Published and accepted

In progress

- M.
Gunzburger, M. Schneier, C. Webster, and G. Zhang, An improved discrete
least-squares/reduced-basis method for parameterized elliptic PDEs, Journal of Scientific Computing, accepted (arXiv:1710.01237).

- P. Jantsch, C. Webster and G. Zhang, On the Lebesgue constants of weighted Leja points for Lagrange interpolation on unbounded domains, IMA Journal on Numerical Analysis, accepted (arXiv:1606.07093).
- E. Hirvijoki, C. Liu, G. Zhang, D. del-Castillo-Negrete, and D. Brennan, A fluid-kinetic framework for self-consistent runaway-electron simulations, Physics of Plasmas, 25 (2018), pp. 062507.
- J.
Yang, G. Zhang and W. Zhao, A first-order numerical scheme for
forward-backward stochastic differential equations in bounded domains, Journal of Computational Mathematics, 36 (2018), pp. 237-258. [PDF, bibtex]

- S.
Mo, D. Lu, X. Shi, G. Zhang, M. Ye, J. Wu and J. Wu, A Taylor
expansion-based adaptive design strategy for global surrogate modeling
with applications in multiphase flow simulation, Water Resources Research, 53 (2017), pp. 10802-10823. [PDF, bibtex]

- H. Tran, C. Webster and G. Zhang, Analysis of quasi-optimal polynomial approximations for parameterized PDEs with deterministic and stochastic coefficients, Numerishe Mathematik, 137 (2017), pp. 451-493. [PDF, bibtex]
- G. Zhang, and D. del-Castillo-Negrete, A backward Monte-Carlo method for time-dependent runaway electron simulations, Physics of Plasmas, 24 (2017), pp. 092511. [PDF, bibtex]

- W. Zhao, W. Zhang and G. Zhang, Second-order numerical
schemes for decoupled forward-backward stochastic differential
equations with jumps, Journal of Computational Mathematics, 35 (2017), pp. 213-244. [PDF, bibtex]

- Q. Guan, M. Gunzburger, C. Webster and G. Zhang, Reduced basis methods for nonlocal diffusion problems with random input data, Computer Methods in Applied Mechanics and Engineering, 317 (2017), pp. 746-770. [PDF, bibtex]
- M. Xi, D. Lu, D. Gui, Z. Qi and G. Zhang, Calibration of an
agricultural-hydrological model (RZWQM2) using surrogate global
optimization, Journal of Hydrology, 544 (2017), pp. 456-466. [PDF, bibtex]

- D.
Lu, G. Zhang, C.
Webster and C. Barbier, An improved multilevel Monte Carlo method for
estimating probability distribution functions in stochastic oil
reservoir simulations, Water Resources Research, 52 (2016), pp. 9642-9660. [PDF, bibtex]

- F. Bao, Y. Tang, M. Summers, G. Zhang, C. Webster, V. Scarola and
T.A. Maier, Efficient stochastic optimization for analytic
continuation, Physical Review B, 94 (2016), pp. 125149. [PDF, bibtex]

- D. Galindo, P. Jantsch, C. Webster and G. Zhang,
Accelerating hierarchical stochastic collocation methods for partial
differential equations with random input data, SIAM/ASA Journal on Uncertainty Quantification, 4 (2016), pp. 1111-1137. [PDF, bibtex]

- G. Zhang, C. Webster, M.
Gunzburger and J. Burkardt, Hyperspherical sparse approximation techniques for high-dimensional discontinuity detection, SIAM Review, 58 (2016), pp. 517-551. [PDF, bibtex]

- F. Bao, Y. Cao, C. Webster and G. Zhang, An efficient meshfree implicit filter for nonlinear filtering problems, International Journal for Uncertainty Quantification, 6 (2016), pp. 19-33. [PDF, bibtex]

- G. Zhang, W. Zhao, M. Gunzburger and C. Webster, Numerical methods for a class of nonlocal diffusion problems with the use of backward SDEs, Computers & Mathematics with Applications, 71 (2016), pp. 2479-2496. [PDF, bibtex]
- H. Tran, C. Webster and G. Zhang, A sparse grid method for Bayesian uncertainty quantification with application to large eddy simulation turbulence models, Springer Lecture Notes on CS&E, 109 (2016), pp. 291-313. [PDF, bibtex]
- N. Dexter, C. Webster and G. Zhang, Explicit cost bounds of stochastic Galerkin approximations for parametertized PDEs with random coefficients, Computers & Mathematics with Applications, 71 (2016), pp. 2231-2256. [PDF, bibtex]
- G. Zhang, C. Webster, M.
Gunzburger and J. Burkardt, A hyper-spherical adaptive sparse-grid method for high-dimensional discontinuity detection, SIAM Journal of Numerical Analysis, 53 (2015), pp. 1508-1536. [PDF, bibtex]

