Publications
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Y. Geng, J. Singh, L. Ju, B. Kramer, and Z. Wang
Gradient Preserving Operator Inference: Data-Driven Reduced-Order Models for Equations with Gradient Structure.
Comput. Meth. Appl. Mech. Eng., Vol. 427, 2024, Article 117033. -
Y. Geng, Y. Teng, Z. Wang and L. Ju
A deep learning method for the dynamics of classic and conservative Allen-Chan equations based on fully-discrete operators.
J. Comput. Phy., Vol. 496, 2024, Article 112589. -
R. Lan, L. Ju, Z. Wang and M. Gunzburger
A second-order implicit-explicit scheme for the baroclinic-barotropic split system of primitive equations.
Commun. Comput. Phys., Vol. 34 (5), 2023, pp. 1306-1331. -
Y. Teng, Z. Wang, L. Ju, A. Gruber and G. Zhang
Level Set Learning and Function Approximation on Sparse Data through Pseudo-Reversible Neural Network.
SIAM J. Sci. Comput., Vol. 45 (3), 2023, pp. A1148-A1171. -
A. Gruber, M. Gunzburger, L. Ju, R. Lan and Z. Wang
Multifidelity Monte Carlo Estimation for Efficient Uncertainty Quantification in Climate-Related Modeling.
Geosci. Model Dev., Vol. 16 (4), 2023, pp. 1213-1229. -
A. Gruber, M. Gunzburger, L. Ju and Z. Wang
Energetically consistent model reduction for metriplectic systems.
Comput. Meth. Appl. Mech. Eng., Vol. 404, 2023, Article 115709. -
A. Gruber, M. Gunzburger, L. Ju and Z. Wang
A multifidelity Monte Carlo method for realistic computational budgets.
J. Sci. Comput., Vol. 94, 2023, Article 2. -
Y. Chen, L. Ji and Z. Wang
A Hyper-Reduced MAC Scheme for the Parametric Stokes and Navier-Stokes Equations.
J. Comp. Phys., Vol. 466, 2022, Article 111412. -
B. Koc, C. Mou, H. Liu, Z. Wang, G. Rozza, and T. Iliescu
Verifiability of the Data-Driven Variational Multiscale Reduced Order Model.
J. Sci. Comput, Vol. 93, 2022, Article 54. -
W. Dahmen, M. Wang and Z. Wang
Nonlinear Reduced DNN Models for State Estimation.
Commun. Comput. Phys. , vol. 32 (1), 2022, pp.1-40 -
W. Hu, J. Liu and Z. Wang
Bilinear Control of Convection-Cooling: From Open-Loop to Closed-Loop.
Appl. Math. Optim., vol. 86, 2022, Article 5. -
R. Lan, L. Ju, Z. Wang, M. Gunzburger and P. Jones
High-Order Multirate Explicit Time- Stepping Schemes for the Baroclinic-Barotropic Split Dynamics in Primitive Equations.
J. Comp. Phys., Vol. 457, 2022, Article 111050. -
A. Gruber, M. Gunzburger, L. Ju and Z. Wang
A Comparison of Neural Network Architectures for Data-Driven Reduced-Order Modeling.
Comput. Meth. Appl. Mech. Eng., Vol. 393, 2022, Article 114764. -
X. Feng, Y. Luo, L. Vo and Z. Wang
An Efficient Iterative Method for Solving Parameter- Dependent and Random Diffusion Problems.
J. Sci. Comput., Vol. 90, 2022, Article 72. -
H. Sharma, Z. Wang and B. Kramer
Hamiltonian Operator Inference: physics-preserving Learning of Reduced-order Models for Hamiltonian Systems.
Physica D: Nonlinear Phenomena, Vol. 431, 2022, 133122. -
 
  
J. Liu and Z. Wang
A ROM-accelerated Parallel-in-time Preconditioner for Solving All-at- once Systems from Evolutionary PDEs.
Appl. Math. Comput., Vol. 416, 2021, 126750. -
 
  
L. Feng, G. Fu and Z. Wang
A FOM/ROM Hybrid Approach for Accelerating Numerical Simulations.
J. Sci. Comput., Vol. 89, 2021, Article 61. -
 
