XIANGXIONG ZHANG

Associate Professor
Department of Mathematics
Purdue University
150 N. University Street,
West Lafayette, IN 47907-2067
Office: MATH 406
Office phone: +1 765 49-63354
zhan1966@purdue.edu
Research interests: applied math, numerical analysis and scientific computing, including numerical PDEs and optimization algorithms.

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. arXiv PDF
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

Spring 2023: MA 598 Topics on optimization