Research
My research areas are
(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 and Learning Algorithms.
Papers on arXiv
Papers on MathSciNet
Recent papers
" 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., DOI: 10.1137/23M1575913, arXiv:2305.18038
"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., DOI: 10.1007/s10208-023-09611-0
Collaborators: James Adler, Randolph Bank, Xi Chen, Michael Holst, Xiaozhe Hu, Qingguo Hong, Zhengqi Liu, Jonathan Siegel, Xinyuan Wu, Jinchao Xu, Ludmil Zikatanov, Cheng Zuo