Hai Zhu, Ph. D.
▎Assistant Professor of Mathematics
▎PDE Fast Algorithms and Constrained Optimization
◢ Email：hzhu@westlake.edu.cn
“We can only see a short distance ahead, but we can see plenty there that needs to be done.”
——Alan Turing
Biography
Hai Zhu received his B.S. degree in Mathematics and Applied Mathematics from Zhejiang University in 2013, and his M.S. degree in Applied Mathematics from the University of Washington in 2015. He obtained his Ph.D. in Applied and Interdisciplinary Mathematics from the University of Michigan in 2021. From 2021 to 2022, he held a postdoctoral assistant professor position at the University of Michigan. From 2022 to 2025, he was a Flatiron Research Fellow at the Flatiron Institute in New York City. He joined the Institute for Theoretical Sciences, Westlake University in September 2025.
Research
Dr. Zhu, Hai's research interest is in applied and computational mathematics. His representative contributions include: in the field of fast PDE solvers, he proposed a dimension reduction quadrature framework for three-dimensional singular integrals, combining exact forms in differential geometry with quaternion-based harmonic function approximation; in the study of viscous biofluid dynamics, he developed numerical methods for optimizing the swimming efficiency and shape of microswimmers; in the numerical simulation of quantum many-body theory, he combined adaptive mesh refinement with interpolative separable density fitting decomposition to design fast algorithms suitable for large-scale electronic structure simulations.
Representative Publications
1) Hai Zhu, and Shravan Veerapaneni. "High-Order Close Evaluation of Laplace Layer Potentials: A Differential Geometric Approach." SIAM Journal on Scientific Computing, vol. 44, no. 3, 2022, pp. A1381–404, https://doi.org/10.1137/21M1423051.
2) Shidong Jiang, and Hai Zhu. "Recursive Reduction Quadrature for the Evaluation of Laplace Layer Potentials in Three Dimensions." 2024-11, https://doi.org/10.48550/arxiv.2411.08342.
3) Hanliang Guo, Hai Zhu, Ruowen Liu, Marc Bonnet, and Shravan Veerapaneni. "Optimal Slip Velocities of Micro-Swimmers with Arbitrary Axisymmetric Shapes." Journal of Fluid Mechanics, vol. 910, 2021, https://doi.org/10.1017/jfm.2020.969.
4) Thomas G. Anderson, Hai Zhu, and Shravan Veerapaneni. "A Fast, High-Order Scheme for Evaluating Volume Potentials on Complex 2D Geometries via Area-to-Line Integral Conversion and Domain Mappings." Journal of Computational Physics, vol. 472, 2023, pp. 111688-, https://doi.org/10.1016/j.jcp.2022.111688.
5) Bowei Wu, Hai Zhu, Alex Barnett, and Shravan Veerapaneni. "Solution of Stokes Flow in Complex Nonsmooth 2D Geometries via a Linear-Scaling High-Order Adaptive Integral Equation Scheme." Journal of Computational Physics, vol. 410, 2020, pp. 109361-, https://doi.org/10.1016/j.jcp.2020.109361.
6) Ruowen Liu, Hai Zhu, Hanliang Guo, Marc Bonnet, and Shravan Veerapaneni. "Shape Optimization of Slip-Driven Axisymmetric Microswimmers." SIAM Journal on Scientific Computing, vol. 47, no. 2, 2025, pp. A1065–90, https://doi.org/10.1137/24M1659649.
Contact Information
Email：hzhu@westlake.edu.cn
