Qingguo Hong's Homepage

About me

I am currently Assistant Professor at Department of Mathematics and Statistics at Missouri University of Science and Technology. My research interest includes machine learning,  numerical methods for partial differential equations, and iterative methods.

Papers

   26.   W. Hao, Q. Hong, X. Jin and Y. Wang,  Gauss Newton method for solving variational problems of PDEs with neural network discretizations, submitted, arXiv: 2306.08727. [link]

    25.   Q. Zhai, Q. Hong, and X. Xie,  A new reduced basis method for parabolic equations based on single-eigenvalue acceleration,  submitted, arXiv:2302.07462. [link]

    24.   Q. Hong, J. Siegel, Q. Tan and J. Xu, On the activation dependence of the spectral bias of neural networks, submitted, arXiv:2208.04924. [link]

    23.  D. M. William and Q. Hong, Generalized Korn's inequalities for piecewise $H^2$ vector fields, submitted, arXiv:2207.00695. [link]  

    22.  Q. Hong*, Y. J. Lee and J. Xu, A sharp Korn's inequality for piecewise $H^1$ space and its applications, submitted, arXiv:2207.02060. [link]

    21.  J. W. Siegel, Q. Hong, X. Jin, W. Hao and J. Xu,  Greedy training algorithms for neural networks and applications to PDEs, Journal of Computational Physics, 2023, Vol. 484: 112084 [link]

    20.  Q. Hong, L. Ma, J. Xu and L-Q. Chen, An efficient iterative method for dynamical Ginzburg-Landau equations, Journal of Computational Physics, 2023, Vol. 474: 111794. [link]

    19.  Q. Hong*, J. Kraus, M. Lymbery and F. Philo, A new practical framework for the stability analysis of perturbed saddle-point problems and applications, Mathematics of Computation, 2023, Vol. 92, pp. 607-634. [link] 

    18.  Q. Hong*, J. Kraus, M. Kuchta, M. Lymbery, K. Mardal, M. Rognes, Robust approximation of generalized Biot-Brinkman problems, Journal of Scientific Computing, 2022, Vol. 93, pp. 1-28. [link]

    17.  Q. Hong, Y. Li, and J. Xu, Extended Galerkin analysis in finite element exterior calculus, Mathematics of Computation, 2022, Vol. 91, pp. 1077-1106. [link]

    16.  Q. Hong, J. Hu, L. Ma and J. Xu, New discontinuous Galerkin analysis algorithms and analysis for linear elasticity with strongly symmetric stress tensor, Numerische Mathematik, 2021, Vol. 149, pp. 645-678. [link]

    15.  Q. Hong, S. Wu and J. Xu, An extended Galerkin analysis for elliptic problems, Science China: Mathematics, 2021, Vol. 64, pp. 2141-2158. [link]    

    14.   Q. Hong and J. Xu, Uniform stability and error analysis for some discontinuous Galerkin methods, Journal of Computational Mathematics, 2021, Vol. 39, pp. 283-310. [link]   

    13.   S. Chen, Q. Hong, J. Xu and K. Yang, Robust preconditioners for poroelasticity, Computer Methods in Applied Mechanics and Engineering, 2020, Vol. 369, https://doi.org/10.1016/j.cma.2020.113229. [link]

    12.   Q. Hong, J. Kraus, M. Lymbery and  F. Philo, Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models,
           Mathematical Models and Methods in Applied Sciences, 2020, Vol. 30(13), pp. 2523-2555. [link]

    11.   Q. Hong, C. Liu and J. Xu, An abstract stabilization method with applications to nonlinear incompressible elasticity, Mathematica Numerical Sinica, 2020, Vol. 42(3), pp. 298-209. [link]   

    10.   Q. Hong, J. Kraus, M. Lymbery and M. F. Wheeler, Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems, Multiscale Modeling and Simulation,  
            2020, Vol. 18(2), pp. 916-941. [link]

9.  Q. Hong, J. Kraus, M. Lymbery and F. Philo, Conservative discretizations and parameter robust preconditioners for multiple-network flux-based poroelasticity models, Numerical Linear Algebra with Applications, 2019, Vol. 26, e2242. [link]

8.  W. Wang and  Q. Hong*, Two-grid economical algorithms for parabolic integro-differential equations with nonlinear memory, Applied Numerical Mathematics, 2019, Vol. 142, pp. 28-46. [link]