  
R. Lan, W. Leng, Z. Wang, L. Ju and M. Gunzburger
Parallel Exponential Time Differencing Methods for Geophysical Flow Simulations.
Comput. Meth. Appl. Mech. Eng., vol. 387, 2021, 114151. -
 
  
C. Mou, Z. Wang, D. Wells, X. Xie and T. Iliescu
Reduced Order Models for the Quasi- Geostrophic Equations: A Brief Survey.
Fluids, vol. 6(1), 2021, 16. -
 
  
X. Meng, T. Hoang, Z. Wang, and L. Ju
Localized exponential time differencing methods for shallow water equations: algorithms and numerical study.
Commun. Comput. Phys., Vol. 29(1), 2021, pp. 80-110. -
 
  
A. Gruber, M. Gunzburger, L. Ju, Y. Teng and Z. Wang
Nonlinear Level Set Learning for Function Approximation on Sparse Data with Applications to Parametric Differential Equations.
Numer. Math. Theor. Meth. Appl., Vol. 14(4), 2021, pp. 839-861. -
 
  
G. Fu and Z. Wang
POD-(H)DG method for incompressible flow simulations.
J. Sci. Comput., Vol. 85, 2020, Article 24. -
 
  
L. Ju, W. Leng, Z. Wang, and S. Yuan
Numerical investigation of ensemble methods with block iterative solvers for evolution problems.
Discrete Contin. Dyn. Syst. Ser. B., Vol. 25(12), 2020, pp. 4905-4923. -
 
  
T. Hoang, L. Ju, and Z. Wang
Nonoverlapping localized Exponential time differencing methods for diffusion problems.
J. Sci. Comput., Vol. 82, 2020, Article 37. -
 
  
T. Hoang, L. Ju, W. Leng, and Z. Wang
High order explicit local time-stepping methods for hyperbolic conservation laws.
Math. Comp., vol. 89, 2020, pp. 1807-1842. -
 
  
M. Gunzburger, N. Jiang and Z. Wang
An efficient algorithm for simulating ensembles of parameterized flow problems,
IMA J. Numer. Anal., vol. 39 (3), 2019, pp. 1180-1205. -
 
  
M. Gunzburger, N. Jiang and Z. Wang
A second-order time-stepping scheme for simulating ensembles of parameterized flow problems,
Comput. Math. Appl. Math., vol. 19 (3), 2019, pp. 681-701. -
J. Liu and Z. Wang
Non-commutative discretize-then-optimize algorithms for elliptic PDE-constrained optimal control problems.
J. Comp. Appl. Math., vol. 362, 2019, pp. 596-613. -
 
  
T. Hoang, W. Leng, L. Ju, Z. Wang, and K. Pieper
Conservative explicit local time-stepping schemes for the shallow water equations.
J. Comp. Phys., vol. 382, 2019, pp. 152-176. -
 
  
Y. Luo and Z. Wang
A Multilevel Monte Carlo Ensemble Scheme for Solving Random Parabolic PDEs.
SIAM J. Sci. Comput., vol. 41 (1), 2019, pp. A622–A642. -
 
  
Y. Luo and Z. Wang
An ensemble algorithm for numerical solutions to deterministic and random parabolic PDEs.
SIAM J. Numer. Anal., vol. 56 (2), 2018, pp. 859-876. -
 
  
T. Hoang, L. Ju and Z. Wang
Overlapping localized exponential time differencing methods for diffusion problems.
Comm. Math. Sci., vol. 16 (6), 2018, pp. 1531-1555. -
 
  
J. Liu and Z. Wang
Efficient time domain decomposition algorithms for parabolic PDE-constrained optimization problems,
Comput. Math. Appl., vol. 75 (6), 2018, pp. 2115-2133. -
 
  
H. Fu, H. Wang, and Z. Wang
POD/DEIM Reduced-Order Modeling of Time-Fractional Partial Differential Equations with Applications in Parameter Identification.
J. Sci. Comput., vol. 74 (1), 2018, pp. 220-243. -
 
  
X. Xie, D. Wells, Z. Wang, and T. Iliescu
Numerical analysis of the Leray reduced order model.
J. Comp. Appl. Math., vol. 328, 2018, pp. 12-29. -
 
  
B. Cockburn and Z. Wang
Adjoint-based, superconvergent Galerkin approximations of linear functionals.
J. Sci. Comput., vol. 73 (2-3), 2017, pp. 644-666. -
 