- M. Gunzburger, C. Webster and G. Zhang, Sparse collocation methods for stochastic interpolation and quadrature, Handbook of Uncertainty Quantification, pp. 1-46, Springer International Publishing, Switzerland, 2016. [PDF, bibtex]

- V.
Reshniak, A. Khaliq, D. Voss and G. Zhang, Split-step Milstein methods
for multi-channel stiff stochastic differential systems, Applied Numerical Mathematics, 89 (2015), pp. 1-23. [PDF, bibtex]

- F. Bao, Y. Cao, C. Webster and G. Zhang,
A hybrid sparse-grid approach for nonlinear filtering problems based on adaptive domain of the Zakai equation approximations, SIAM/ASA Journal on Uncertainty Quantification, 2 (2014), pp. 784-804. [PDF, bibtex]

- M. Gunzburger, C. Webster and G. Zhang, Stochastic finite element methods for partial differential equations with random input data, Acta Numerica, 23 (2014), pp. 521-650. [PDF, bibtex]
- C.
Webster, G. Zhang and M. Gunzburger, An adaptive sparse-grid-based
iterative ensemble Kalman filter approach for parameter field
estimation, International Journal of Computer Mathematics, 91 (2014), pp. 798-817. [PDF, bibtex]

- X. Zhang, C. Liu, B. Hu and G. Zhang, Uncertainty analysis of multi-rate kinetics of uranium desorption from sediments, Journal of Contaminant Hydrology, 156 (2014), pp. 1-15. [PDF, bibtex]

- M. Gunzburger, C. Webster, G. Zhang,
An adaptive wavelet stochastic collocation method for irregular
solutions of partial differential equations with random input data, Springer Lecture Notes on CS&E, 97 (2014), pp. 137-170. [PDF, bibtex]

- G. Zhang, D. Lu, M. Ye, M. Gunzburger and C. Webster, An
efficient surrogate modeling approach in Bayesian uncertainty analysis,
AIP Conference Proceedings, 1558 (2013), pp. 898-901. [PDF, bibtex]

- G. Zhang,
D. Lu, M. Ye, M. Gunzburger and C. Webster, An adaptive sparse-grid
high-order stochastic collocation method for Bayesian inference in
groundwater reactive transport modeling, Water Resources Research, 49 (2013), pp. 6871-6892. [PDF, bibtex]

- G. Zhang, M. Gunzburger and W. Zhao, A sparse-grid method for multi-dimensional backward stochastic differential equations, Journal of Computational Mathematics, 31 (2013), pp. 221-248. [PDF, bibtex]

- G. Zhang
and M. Gunzburger, Error analysis of a stochastic collocation method
for parabolic partial differential equations with random input data, SIAM Journal on Numerical Analysis, 50 (2012), pp. 1922-1940. [PDF, bibtex]

- W. Zhao, Y. Li and G. Zhang, A generalized theta-scheme for solving backward stochastic differential equations, Discrete and Continuous Dynamical Systems - Series B, 17 (2012), pp. 1585-1603. [PDF, bibtex]

- W. Zhao, G. Zhang and L. Ju, A stable multi-step scheme for solving backward stochastic differential equations, SIAM Journal on Numerical Analysis, 48 (2010), pp. 1369-1394. [PDF, bibtex]

In progress

- L. Mu and G. Zhang, A domain-decomposition model reduction method for linear convection-diffusion equations with random coefficients, SIAM Journal on Scientific Comptuing, in revision (arXiv:1802.04187).
- M. Stoyanov and G. Zhang, A multilevel reduced-basis method for parameterized partial differential equations, SIAM Journal on Scientific Comptuing, submitted.
- X. Xie, G. Zhang and C. Webster, Non-intrusive inference reduced order model for fluids using linear multistep neural network, submitted (arXiv:1809.07820).
- G. Zhang and D. del-Castillo-Negrete, An improved backward Monte-Carlo method for runaway electron simulations with time-dependent electrical fields, preprint.
- G. Zhang and D. del-Castillo-Negrete, A probabilistic adaptive semi-Lagrangian algorithm for the time-dependent anisotropic heat transport equation, submitted.
- M. Yang, G. Zhang and Y. Cao, An efficient probabilistic scheme for quasi-linear nonlocal diffusion equations in three-dimensional irregular domains with applications in groundwater flow, preprint.
- G. Zhang and J. Hinkle, ResNet-based isosurface learning for
dimensionality reduction in high-dimensional function approximation
with limited data, preprint (arXiv:1902.10652)