7.  Q. Hong, F. Wang, S. Wu and J. Xu, A unified study of continuous and discontinuous Galerkin methods, Science China: Mathematics, 2019, Vol. 62, pp. 1-32. [link]

6.  Q. Hong and J. Kraus, Parameter-robust stability of classical three-field formulation of Biot’s consolidation model, Electronic Transactions on Numerical Analysis, 2018, Vol. 48, pp. 202-226. [link]

5.  Q. Hong and J. Kraus, Uniformly stable discontinuous Galerkin discretization and robust iterative solution methods for the Brinkman problem, SIAM Journal on Numerical Analysis, 2016, Vol. 54, pp. 2750-2774. [link]

4.  Q. Hong, J. Kraus, J. Xu and L. Zikatanov, A robust multigrid method for discontinuous Galerkin discretizations of Stokes and linear elasticity equations, Numerische Mathematik, 2015, Vol. 132, pp. 23-49. [link]

3. Q. Hong and J. Kraus, Uniformly stable discontinuous Galerkin discretization and robust iterative solution methods for the Brinkman problem, Technical Report, RICAM 2014-36. [link]

2. Q. Hong, J. Kraus, J. Xu and L. Zikatanov, A robust multigrid method for discontinuous Galerkin discretizations of Stokes and linear elasticity equations, Technical Report, RICAM 2013-19. [link]

1.  Q. Hong*, J. Hu, S. Shu and J. Xu, A discontinuous Galerkin method for the fourth-order curl problem, Journal of Computational Mathematics, 2012, Vol. 30, pp. 565-578. [link]

Teaching

      ·       Spring 2023, The Pennsylvania State University-MATH 451 & CMPSC 451-004: Numerical Computations.

         ·       Fall 2022, The Pennsylvania State University-MATH 451 & CMPSC 451-002: Numerical Computations.

         ·       Fall 2022, The Pennsylvania State University-MATH 451 & CMPSC 451-003: Numerical Computations.

       ·      Spring 2022, The Pennsylvania State University-MATH 452-001: Deep Learning Algorithms and Analysis.

       ·       Fall 2021, The Pennsylvania State University-MATH 455 & CMPSC 455-001: Introduction to Numerical Analysis I.

       ·      Fall 2021, The Pennsylvania State University-MATH 455 & CMPSC 455-002: Introduction to Numerical Analysis I.

       ·      Fall 2021, The Pennsylvania State University-MATH 455 & CMPSC 455-003: Introduction to Numerical Analysis I.

·       Fall 2020, The Pennsylvania State University-MATH 251: Ordinary and Partial Differential Equations.

·       Spring 2020, The Pennsylvania State University-MATH 140: Calculus with Analytic Geometry I.

·       Fall 2019, The Pennsylvania State University-MATH 455 & CMPSC 455-001: Introduction to Numerical Analysis I.

·       Fall 2019, The Pennsylvania State University-MATH 455 & CMPSC 455-002: Introduction to Numerical Analysis I.

·       Spring 2019, The Pennsylvania State University-MATH 451 & CMPSC 451: Numerical Computations.

·       Spring 2019, The Pennsylvania State University-MATH 251: Ordinary and Partial Differential Equations.

·       Fall 2018, The Pennsylvania State University-MATH 230: Calculus and Vector Analysis.

·       Spring 2018, The Pennsylvania State University-MATH 021: College Algebra I.

·       Summer 2017, The Pennsylvania State University-CCMA Special Summer Course: Multilevel Iterative Methods for Discretized PDEs. 

.    Summer 2016, University of Jyvaskyla, Jyvaskyla-Summer School Course: An Introduction to the Theory and Practice of Multigrid Methods.

Invited Presentations

        ·  A priori error analysis ans greedy training algorithms for neural networks solving PDEs, City University of Hong Kong, October 19, 2022. 

        ·  On the activation function dependence of the spectral bias of neural networks, AMS Fall Eastern Sectional Meeting, University of Massachusetts Amherst, October 1-2, 2022.

        ·  Greedy training algorithms for neural networks and applications to PDEs, AMS Fall Eastern Sectional Meeting, University of Massachusetts Amherst, October 1-2, 2022.

       ·   A new framework for the stability analysis of perturbed saddle-point problems and applications, 15th World Congress on Computational Mechanics & 8th Asian Pacific Congress on Computational Mechanics, Japan, July 31-August 15, 2022.

