Research

My research areas include:

1. Finite Element Methods, including adaptivity, iterative solvers, Finite Element Exterior Calculus, superconvergence;

2. Structure-Preserving Methods, such as Energy-Preserving Methods for dynamical systems and finite element exterior calculus;

3. Adaptive Algorithm for more general problems, such as Reduced Basis Methods, Learning and Rational  Approximation Algorithms.

Papers on arXiv

My Google Scholar

Papers on MathSciNet

Recent papers

"Some new convergence analysis and applications of POD-greedy algorithms", arXiv:2407.09933

"Rational empirical interpolation methods with applications", arXiv:2406.19339

" Reduced Krylov basis methods for parametric partial differential equations",  arXiv:2405.07139

"A new analysis of empirical interpolation methods and Chebyshev greedy algorithms", arXiv:2401.13985

"A reduced conjugate gradient basis method for fractional diffusion", SIAM J. Sci. Comput., S68-S87 (2024)

"Entropy-based convergence rates for greedy algorithms", Mathematical Models and Methods in Applied Sciences, Vol. 34, No. 5 (2024) 779-802.

"Paramter-free preconditioning for nearly incompressible linear elasticity", Computers&Mathematics with Applications, 154 (2024) 39-44

"Nodal auxiliary space preconditioning for the surface de Rham complex", Found. Comput. Math., Vol. 24 (2024) 1019-1048 

Collaborators: James Adler, Randolph Bank, Xi Chen, Michael Holst, Xiaozhe Hu, Qingguo Hong, Aidi Li, Zhengqi Liu, Jonathan Siegel, Yupeng Wang, Xinyuan Wu, Jinchao Xu, Ludmil Zikatanov, Cheng Zuo