Book

D. Xiu, Numerical Methods for Stochastic Computations: A Spectral Method Approach, Princeton University Press, 2010. ISBN-10: 0691142122, ISBN-13: 978-0691142128.

Publication

1. D. Xiu and G.E. Karniadakis, A Semi-Lagrangian High-Order Method for Navier-Stokes Equations, J. Comput. Phys. 172, 658-684 (2001).

2. D. Xiu and G.E. Karniadakis, Modeling Uncertainty in Flow Simulations via Generalized Polynomial Chaos, J. Comput. Phys. 187, 137-167 (2003).

3. D. Xiu and G.E. Karniadakis, The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations, SIAM J. Sci. Comput., 24(2), 619-644 (2002).

4. J. Xu, D. Xiu and G.E. Karniadakis, A Semi-Lagrangian Method for Turbulence Simulations Using Mixed Spectral Discretizations, J. Sci. Comput. 17, 585-597 (2002).

5. D. Xiu, D. Lucor, C.-H. Su and G.E. Karniadakis, Stochastic Modeling of Flow-Structure Interactions using Generalized Polynomial Chaos, J. Fluids Engrg. 124, 51-59 (2002).

6. D. Xiu and G.E. Karniadakis, Modeling Uncertainty in Steady State Diffusion Problems via Generalized Polynomial Chaos, Comput. Methods Appl. Mech. Engrg. 191, 4927-4948 (2002).

7. D. Lucor, D. Xiu, C.-H. Su and G.E. Karniadakis, Predictability and Uncertainty in CFD, Int. J. Numer. Methods Fluids, 43, 483-505 (2003).

8. D. Xiu and G.E. Karniadakis, A New Stochastic Approach to Transient Heat Conduction Modeling with Uncertainty, Int. J. Heat & Mass Transfer, 46(24), 4681-4693 (2003).

9. X. Wan, D. Xiu and G.E. Karniadakis, Stochastic Solutions for the Two-dimensional Advection-Diffusion Equation, SIAM J. Sci. Comput., 26(2), 578-590 (2004).

10. D. Xiu and G.E. Karniadakis, Supersensitivity Due to Uncertain Boundary Conditions, Int. J. Numer. Meth. Engng., 61(12), 2114-2138 (2004).

11. D. Xiu, S.J. Sherwin, S. Dong and G.E. Karniadakis, Strong and Auxiliary Forms of the Semi-Lagrangian Method for Incompressible Flows, J. Sci. Comput., 25, 323-346 (2005).

12. D. Xiu, and D.M. Tartakovsky, A Two-scale Non-perturbative Approach to Uncertainty Analysis of Diffusion in Random Composites, SIAM J. Multiscale Modeling & Simulation, 2(4), 662-674 (2004).

13. S. Sirisup, G.E. Karniadakis, D. Xiu and I.G. Kevrekidis, Equation-free/Galerkin-free POD-assisted Computation of Incompressible Flows, J. Comput. Phys., 207, 568-587 (2005).

14. D. Xiu and D.M. Tartakovsky, Numerical Methods for Differential Equations in Random Domains, SIAM J. Sci. Comput., 28(3), 1167-1185 (2006).

15. D. Xiu and I.G. Kevrekidis, Equation-free, Multiscale Computation for Unsteady Random Diffusion, SIAM J. Multiscale Modeling & Simulation, 4(3), 915-935 (2005).

16. D. Xiu and J.S. Hesthaven, High Order Collocation Methods for Differential Equations with Random Inputs, SIAM J. Sci. Comput., 27(3), 1118-1139 (2005).

17. D. Xiu, R. Ghanem and I.G. Kevrekidis, An Equation-free, Multiscale Computational Approach to Uncertainty Quantification for Dynamical Systems, IEEE Computing in Science and Engineering Journal (CiSE), 7(3), 16-23 (2005).

18. D.M. Tartakovsky and D. Xiu, Stochastic Analysis of Transport in Tubes with Rough Walls, J. Comput. Phys., 217(1), 248-259 (2006).

19. D. Xiu and J. Shen, An Efficient Spectral Method for Acoustic Scattering from Rough Surfaces, Comm. Comput. Phys., 2(1), 54-72 (2007)

20. D. Xiu, Efficient Collocational Approach for Parametric Uncertainty Analysis, Comm. Comput. Phys., 2(2), 293-309 (2007)

21. S.E. Geneser, R.M. Kirby, D. Xiu and F.B. Sachse, Stochastic Markovian Modeling of Electrophysiology of Ion Channels: Reconstruction of Standard Deviations in Macroscopic Currents, J. Theo. Bio., 245(4), 627-637 (2007).

22. D. Xiu and S.J. Sherwin, Parametric Uncertainty Analysis of Pulse Wave Propagation in a Model of a Human Arterial Networks, J. Comput. Phys., 226, 1385-1407 (2007).

23. D. Xiu, Fast Numerical Methods for Robust Optimal Design, Eng. Opt., 40(6), 489-504 (2008).

24. D. Gottlieb and D. Xiu, Galerkin Method for Wave Equations with Uncertain Coefficients, Comm. Comput. Phys., 3(2), 505-518 (2008).

25. D. Xiu, Numerical Integration Formulas of Degree Two, Appl. Numer. Math., 58(10), 1515-1520 (2008)

26. J. Li and D. Xiu, On Numerical Properties of the Ensemble Kalman Filter for Data Assimilation, Comput. Methods Appl. Mech. Engrg., 197, 3574-3583 (2008).

