My research focuses on developing and analyzing efficient numerical methods for problems arising in science and engineering.
My research interests span traditional numerical methods and machine learning and data science. Some of the topics I investigate include neural networks for multiscale and singularly perturbed problems, nonlinear approximations by neural networks and radial basis functions for PDEs, error estimates of neural networks for conditionally stable PDEs, unfitted finite element methods for interface problems, and numerical methods for nonlocal PDEs.
At WPI, I mainly work with Prof. Zhongqiang Zhang and Prof. Marcus Sarkis.
Research Interests
Numerical Analysis and Scientific Computing; Numerical Methods for PDEs
Finite Element Methods; Discontinuous Galerkin Methods; Collocation Methods
Scientific Machine Learning
Numerical Methods for Nonlocal PDEs
Scholarly Work
12. Qiao Zhuang, Chris Ziyi Yao, Zhongqiang Zhang and George Em Karniadakis. Two-scale Neural Networks for Partial Differential Equations with Small Parameters. Submitted. (https://arxiv.org/pdf/2402.17232.pdf)
11. Qiao Zhuang, Alfa Heryudono, Fanhai Zeng and Zhongqiang Zhang. Collocation Methods for Integral Fractional Laplacian and Fractional PDEs Based on Radial Basis Functions. Applied Mathematics and Computation, 469:128548, (2024).
10. Qiao Zhuang, Zhongqiang Zhang, Marcus Sarkis and Tao Lin. Higher Degree Rectangular Immersed Finite Elements Discontinuous Galerkin Methods for Elliptic Interface Problems. Submitted.
9. Jin Wang, Xu Zhang and Qiao Zhuang*. An Immersed Crouzeix-Raviart Finite Element Method for Navier-Stokes Interface Problems With Moving Interfaces. International Journal of Numerical Analysis and Modeling, 19(4):563-586, (2022) .
8. Qiao Zhuang and Jin Wang. A spatial epidemic model with a moving boundary. Infectious Disease Modelling 6, 1046-1060, (2021).
7. Slimane Adjerid, Tao Lin and Qiao Zhuang*. Error estimates for an immersed finite element method for second order hyperbolic equations in inhomogeneous media. Journal of Scientific Computing 84:35, (2020).
