Tu X., Wang B., Zhang J. "Analysis of BDDC algorithms for Stokes problems with hybridizable discontinuous Galerkin discretizations", Electron. Trans. Numer. Anal., 52:553 -570(2020). Link to the published verion .

  20. Tu X., Wang B. "A BDDC algorithm for the Stokes problem with weak Galerkin discretizations", Comput. Math. Appl. 76: 377-392 (2018). Link to the published verion .

  21. Zampini S., Tu X., "Adaptive multilevel BDDC deluxe algorithms for flow in porous media", SIAM J. Sci. Comput. 39: A1389-A1415(2017). Link to the published verion .

  22. Tu X., Wang B., "A BDDC algorithm for second-order elliptic problems with hybridizable discontinuous Galerkin discretizations", Electron. Trans. Numer. Anal., 45:354 -370(2016). Link to the published verion .

  23. Brune P., Knepley M., Smith B., and Tu X, "Composing scalable nonlinear algebraic solvers", SIAM Rev. , 57: 535-565(2015). Link to the published verion .

  24. Tu X., Li J., "A FETI-DP type domain decomposition algorithm for three- dimensional incompressible Stokes equations", SIAM J. Numer. Anal., 53: 720-742(2015). Link to the published verion .

  25. Smith B., Tu X., "Domain Decomposition", Chapter of Encyclopedia of Applied and Computational Mathematics, Springer, 375-381(2015). Link to the published verion .

  26. Li J., Tu X., "A FETI-DP algorithm for incompressible Stokes Equation with continuous pressures", Domain Decomposition Methods in Science and Engineering XXI, Lect. Note. Comput. Sci. Eng.,157 -165(2014). Link to the published verion .

  27. Gander M., Tu X., "On the Origins of Iterative Substructuring Methods",Domain Decomposition Methods in Science and Engineering XXI, Lect. Note. Comput. Sci. Eng., 597-605 (2014). Link to the published verion .

  28. Li J. and Tu X., "A non-overlapping domain decomposition method for incompressible Stokes equations with continuous pressure", SIAM J. Numer. Anal., 51: 1235-1253 (2013). Full text in pdf. Link to the published verion .

  29. Tu X. and Li J., "A unified dual-primal finite element tearing and interconnecting approach for incompressible Stokes equations", Internat. J. Numer. Methods Engrg., 94: 128-149 (2013). Full text in pdf. Link to the published verion .

  30. Liu W., Tu X., and Zhang M., "Poisson-Nernst-Planck Systems for Ion Flow with Density Functional Theory for Hard-Sphere Potential: IV Relations and Critical Potentials. Part II: Numerics", J. Dynam. Differential Equations 24: 955-983 (2012). Full text in pdf. Link to the published verion .

  31. Tu X., "A Three-level BDDC Algorithm for Saddle Point Problems", Numer. Math. 119: 189-217 (2011) Full text in pdf. Link to the published verion.

  32. Li J. and Tu X., "Convergence Analysis of a Balancing Domain Decomposition Method for Solving A Class of Indefinite Linear Systems", Numer. Linear Algebra Appl. 16: 745-773 (2009) Full text in pdf. Link to the published verion.

  33. Kim H. and Tu X., "A Three-level BDDC Algorithm for Mortar Discretization", SIAM J. Numer. Anal. 47, 1576-1600 (2009) Full text in pdf. Link to the published verion.

  34. Tu X. and Li J. ``BDDC for Nonsymmetric Positive Definite and Symmetric Indefinite Problems''. Domain Decomposition Methods in Science and Engineering XVIII, Lect. Note. Comput. Sci. Eng. 70: 75-86 (2009) Full text in pdf. Link to the published verion.

  35. Tu X. and Li J., "A Balancing Domain Decomposition Method by Constraints for Advection-Diffusion Problems", Commun. Appl. Math. Comput. Sci, 3:25-60 (2008) Full text in pdf. Link to the published verion.

  36. Tu X., "Three-Level BDDC in Three Dimensions'', SIAM J. Sci. Comput. 29, 1759--1780 (2007) Full text in pdf. Link to the published verion.

  37. Dryja M. and Tu X., "A Domain Decomposition Discretization of Parabolic Problems'', Numer. Math. 107, 625--640 (2007) Full text in pdf. Link to the published verion.

  38. Tu X., "A BDDC Algorithm for Flow in Porous Media with a Hybrid Finite Element Discretization'', Electron. Trans. Numer. Anal. 26, 146-160 (2007) Full text in pdf. Link to the published verion.

  39. Tu X., "Three-level BDDC in Two Dimensions'', Internat. J. Numer. Methods Engrg. 69, 33-59 (2007) Full text in pdf. Link to the published verion.

  40. Tu X. ``Three-level BDDC''. Domain Decomposition Methods in Science and Engineering XVI, Lect. Note. Comput. Sci. Eng. 55: 437-444 (2007) Link to the published version.

  41. Tu X., "A BDDC Algorithm for Mixed Formulation of Flow in Porous Media'', Electron. Trans. Numer. Anal. 20 (2005), 164-179. Full text in pdf. Link to the published verion.

  42. Sarkis M. and Tu X., "Singular function mortar finite element methods''. Comput. Methods Appl. Math. 3 (2003), no. 1, 202--218. Full text in pdf. Link to the published verion.

  43. Tu X.and Sarkis M. ``Singular function enhanced mortar finite element''. Domain Decomposition Methods in Science and Engineering XIV: 475-482 (2003) Full text in pdf.

  44. Huang H. and Tu X. `` Existence and stability of multiple equilibria in a size-structured cannibalism population model''. (Chinese) Journal of Beijing Normal University (Natural Science) 38 (2002), no. 1, 1--6.

  45. Huang H. and Tu X. ``The Effect of Cannibalism in the Dynamics of the Size-Structured Population Model''. (Chinese) Journal of Beijing Normal University (Natural Science) 37 (2001), no. 5, 580--585.

  46. Huang H. and Tu X. ``The Regulation Effect of Cannibalism in the Dynamics of the Population Model ''. (Chinese) Journal of Beijing Normal University (Natural Science) 36 (2000), no. 6, 735--740.

Submitted Papers


Other Publications


  1. Tu X. `` BDDC Domain Decomposition Algorithms: Methods with Three Levels and for Flow in Porous Media", Ph.D. Dissertation, Courant Institute of Mathematical Sciences, New York University (2006) Full text in pdf.

  2. Tu X., "Enhanced Singular Function Mortar Finite Element Methods", M.S. Thesis, Worcester Polytechnic Institute (2002) Full text in pdf.