Research interests: applied math, numerical analysis and
scientific computing, including numerical PDEs and
optimization algorithms.
Selected recent work:
S. Zheng, H. Yang, and X. Zhang, On the convergence
of orthogonalization-free conjugate gradient method for
extreme eigenvalues of Hermitian matrices: a Riemannian
optimization interpretation. PDF
Z. Chen, J. Lu, Y. Lu and X. Zhang, On the convergence of
Sobolev gradient flow for the Gross-Pitaevskii eigenvalue
problem. arXiv
X. Liu, J. Shen and X. Zhang, An efficient and robust SAV
based algorithm for discrete gradient systems arising
from optimizations. PDF
C. Liu, Y. Gao and X. Zhang, Structure preserving schemes
for Fokker-Planck equations of irreversible processes.
arXiv
S. Zheng, W. Huang, B. Vandereycken and X. Zhang,
Riemannian optimization using three different metrics for
Hermitian PSD fixed-rank constraints: an extended version. arXivPDF
C. Fan, X. Zhang and J. Qiu, Positivity-preserving high
order finite difference WENO schemes for the compressible
Navier-Stokes equations, Journal
of Computational Physics, 467 (2022): 111446. PDF
H. Li, D. Appelö and X. Zhang, Accuracy of spectral
element method for wave, parabolic and Schrödinger
equations, SIAM Journal
on Numerical Analysis 60(1):339–363, 2022. PDF. See Section
2.8 in here for
detailed discussion of Neumann b.c..
L. Cross and X. Zhang, On the monotonicity of high order
discrete Laplacian, submitted. PDF