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.

Y. Chen, D. Xiu and X. Zhang, On enforcing non-negativity in polynomial approximations in high dimensions, to appear in SIAM Journal on Scientific Computing. PDF arXiv
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, 519 (2024), pp. 113440. 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, Communications in Computational Physics, 36 (2024), pp. 1157-1185. DOI PDF arXiv Demonstration 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, to appear in Computational Optimization and Applications. PDF. An extended version with more details is on arXiv.