Publications

Refereed Journal Articles

    In Print

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. W. Dahmen, M. Wang and Z. Wang
    Nonlinear Reduced DNN Models for State Estimation.
    Commun. Comput. Phys. , vol. 32 (1), 2022, pp.1-40

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16.     

    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.

  17.     

    L. Feng, G. Fu and Z. Wang
    A FOM/ROM Hybrid Approach for Accelerating Numerical Simulations.
    J. Sci. Comput., Vol. 89, 2021, Article 61.

  18.     

    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.

  19.     

    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.

  20.     

    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.

  21.     

    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.

  22.     

    G. Fu and Z. Wang
    POD-(H)DG method for incompressible flow simulations.
    J. Sci. Comput., Vol. 85, 2020, Article 24.

  23.     

    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.

  24.     

    T. Hoang, L. Ju, and Z. Wang
    Nonoverlapping localized Exponential time differencing methods for diffusion problems.
    J. Sci. Comput., Vol. 82, 2020, Article 37.

  25.     

    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.

  26.     

    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.

  27.     

    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.

  28. 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.

  29.     

    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.

  30.     

    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.

  31.     

    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.

  32.     

    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.

  33.     

    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.

  34.     

    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.

  35.     

    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.

  36.     

    B. Cockburn and Z. Wang
    Adjoint-based, superconvergent Galerkin approximations of linear functionals.
    J. Sci. Comput., vol. 73 (2-3), 2017, pp. 644-666.

  37.     

    L. Ju and Z. Wang
    Exponential Time Differencing Gauge Method for Incompressible Viscous Flows.
    Commun. Comput. Phys., vol. 22, 2017, pp. 517-541.

  38.     

    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.

  39.     

    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.

  40.     

    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.

  41.     

    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.

  42.     

    Z. Wang, B. McBee and T. Iliescu
    Approximate Partitioned Methods of Snapshots for POD.
    J. Comput. Appl. Math., vol. 307, 2016, pp. 374-384.

  43.      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.

  44.      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.

  45.      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.

  46.      T. Iliescu and Z. Wang
    Variational Multiscale Proper Orthogonal Decomposition: Navier-Stokes Equations.
    Numer. Meth. Partial. Diff. Eqs., vol. 30, 2014, pp. 641-663.

  47.      T. Iliescu and Z. Wang
    Variational Multiscale Proper Orthogonal Decomposition: Convection-Dominated Convection-Diffusion-Reaction Equations.
    Math. Comp., vol. 82, 2013, pp. 1357-1378.

  48.      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.

  49.      J. Huang, Z. Wang and R. Zhu
    Asymptotic Error Expansions for Hypersingular Integrals.
    Adv. Comput. Math., vol. 38 (2), 2013, pp. 257-279.

  50.      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.

  51.      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.

  52.            O. Roderick, M. Anitescu and Z. Wang
    Reduced Order Approximations in Uncertainty Analysis of Nuclear Engineering Applications.
    Trans. Am. Nucl. Soc., vol. 106, 2012.

  53.      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.

  54.      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.

  55.      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.

  56.      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.

  57.      J. Borggaard, T. Iliescu and Z. Wang
    Artificial Viscosity Proper Orthogonal Decomposition.
    Math. Comput. Model., vol. 53 (1-2), 2011, pp. 269-279.

  58.            O. Roderick, Z. Wang and M. Anitescu
    Dimensionality Reduction for Uncertainty Quantification of Nuclear Engineering Models.
    Trans. Am. Nucl. Soc., vol. 104, 2011.

  59.      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.

  60.      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.

  61.      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.

  62.      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.

  63.      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.

    64. several papers in Chinese

  64. 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.

  65. 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.

  66. 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.

  67. 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.

Refereed Proceedings

  1. Y. Teng, X. Zhang, Z. Wang and L. Ju
    Learning Green’s Functions of Linear Reaction- Diffusion Equations with Application to Fast Numerical Solver.
    Proceeding of Machine Learning Research, 3rd Annual Conference on Mathematical and Scientific Machine Learning, 2022

  2. 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.

  3. 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.

  4. I. Akhtar, J. Borggaard, T. Iliescu and Z. Wang
    Closure for Improved Reduced-order Models using High Performance Computing.
    AIAA 2010-1276.

  5. J. Borggaard, A. Duggleby, A. Hay, T. Iliescu and Z. Wang
    Reduced-order Modeling of Turbulent Flows.
    In Proceedings of MTNS, 2008.

Disserations

  1.    Z. Wang
    Reduced-Order Modeling of Complex Engineering and Geophysical Flows: Analysis and Computations.
    PhD thesis, Virginia Tech, 2012.

Scholar Citations