My Graduation

Hi, I'm Yunhui He

About me

I am an Assistant Professor in the Department of Mathematics at the University of Houston. My research interests lie primarily in the field of numerical analysis and scientific computing. Specifically, I am interested in
finite element methods for the numerical solution of partial differential equation and local Fourier analysis for multigrid methods, and acceleration methods, such as Anderson acceleration and nonlinear GMRES.

Mailing Address:
Department of Mathematics
University of Houston
3551 Cullen Blvd, Room 641
Houston, Texas 77204-3008
USA

Email: yhe43@central.uh.edu

News !

  • 1. I have a postdoctoral position available. If you are interested in, please check Apply Online. The research focus on the development of efficient solution algorithms for linear and nonlinear problems. Duties will include development and analysis of algorithms and their implementation in a high-performance computing environment. If you have any question, please feel free to contact me.
  • 2. From December 08 to December 12, 2025, my colleagues and I will host the CBMS Conference on Research at the Interface of Applied Mathematics and Machine Learning received support from NSF (DMS-2430460).
  • 3. I have projects for graduate students. If you are interested, you can find the application process here, and more information on the program at the Mathematics Department can be found here.

    • Research Interests

    • Finite Element and Finite Difference Methods
    • Multigrid Methods
    • Local Fourier Analysis
    • Preconditioning
    • Acceleration Methods

    You can find me on:

    Education

    • 2015--2018, PhD in Mathematics, Memorial University of Newfoundland, Canada. Supervisor: Prof. Scott MacLachlan
    • 2012--2015, Master of Natural Science in Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China. Supervsior: Prof. Hehu Xie
    • 2008--2012, Bachelor of Science in Mathematics and Applied Mathematics, Capital Normal University, Beijing, China

    Professional Experience

    • 09/2023--present: Assistant Professor at Department of Mathematics, University of Houston
    • 09/2021--08/2023: Postdoctoral Research Fellow at Department of Computer Science, The University of British Columbia, Working with Prof. Chen Greif
    • 09/2019--08/2021: Postdoctoral Fellow at Department of Applied Mathematics, University of Waterloo, Working with Prof. Hans De Sterck and Prof. Sander Rhebergen
    • 09/2018--08/2019: Postdoctoral Fellow at Department of Mathematics and Statistics, Memorial University of Newfoundland, Working with Prof. Scott MacLachlan

    Publications

    Submitted Manuscripts

      1. Yovel, R., He, Y., Treister, E.: Vanka-smoothed Shifted Laplacian multigrid preconditioners for the Helmholtz equations, 2025.
      2. He, Y., Mang, A.: A generalized alternating NGMRES method for PDE-constrained optimization problems governed by transport equations, 2025.
      3. He, Y., Leveque, S.: A generalized alternating Anderson acceleration method, 2025.
      4. Vasilyeva, M., Southworth, B., He, Y., Wang, M.: Implicit-explicit scheme with multiscale Vanka two-grid solver for heterogeneous unsaturated poroelasticity, 2025.
      5. Niu, C., He, Y., Hu, X.: Rejuvenating AMLI-cycle: from Chebyshev polynomial to momentum acceleration, 2025.
      6. Leveque, S., He, Y., Olshanskii, M.: An augmented Lagranian preconditioner for Navier-Stokes equations with Runge-Kutta in time, 2025.
      7. He, Y.: Convergence analysis of an alternating nonlinear GMRES on linear systems, 2025.
      8. He, Y.: The worst-case root-convergence factor of GMRES(1), 2025.