27. D. Xiu and J. Shen, Efficient Stochastic Galerkin Methods for Random Diffusion Equations, J. Comput. Phys., 228, 266-281 (2009).

28. D. Xiu, Fast Numerical Methods for Stochastic Computations: a Review, Comm. Comput. Phys., 5, 242-272 (2009).

29. R. Archibald, A. Gelb, R. Saxena and D. Xiu, Discontinuity Detection in Multivariate Space for Stochastic Simulations, J. Comput. Phys., 228(7), 2676-2689 (2009).

30. J. Li and D. Xiu, A Generalized Polynomial Chaos Based Ensemble Kalman Filter with High Accuracy, J. Comput. Phys., 228, 5454-5469 (2009).

31. Y. Marzouk and D. Xiu, A Stochastic Collocation Approach to Bayesian Inference in Inverse Problems, Comm. Comput. Phys., 6(4), 826-847 (2009).

32. G.T. Buzzard and D. Xiu, Variance-based Global Sensitivity Analysis via Sparse-grid Interpolation and Cubature, Comm. Comput. Phys., 9(3), 542-567 (2011).

33. R. Pulch and D. Xiu, Generalised Polynomial Chaos for Linear Conservation Laws, J. Sci. Comput., 51, 293-312 (2012).

34. X. Guo, J. Li, D. Xiu and A. Alexeenko, Uncertainty Quantification Models for Microscale Squeeze-Film Damping, Int. J. Numer. Methods Eng., 84, 1257-1272 (2010).

35. J. Jakeman, M. Eldred and D. Xiu, Numerical Approach for Quantification of Epistemic Uncertainty, J. Comput. Phys., 229, 4648-4663 (2010).

36. A. Narayan and D. Xiu, Distributional Sensitivity for Uncertainty Quantification, Comm. Comput. Phys., 10(1), 140-160 (2011).

37. Jing Li and D. Xiu, Evaluation of Failure Probability via Surrogate Models, J. Comput. Phys., 229, 8966-8980 (2010).

38. J. Jakeman, R. Archibald and D. Xiu, Characterization of Discontinuities in High-dimensional Stochastic Problmes on Adaptive Sparse Grids, J. Comput. Phys., 230, 3977-3997 (2011).

39. P. Tsuji, D. Xiu and L. Ying, A Fast Method for High-frequency Acoustic Scattering from Random Scatterers, Int. J. Uncertainty Quantification, 1, 99-117 (2011).

40. J. Li, J. Li and D. Xiu, An Efficient Surrogate-based Method for Computing Rare Failure Probability, J. Comput. Phys., 230, 8683-8697 (2011) .

41. L. Yan, L. Guo and D. Xiu, Polynomial Approximation via l1-minimization in High Dimensional Space, Int. J. Uncertainty Quantification, 2(3), 279-293, (2012).

42. A. Narayan and D. Xiu, Stochastic Collocation Methods on Unstructured Grids in High Dimensions via Interpolation, SIAM J. Sci. Comput., 34(3), A1729-A1752, 2012.

43. H. Tiesler, R.M. Kirby, D. Xiu, T. Preusser, Stochastic Collocation for Optimal Control Problems with Stochastic PDE Constraints, SIAM J. Control Opt., 50(5), 2659-2682, (2012).

44. A. Narayan, Y. Marzouk and D. Xiu, Sequential Data Assimilation with Multiple Models, J. Comput. Phys., 231, 6401-6418 (2012).

45. K. Potter, R.M. Kirby, D. Xiu and C.R. Johnson, Interactive Visualization of Probability and Cumulative Density Functions, Int J. Uncertainty Quantification, 2(4), 397-412 (2012).

46. C. Yang, D. Xiu and R.M. Kirby, Visualization of Covariance and Cross-covariance Fields, Int. J. Uncertainty Quantification, 3(1), 25-38 (2013).

47. J. Li and D. Xiu, Computation of Failure Probability Subject to Epistemic Uncertainty, SIAM J. Sci. Comput., 34(6), A2946-A2964 (2012).

48. J. Li, X. Qi and D. Xiu, On Upper and Lower Bounds for Quantity of Interest in Problems Subject to Epistemic Uncertainty, SIAM J. Sci. Comput., 36(2), A363-A376 (2014).

49. J. Li and D. Xiu, Surrogate Based Method for Evaluation of Failure Probability Under Multiple Constraints, SIAM J. Sci. Comput., 36(2), A828-A845 (2014).

50. A. Narayan and D. Xiu, Constructing Nested Nodal Sets for Multivariate Polynomial Interpolation, SIAM J. Sci. Comput., 35(5), A2293-A2315, 2013.

51. J. Jakeman, A. Narayan and D. Xiu, Minimal Multi-element Stochastic Collocation for Uncertainty Quantification of Discontinuous Functions, J. Comput. Phys., 242, 790-808 (2013).

52. X. Chen, E.-J. Park and D. Xiu, A Flexible Numerical Approach for Quantification of Epistemic Uncertainty, J. Comput. Phys., 240, 211-224, 2013.

53. A. Narayan, C. Gittelson and D. Xiu, A Stochastic Collocation Algorithm with Multifidelity Models, SIAM J. Sci. Comput., 36(2), A495-A521 (2014).

54. X. Zhu, A. Narayan and D. Xiu, Computational Aspects of Stochastic Collocation with Multi-fidelity Models, SIAM J. UQ., 2013 (submitted).

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