Research interests: applied math, numerical analysis and
scientific computing, including numerical PDEs and
optimization algorithms.
Selected recent work:
C. Liu, G. Buzzard and X. Zhang, An optimization based
limiter for enforcing positivity in a semi-implicit
discontinuous Galerkin scheme for compressible Navier–Stokes
equations, Journal of Computational Physics,
Volume 519, 113440, 2024. PDF
Z. Chen, J. Lu, Y. Lu and X. Zhang, Fully discretized
Sobolev gradient flow for the Gross-Pitaevskii eigenvalue
problem, to appear in Mathematics of Computation.arXiv
X. Liu, J. Shen and X. Zhang, A simple GPU implementation
of spectral-element methods for solving 3D Poisson type
equations on rectangular domains and its applications, to
appear in Communications in Computational Physics. PDFarXivDemonstration for
how to run the code
T. Yu, S. Zheng, J. Lu, G. Menon and X. Zhang, Riemannian
Langevin Monte Carlo schemes for sampling PSD matrices with
fixed rank. PDF arXiv
S. Zheng, W. Huang, B. Vandereycken and X. Zhang,
Riemannian optimization using three different metrics for
Hermitian PSD fixed-rank constraints. PDF.
An extended version with more details is on arXiv.