    Refereed Publications

      1. He, Y.: Convergence analysis for nonlinear GMRES, IMA Journal of Numerical Analysis, accepted, 2025.
      2. Greif, C., He, Y.: Convergence properties of nonlinear GMRES applied to linear systems, SIAM Journal on Matrix Analysis and Applications, accepted, 2025.
      3. He, Y.: Some theoretical results on the finite convergence property and the temporary stalling behavior of Anderson acceleration on linear systems, Journal of Computational and Applied Mathematics, 474, 116925, 2025.
      4. He, Y., Olshanskii, M.: A preconditioner for the grad-div stabilized equal-order finite elements discretizations of the Oseen problem, SIAM Journal on Scientific Computing, 47 (3), A1486-A1506, 2025.
      5. Greif, C., He, Y.: Monolithic multigrid for the marker-and-cell discretization of the Stokes-Darcy equations, Journal of Computational and Applied Mathematics, 463, 116518, 2025.
      6. Nataj, S., He, Y.: Anderson acceleration for nonlinear PDEs discretized by space-time spectral methods, Computers & Mathematics with Applications, 167: 199--206, 2024.
      7. De Sterck, H., He, Y., Krzysik, O.: Anderson acceleration as a Krylov method with application to asymptotic convergence analysis, Journal of Scientific Computing, 99(1), 12, 2024.
      8. Greif, C., He, Y.: Block preconditioners for the Marker and Cell discretization of the Stokes-Darcy equations , SIAM Journal on Matrix Analysis and Applications, 44(4), 1540-1565, 2023.
      9. He, Y. : A Vanka-based parameter-robust multigrid relaxation for the Stokes-Darcy Brinkman problems, Numerical Linear Algebra with Applications, e2514, 2023.
      10. Greif, C., He, Y.: A closed-form multigrid smoothing factor for an additive Vanka-type smoother applied to the Poisson equation, Numerical Linear Algebra with Applications, e2500, 2023.
      11. Thompson, J., Brown, J., He, Y.: Local Fourier analysis of p-multigrid for high-order finite element operators, SIAM Journal on Scientific Computing, 45(3), S351-S370, 2023.
      12. He, Y. : Optimal smoothing factor with coarsening by thee for the MAC scheme for the Stokes equations, Computers & Mathematics with Applications, 132:63-72, 2023.
      13. He, Y. : Novel mass-based multigrid relaxation schemes for the Stokes equations, Applied Mathematics and Computation, 440, 127665, 2023.
      14. He, Y., Liu, J. : Smoothing analysis of two robust multigrid methods for elliptic optimal control problems, SIAM Journal on Matrix Analysis and Applications, 44(1):1-26, 2023.
      15. He, Y., Liu, J., Wang, X. : Optimized sparse approximate inverse smoothers for solving Laplacian linear systems, Linear Algebra and Its Applications, 656:304-323, 2023.
      16. He, Y. : A novel multigrid method for elliptic distributed control problems, Journal of Computational and Applied Mathematics, 419, 114771, 2023.
      17. Adler, J.H., He, Y., Hu, X., MacLachlan, S.P., Ohm, P.: Monolithic multigrid for a reduced-quadrature discretization of poroelasticity, SIAM Journal on Scientific Computing, 45(3), 2023.
      18. De Sterck, H., He, Y.: Linear asymptotic convergence of Anderson Acceleration: fixed-point analysis, SIAM Journal on Matrix Analysis and Applications, 43(4):1755-1783, 2022.
      19. He, Y., Liu, J. : A Vanka-type multigrid solver for complex-shifted Laplacian systems from diagonalization-based parallel-in-time algorihtms, Applied Mathematics Letters, 132, 108125, 2022.
      20. Voronin, A., He, Y., MacLachlan, S., Olson, L., Tuminaro, R.: Low-order preconditioning of the Stokes equations, Numerical Linear Algebra with Applications, 29(3):e2426, 2022.
      21. He, Y., Rhebergen, S., De Sterck, H.: Local Fourier analysis of multigrid for hybridized and embedded discontinuous Galerkin methods, SIAM Journal on Scientific Computing, 43(5):S612-S636, 2021.
      22. Wang, D., He, Y., De Sterck, H.: On the asymptotic linear convergence speed of Anderson acceleration applied to ADMM, Journal of Scientific Computing, 88(2):38, 2021.
      23. He, Y.: A generalized and unified framework of local Fourier analysis using matrix-stencils, SIAM Journal on Matrix Analysis and Applications, 42(3):1096-1118, 2021.
      24. He, Y.: Independence of placement for local Fourier analysis, Numerical Linear Algebra with Applications, 28(6):e2388, 2021.
      25. De Sterck, H., He, Y.: On the asymptotic linear convergence speed of Anderson acceleration, Nesterov acceleration, and nonlinear GMRES, SIAM Journal on Scientific Computing, 43(5):S21-S46, 2021.
      26. Brown, J., He, Y., MacLachlan, S.P., Menickelly, M., Wild, S.: Tuning multigrid methods with robust optimization and local Fourier analysis, SIAM Journal on Scientific Computing, 43(1):A109-A138, 2021.
      27. Farrell, P.E., He, Y., MacLachlan, S.P.: A local Fourier analysis of additive Vanka relaxation for the Stokes equations, Numerical Linear Algebra with Applications, 28(3):e2306, 2021.
      28. He, Y., MacLachlan, S.P.: Two-level Fourier analysis of multigrid for higher-order finite-element discretizations of the Laplacian, Numerical Linear Algebra with Applications, 27(3):e2285, 2020.
      29. Brown, J., He, Y., MacLachlan, S.P.: Local Fourier analysis of Balancing Domain Decomposition by Constraints algorithms, SIAM Journal on Scientific Computing, 41(5):S346-S369, 2019.
      30. Zhang, N., Han, X., He, Y., Xie, H., You, C.: An algebraic multigrid method for eigenvalue problems and its numerical tests, East Asian Journal on Applied Mathematics, accepted 2019, 11(1), 1-19, 2021.
      31. He, Y., MacLachlan, S.P.: Local Fourier analysis for mixed finite-element methods for the Stokes equations, Journal of Computational and Applied Mathematics, 35:161-183, 2019.
      32. Adler, J. H., He, Y., Hu, X., MacLachlan, S.P.: Vector-potential finite-element formulations for two-dimensional resistive magnetohydrodynamics, Computers and Mathematics with Applications, 77(2):476-493, 2019.
      33. He, Y., Li, Y., Xie, H., You, C., Zhang, N.: A multilevel Newton's method for eigenvalue problems, Applications of Mathematics, 63(3):281-303, 2018.
      34. He, Y., MacLachlan, S.P.: Local Fourier analysis of block-structured multigrid relaxation schemes for the Stokes equations, Numerical Linear Algebra with Applications, 24(3):e2147, 2018.
      35. Zhang, X., He, Y.: Modified interpolatory projection method for weakly singular integral equation eigenvalue problems, Acta Mathematicae Applicatae Sinica, accepted 2015, 35(2):327-339, 2019.
      36. Chen, H., He, Y., Li, Y., Xie, H.: A multigrid method based on shifted-inverse power technique for eigenvalue problems, European Journal of Mathematics: 1(1):207-228, 2015.

