My Graduation

Hi, I'm Yunhui He

About me

I'm currently a postdoctoral research fellow at Department of Computer Science, The University of British Columbia, Canada. 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.

Mailing Address:
Department of Computer Science
The University of British Columbia
201 - 2366 Main Mall
Vancouver BC, V6T 1Z4
Canada

Email: yunhui.he@ubc.ca

News !

  • I am going to give a talk at 2022 SIAM Annual Meeting , July 11-15, 2022.
  • I am going to give a talk at CAIMS Annual Meeting 2022 , June 13-16, 2022.
  • I am going to give a talk at CMS 22 Summer Conference , June 3-6, 2022.
  • I am going to give a talk at SIAM PNW Conference , May 20-22, 2022.
  • I am going to give a talk at 17th Copper Mountain Conference On Iterative Methods , April 4-8, 2022.
  • I am going to give a talk at CMS 21 Winter Conference , December 2-7, 2021.

    • Research Interests

    • Finite Element and Finite Difference Methods
    • Multigrid Methods
    • Local Fourier Analysis
    • Preconditioning
    • Optimization Methods
    • Optimal Control

    You can find me on:

    Education

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

    Professional Experience

    • 09/2021--Present: 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. Nataj, S., He, Y.: Anderson acceleration for nonlinear PDEs discretized by space-time spectral methods, submitted.
      2. De Sterck, H., He, Y., Krzysik, O.: Anderson Acceleration as a Krylov method with application to asymptotic convergence analysis, submitted.

    Refereed Publications

      1. Greif, C., He, Y.: Block preconditioners for the Marker and Cell discretization of the Stokes-Darcy equations , to appear, SIAM Journal on Matrix Analysis and Applications, 2023.
      2. He, Y. : A Vanka-based parameter-robust multigrid relaxation for the Stokes-Darcy Brinkman problems, Numerical Linear Algebra with Applications, e2514, 2023.
      3. 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.
      4. 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), 2023.
      5. 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.
      6. He, Y. : Novel mass-based multigrid relaxation schemes for the Stokes equations, Applied Mathematics and Computation, 440, 127665, 2023.
      7. 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.
      8. 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.
      9. He, Y. : A novel multigrid method for elliptic distributed control problems, Journal of Computational and Applied Mathematics, 419, 114771, 2023.
      10. 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.
      11. 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.
      12. 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.
      13. 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.
      14. 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.
      15. 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.
      16. 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.
      17. He, Y.: Independence of placement for local Fourier analysis, Numerical Linear Algebra with Applications, 28(6):e2388, 2021.
      18. 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.
      19. 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.
      20. 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.
      21. 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.
      22. 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.
      23. 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.
      24. 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.
      25. 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.
      26. 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.
      27. 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.
      28. 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.
      29. 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. Greif, C., He, Y.: A note on using the mass matrix as a preconditioner for the Poisson equation, arXiv , 2021.
      2. He, Y., Xie, H.: Convergence analysis of shift-inverse method with Richardson iteration for eigenvalue problem, arXiv , 2018.

    Teaching Experience

    • 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