# 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 !*

## 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

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

### Refereed Publications

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

### PhD Thesis

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

### Other Manuscripts

## 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