  
L. Ju and Z. Wang
Exponential Time Differencing Gauge Method for Incompressible Viscous Flows.
Commun. Comput. Phys., vol. 22, 2017, pp. 517-541. -
 
  
D. Wells, Z. Wang, X. Xie and T. Iliescu
An Evolve-Then-Filter Regularized Reduced Order Model For Convection-Dominated Flows.
Int. J. Numer. Meth. Fluids, vol. 84, 2017, pp. 598-615. -
 
  
Y. Gong, Q. Wang and Z. Wang
Structure-Preserving Galerkin POD Reduced-Order Modeling of Hamiltonian Systems.
Comput. Meth. Appl. Mech. Eng., vol. 315, 2017, pp. 780-798. -
 
  
X. Xie, D. Wells, Z. Wang, and T. Iliescu
Approximate Deconvolution Reduced Order Modeling,
Comput. Meth. Appl. Mech. Eng., vol. 313, 2017, pp. 512-534. -
 
  
J. Borggaard, Z. Wang and L. Zietsman
A Goal-Oriented Model Reduction Approach for Complex Systems,
Comput. Math. Appl., vol. 71 (11), 2016, pp. 2155–2169. -
 
  
Z. Wang, B. McBee and T. Iliescu
Approximate Partitioned Methods of Snapshots for POD.
J. Comput. Appl. Math., vol. 307, 2016, pp. 374-384. -
 
   L. Rondi, F. Santosa and Z. Wang
A Variational Approach to the Inverse Photolithography Problem.
SIAM J. Appl. Math., vol. 76 (1), 2016, pp. 110-137. -
 
   Z. Wang
Nonlinear Model Reduction Based on the Finite Element Method With Interpolated Coefficients: Semilinear Parabolic Equations.
Numer. Meth. Partial. Diff. Eqs., vol. 31 (6), 2015, pp. 1713-1741. -
 
   T. Iliescu and Z. Wang
Are the Snapshot Difference Quotients Needed in the Proper Orthogonal Decomposition?
SIAM J. Sci. Comput., vol. 36 (3), 2014, pp. A1221-A1250. -
 
   T. Iliescu and Z. Wang
Variational Multiscale Proper Orthogonal Decomposition: Navier-Stokes Equations.
Numer. Meth. Partial. Diff. Eqs., vol. 30, 2014, pp. 641-663. -
 
   T. Iliescu and Z. Wang
Variational Multiscale Proper Orthogonal Decomposition: Convection-Dominated Convection-Diffusion-Reaction Equations.
Math. Comp., vol. 82, 2013, pp. 1357-1378. -
 
   E. Foster, T. Iliescu, and Z. Wang
A Finite Element Discretization of the Streamfunction Formulation of the Stationary Quasi-Geostrophic Equations of the Ocean.
Comput. Meth. Appl. Mech. Eng., vol. 261-262, 2013, pp. 105-117. -
 
   J. Huang, Z. Wang and R. Zhu
Asymptotic Error Expansions for Hypersingular Integrals.
Adv. Comput. Math., vol. 38 (2), 2013, pp. 257-279. -
 
   Z. Wang, I. Akhtar, J. Borggaard and T. Iliescu
Proper Orthogonal Decomposition Closure Models for Turbulent Flows: A Numerical Comparison.
Comput. Meth. Appl. Mech. Eng., vol. 237-240, 2012, pp. 10-26. -
 
   I. Akhtar, Z. Wang, J. Borggaard and T. Iliescu
A New Closure Strategy for Proper Orthogonal Decomposition Reduced-Order Models.
J. Comp. Nonlinear Dynamics, vol. 7 (3), 034503, 2012. -
           O. Roderick, M. Anitescu and Z. Wang
Reduced Order Approximations in Uncertainty Analysis of Nuclear Engineering Applications.
Trans. Am. Nucl. Soc., vol. 106, 2012. -
 
   W. Feng, X. He, Z. Wang and X. Zhang
Non-Iterative Domain Decomposition Methods for a Non-Stationary Stokes-Darcy Model with Beavers-Joseph Interface Condition.
Appl. Math. Comput., vol. 219 (2), 2012, pp. 453-463. -
 
