Multiscale modeling and efficient numerical methods; numerical simulation of open quantum systems and quantum digital twins; data assimilation; numerical analysis of partial differential equations in complex media.
Gregory Nested Picard Iteration Schemes for Open Quantum Systems Governed by the Lindblad Equation (with D. Appelo, Y. Cheng), 2026, submitted, avaliable at Arxiv [link]
High Order Low Rank CPTP scheme for Lindblad Equations with Time-dependent Hamiltonian (with D. Appelo, Y. Cheng), 2026, Journal of Computational Physics, accepted, avaliable at Arxiv [link]
Floe-size distribution of sea ice: a stochastic theory (with S. Stechmann, B. Montemuro, C. Nan, M. Georgy, E. Tollar and Y. Zhang), 2025, submitted
LEMDA: A Lagrangian-Eulerian Multiscale Data Assimilation Framework (with Q. Deng , N. Chen , S. Stechmann), 2025, Journal of Advances in Modeling Earth Systems 17(2). [download]
Space-time Non-local multi-continua upscaling for parabolic equations with moving channelized media (with W. Leung, E. Chung), Journal of Computational and Applied Mathematics 469 (2025): 116669, [download]
Partially Explicit Time Discretization for Time Fractional Diffusion Equation (with A. Alikhanov, Y. Efendiev and W. Leung), 2022, Fract. Calc. Appl. Anal., 25(5), 1908-1924. [download]
Wavelet-based Edge Multiscale Parareal Algorithm for Parabolic Equations with Heterogeneous Coefficients and Rough Initial Data (with G. Li), J. Comput. Phys. (2021), [download]
Convergence of the CEM-GMsFEM for Stokes flows in heterogeneous perforated domains (with E. Chung, S. Pun), J. Comput. Appl. Math 389 (2021), [download]
Homogenization of time-fractional diffusion equations with periodic coefficients (with G. Li), J. Comput. Phys., 408 (2020), [download]
Total domination polynomials of graphs (with E. Shan, S. Wang, C. Wang, B. Wei), https://arxiv.org/abs/1607.00400#
k-Distance domination polynomials of cycles (with E. Shan), Commun. Appl. Math. Comput. 30 (2016), no. 4, 561–571.