    PhD Thesis

      1. He, Y.: Local Fourier analysis for saddle-point problems, PhD Thesis, August 2018.

    Other Manuscripts

      1. He, Y., Li, Y.: Parameter-robust Braess-Sarazin-type smoothers for linear elasticity problems, arXiv , 2022
      2. Greif, C., He, Y.: A note on using the mass matrix as a preconditioner for the Poisson equation, arXiv , 2021
      3. He, Y., Xie, H.: Convergence analysis of shift-inverse method with Richardson iteration for eigenvalue problem , arXiv , 2018

    Teaching Experience

    • S 2026: MATH 6371 (Numerical Analysis), University of Houston
    • F 2025: MATH 6370 (Numerical Analysis), University of Houston
    • S 2025: MATH 2318 (Linear Algebra), University of Houston
    • F 2024: MATH 2318 (Linear Algebra), University of Houston
    • S 2024: MATH 3363 (Introduction to Partial Differential Equations), University of Houston
    • F 2023: MATH 4364 (Introduction to Numerical Analysis in Scientific Computing), University of Houston
    • F 2022: MATH 100 (Differential Calculus), The University of British Columbia
    • F 2022: CPSC 402 (Numerical Linear Algebra), The University of British Columbia
    • W 2021: SYDE 211 (Calculus III and ODE), Online, University of Waterloo
    • F 2020: SYDE 211 (Calculus III and ODE), Online, University of Waterloo
    • W 2020: MATH 127 (Calculus I), University of Waterloo
    • F 2019: MATH 217 (Calculus III), University of Waterloo
    • F 2018: MATH 1000 (Calculus I), Memorial University