   P. Cheng, J. Huang and Z. Wang
Nystrom Methods and Extrapolation for Solving Steklov Eigensolutions and its Application in Elasticity.
Numer. Meth. Partial. Diff. Eqs., vol. 28 (6), 2012, pp. 2021-2040. -
 
   P. Cheng, X. Luo, Z. Wang and J. Huang
Mechanical Quadrature Methods and Extrapolation Algorithms for Boundary Integral Equations with Linear Boundary Conditions in Elasticity.
J. Elasticity, vol. 108 (2), 2012, pp. 193-207. -
 
   Z. Wang, I. Akhtar, J. Borggaard and T. Iliescu
Two-Level Discretizations of Nonlinear Closure Models for Proper Orthogonal Decomposition.
J. Comput. Phys., vol. 230 (1), 2011, pp. 126-146. -
 
   J. Borggaard, T. Iliescu and Z. Wang
Artificial Viscosity Proper Orthogonal Decomposition.
Math. Comput. Model., vol. 53 (1-2), 2011, pp. 269-279. -
           O. Roderick, Z. Wang and M. Anitescu
Dimensionality Reduction for Uncertainty Quantification of Nuclear Engineering Models.
Trans. Am. Nucl. Soc., vol. 104, 2011. -
 
   O. San, A. E. Staples, Z. Wang and T. Iliescu
Approximate Deconvolution Large Eddy Simulation of a Barotropic Ocean Circulation Model.
Ocean Modelling, vol. 40, 2011, pp. 120-132. -
 
   P. Cheng, J. Huang and Z. Wang
Mechanical Quadrature Methods and Extrapolation for Solving Nonlinear Boundary Helmholtz Integral Equations.
Appl. Math. Mech. (Eng. Ed.), vol. 32 (12), 2011, pp. 1505-1514. -
 
   B. Hu and Z. Wang
Combined Hybrid Method Applied in the Reissner-Mindlin Plate Model.
Finite Elem. Anal. Des., vol. 46 (5), 2010, pp. 428-437. -
 
   J. Huang and Z. Wang
Extrapolation Algorithms for Solving Mixed Boundary Integral Equations of the Helmholtz Equation by Mechanical Quadrature Methods.
SIAM J. Sci. Comput., vol. 31 (6), 2009, pp. 4115-4129. -
 
   Z. Wang and B. Hu
Research of Combined Hybrid Method Applied in the Reissner-Mindlin Plate Model.
Appl. Math. Comput., vol. 182 (1), 2006, pp. 49-66. -
J. Liu, B. Hu, Y. Xu and Z. Wang
A semi-discrete mixed finite element method for the Sobolev equation.
Sichuan Daxue Xuebao, vol. 46 (2), 2009, pp. 297-301. -
B. Hu, Z. Wang and Y. Xu
Improvement of the Selective Reduced Integration Element S1 for the Reissner-Mindlin Plate.
Sichuan Daxue Xuebo, vol. 43 (1), 2006, pp. 47-51. -
Y. Zhang, B. Hu and Z. Wang
Combined Hybrid Finite Element Methods for the Poisson Equation.
Sichuan Daxue Xuebao, vol. 42 (3), 2005, pp. 467-470. -
Y. Wu, J. Zhou, Z. Wang and Y. Zeng
Parameter Estimation of Weibull Distribution Using the EM Algorithm Based on Randomly Censored Date.
Sichuan Daxue Xuebao, vol. 42 (5), 2005, pp. 910-913.
several papers in Chinese
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I. Akhtar, Z. Wang, J. Borggaard and T. Iliescu
A Novel Strategy for Nonlinear Closure in Proper Orthogonal Decomposition Reduced-Order Models.
ASME ECTC October 1-2, 2010. -
I. Akhtar, Z. Wang, J. Borggaard and T. Iliescu
Large Eddy Simulation Ideas for Nonlinear Closure in Model Reduction of Fluid Flows.
AIAA 2010-5089. -
I. Akhtar, J. Borggaard, T. Iliescu and Z. Wang
Closure for Improved Reduced-order Models using High Performance Computing.
AIAA 2010-1276. -
J. Borggaard, A. Duggleby, A. Hay, T. Iliescu and Z. Wang
Reduced-order Modeling of Turbulent Flows.
In Proceedings of MTNS, 2008.