       ·   A priori analysis to numerical PDEs by neural network functions, Texas State University, USA, February 18, 2022.

        ·   Parameter-robust iterative methods for Biot and multiple-permeability poroelasticity systems, Morgan State University, USA, December 16-19, 2021.

        ·  Parameter-robust iterative methods for Biot and multiple-permeability poroelasticity systems, Baylor University, USA, November 22, 2021.

        ·  A priori analysis to numerical PDEs by neural network functions, Shanghai Normal University, China, November 16, 2021.

        ·  A priori analysis to numerical PDEs by neural network functions, University of Florida, USA, September 8, 2021.

        ·  An extended Galerkin framework, Texas Tech University, USA, February 17, 2021.

        ·  Parameter-robust iterative methods for Biot and multiple-permeability poroelasticity systems, University of Delaware, USA, October 16, 2020.

        ·  An extended Galerkin framework, Tianyuan Center at Jilin University, China, September 4, 2020.

        ·  Parameter-robust iterative methods for Biot and multiple-permeability poroelasticity systems, Texas State University, USA, November 14-16, 2019.

        ·  Parameter-robust convergence analysisof fixed-stress split iterative method for multiple-permeability poroelasticity systems, SIAM CSS, Iowa State University, USA, October 19-20, 2019.

        ·  Extended Galerkin method, Joint Mathematics Meetings, Baltimore, USA, January 16-19, 2019.

        ·  A discrete Korn’s inequality and related finite elements, International Conference on Multigrid and Multiscale Methods in Computational Sciences, Bruchsal, Germany, December 05-09, 2016.

       ·  A multigrid method for discontinuous Galerkin discretizartions of Stokes and linear elasticity equations, 8th International Congress on Industrial and Applied Mathematics, Beijing, China, August 10-14,     
         2015.

       ·  Uniformly stable discontinuous Galerkin discretization and robust iterative solution methods of the Brinkman problem, 10th International Conference on Large-Scale Scientific Computations, Sozopol,
         Bulgaria, June 08-12, 2015.

       ·  Uniformly stable discontinuous Galerkin discretization and robust iterative solution methods of the Brinkman problem, 6th International Conference on Computational Methods in Applied Mathematics, St.
         Wolfgang, Austria, September 28-October 04, 2014.

       ·  A multigrid method for discontinuous Galerkin discretization of Stokes equations, ENUMATH Conference 2013, Lausanne, Swiss, August 26-30, 2013

       ·  A multigrid method for discontinuous Galerkin discretization of Stokes equations, 9th International Conference on Large-Scale Scientific Computations, Sozopol, Bulgaria, June 03-07, 2013.

Contributed Presentations

      ·   FEM and a development of new neural network, FEM Circus Fall 2022, Carnegie Mellon University, USA, October 21-22, 2022.

      ·   A priori error analysis for applying neural network to numerical PDEs, FEM Circus Fall 2021, The Pennsylvania State University, USA, November 5-6, 2021.

      ·  Convergence analysis of numerical PDEs by neural network functions, FEM Circus Spring 2021, Virtually, USA, April 9-10, 2021.

      ·  A Unified framework and related analysis for elliptic problem, FEM Circus Fall 2019, Virginia Tech University, USA, November 1-2, 2019.

      ·  A unified study of continuous and discontinuous Galerkin methods, Applied Math Days, Rensselaer Polytechnic Institute, USA, April 6-7, 2018.

      ·  Conservative stable discretizations and parameter-robust preconditioners for three-field formulation of Biot’s consolidation model, FEM Circus Spring 2018, The University of Tennessee, USA, March
        16-17, 2018.

      ·  Uniform inf-sup conditions for HDG and WG methods, FEM Circus Fall 2017, University of Mary- land, Baltimore County, USA, October 20-21, 2017.

      ·  A discrete Korn’s inequality and related finite elements, 9th Workshop on Analysis and Advanced Numerical Methods for Partial Differential Equations, St. Wolfgang, Austria, July 04-08, 2016.

      ·  A multigrid algorithm for a discontinuous Galerkin method for the Stokes equations, 6th Workshop on Analysis and Advanced Numerical Methods for Partial Differential Equations, St. Wolfgang, Austria,
        July 08-12, 2013.