Research

Research Interests

  • Uncertainty Quantification
  • Computational Fluid Dynamics
  • Turbulence Modeling
  • Reduced Order Modeling
  • Data Driven Algorithms
  • Ensemble Simulation Models and Algorithms

Publications

1. M. Gunzburger, T. Iliescu, J. Mohebujjaman, M. Schneier, "Nonintrusive Stabilization of Reduced Order Models for Uncertainty Quantification of Time-Dependent Convection-Dominated Flows", To appear 2020, SIAM Journal of Uncertainty Quantification. https://arxiv.org/abs/1810.08746

2. M. Gunzburger, T. Iliescu, M. Schneier, "A Leray Regularized Ensemble-Proper Orthogonal Decomposition Method for Parameterized Convection-Dominated Flows", To appear 2020, IMA Journal of Numerical Analysis. https://academic.oup.com/imajna/advance-article-abstract/doi/10.1093/imanum/dry094/5299776?redirectedFrom=fulltext

3. N. Jiang, M. Schneier, "An Efficient, Partitioned Ensemble Algorithm for Simulating Ensembles of Evolutionary MHD Flows at Low Magnetic Reynolds Number", Numerical Methods for Partial Differential Equations} 34 (2018), 2129-2152. https://onlinelibrary.wiley.com/doi/abs/10.1002/num.22281

4. M. Gunzburger, M. Schneier, C. Webster, G. Zhang, "An Improved Discrete Least-Squares/Reduced-Basis Method for Parameterized Elliptic PDEs", Journal of Scientific Computing, 1573-7691 (2018), 1-16. https://link.springer.com/article/10.1007/s10915-018-0661-6

5. M. Gunzburger, N. Jiang, M. Schneier, "A Higher Order Ensemble-Proper Orthogonal Decomposition Method for the Non-stationary Navier-Stokes Equations", International Journal of Numerical Analysis and Modeling, 15 (2018), 608-627. http://www.math.ualberta.ca/ijnam/Volume-15-2018/No-4-18/2018-45-09.pdf

6. M. Gunzburger, N. Jiang, M. Schneier, "An Ensemble-Proper Orthogonal Decomposition Method for the Nonstationary Navier-Stokes Equations", SIAM Journal on Numerical Analysis, 55 (2017), 286-304. https://epubs.siam.org/doi/abs/10.1137/16M1056444

7. M. Schneier, "Numerical Integration of Rational Bubble Functions with Multiple Singularities", Involve, 8 (2015), 233-251. https://msp.org/involve/2015/8-2/involve-v8-n2-p05-s.pdf