Research interests: applied math, numerical analysis and
scientific computing, including numerical PDEs and
optimization algorithms.
Selected recent work:
Z. Chen, J. Lu, Y. Lu and X. Zhang, Fully discretized
Sobolev gradient flow for the Gross-Pitaevskii eigenvalue
problem,arXiv
C. Liu and X. Zhang, An optimization based limiter for
enforcing positivity in a semi-implicit discontinuous
Galerkin scheme for compressible Navier–Stokes equations. PDF arXiv
X. Zhang, Recent Progress on Qk Spectral Element Method:
Accuracy, Monotonicity and Applications. PDF
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. 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
C. Liu, B. Riviere, J. Shen and X. Zhang, A simple and
efficient convex optimization based bound-preserving high
order accurate limiter for Cahn--Hilliard--Navier--Stokes
system, to appear in SIAM Journal on Scientific
Computing.PDFarXiv
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.
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
X. Liu, J. Shen and X. Zhang, An efficient and robust SAV
based algorithm for discrete gradient systems arising
from optimizations, to appear in SIAM Journal on
Scientific Computing. PDF
L. Cross and X. Zhang, On the monotonicity of Q3 spectral
element method for Laplacian. PDF arXiv:2010.07282