XIANGXIONG ZHANG

ORCID iD   ResearcherID

AMS MathSciNet Author Profile      Most Cited Mathematicians by year of Ph.D.

Google Scholar Citations Profile

Preprint

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• 1. L. Cross and X. Zhang, On the monotonicity of Q3 spectral element method for Laplacian. PDF arXiv:2010.07282
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• 2. 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.
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• 3. 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 


• 4. 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
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• 5. 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. PDF  arXiv  Demonstration for how to run the code
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• 6. H. Li and X. Zhang, A monotone Q1 finite element method for anisotropic elliptic equations, submitted to the special issue in honor of Chi-Wang Shu’s 65th birthday for the Beijing Journal of Pure and Applied Mathematics. PDF arXiv
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• 7. Y. Chen, D. Xiu and X. Zhang,  On enforcing non-negativity in polynomial approximations in high dimensions. PDF
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• 8. X. Zhang, Recent Progress on Qk Spectral Element Method: Accuracy, Monotonicity and Applications, submitted to ICOSAHOM 2023 Conference Proceedings. PDF 
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• 9. 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
  
• 10. Z. Chen, J. Lu, Y. Lu and X. Zhang, Fully discretized Sobolev gradient flow for the Gross-Pitaevskii eigenvalue problem, arXiv

Publications and Accepted Papers in Refereed Journals:

• 42. 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. PDF arXiv  
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• 41. M. Dai, M. Hoeller, Q. Peng, and X. Zhang, Kolmogorov's dissipation number and determining wavenumber for dyadic models. Nonlinearity 37, no. 2 (2024): 025015. DOI arXiv
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• 40. Z. Chen, J. Lu, Y. Lu and X. Zhang, On the convergence of Sobolev gradient flow for the Gross-Pitaevskii eigenvalue problem. SIAM Journal on Numerical Analysis 62 (2024), pp. 667–691. arXiv
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• 39. L. Cross and X. Zhang, On the monotonicity of Q2 spectral element method for Laplacian on quasi-uniform rectangular meshes, Communications in Computational Physics, Vol. 35, No. 1, pp. 160-180, 2024. PDF  doi:10.4208/cicp.OA-2023-0206
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• 38. C. Liu, Y. Gao and X. Zhang, Structure preserving schemes for Fokker-Planck equations of irreversible processes,  Journal on Scientific Computing 98(1):4, 2024. arXiv
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• 37. C. Liu and X. Zhang, A positivity-preserving implicit-explicit scheme with high order polynomial basis for compressible Navier–Stokes equations,  Journal of Computational Physics 493:112496, 2023. PDF
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• 36. M. Dai, B. Vyas and X. Zhang, 1D Model for the 3D Magnetohydrodynamics. Journal of Nonlinear Science, 33, Article number: 87 (2023).  DOI PDF
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• 35. X. Liu, J. Shen and X. Zhang, An efficient and robust SAV based algorithm  for discrete gradient systems arising from optimizations, SIAM Journal on Scientific Computing, Vol. 45, No. 5, pp. A2304--A2324, 2023. PDF
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• 34. B. Ren, Z. Gao, Y. Gu, S. Xie, and X. Zhang, A positivity-preserving and well-balanced high order compact finite difference scheme for shallow water equations, Communications in Computational Physics 35 (2024), pp. 524-552. PDF 
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• 33. H. Li and X. Zhang, A high order accurate bound-preserving compact finite difference scheme for two-dimensional incompressible flow, Communications on Applied Mathematics and Computation, Volume 6, pages 113–141, (2024). Focused Issue in Memory of Prof. Ching-Shan Chou. PDF https://doi.org/10.1007/s42967-022-00227-9
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• 32. 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
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• 31. J. Hu and X. Zhang, Positivity-preserving and energy-dissipative finite difference schemes for the Fokker-Planck and Keller-Segel equations, IMA Journal of Numerical Analysis 43 (2022), pp. 1450–1484. PDF
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• 30. J. Shen and X. Zhang, Discrete Maximum principle of a high order finite difference scheme for a generalized Allen-Cahn equation, Communications in Mathematical Sciences, Volume 20 (2022) Number 5, pp.1409-1436. PDF
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• 29. 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 Hao Li's thesis for detailed discussion of Neumann b.c..
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• 28. C. Fan, X. Zhang and J. Qiu, A positivity-preserving hybrid Hermite WENO scheme for the compressible Navier-Stokes equations,  Journal of Computational Physics, Volume 445, 2021, 110596. PDF
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• 27. M. Li, Y. Cheng, J. Shen and X. Zhang,  A Bound-Preserving High Order Scheme for Variable Density Incompressible Navier-Stokes Equations, Journal of Computational Physics 425 (2021): 109906. PDF
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• 26. H. Li and X. Zhang, On the  monotonicity and discrete maximum principle of the finite difference implementation of C^0-Q^2 finite element method, Numerische Mathematik 145, 437–472 (2020). PDF
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• 25. H. Li and X. Zhang, Superconvergence of high order finite difference schemes based on variational formulation for elliptic equations, Journal of Scientific Computing 82, 36 (2020). PDF    See Section 2.8 in Hao Li's thesis for detailed discussion of Neumann b.c..
  
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• 24. H. Li and X. Zhang, Superconvergence of C^0-Q^k finite element method for elliptic equations with approximated coefficients, Journal of Scientific Computing 82, 1 (2020). PDF
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• 23. H. Li, S. Xie and X. Zhang, A high order accurate bound-preserving compact finite difference scheme for scalar convection diffusion equations, SIAM Journal on Numerical Analysis, 2018, 56(6), 3308-3345. PDF
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• 22. S. Srinivasan, J. Poggie and X. Zhang, A positivity-preserving high order discontinuous Galerkin scheme for convection-diffusion equations,  Journal of Computational Physics, Vol 366, 2018, Pages 120-143. PDF 
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• 21. J. Hu, R. Shu and X. Zhang, Asymptotic-preserving and positivity-preserving implicit-explicit schemes for the stiff BGK equation, SIAM Journal on Numerical Analysis, 2018, 56(2), 942–973. PDF
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• 20. J. Hu and X. Zhang, On a class of implicit-explicit Runge Kutta schemes for stiff kinetic equations preserving the Navier-Stokes limit,  Journal of Scientific Computing, (2017) 73: 797-818. PDF
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• 19. W. Huang, K. Gallivan and X. Zhang, Solving PhaseLift by low-rank Riemannian optimization methods for complex semidefinite constraints. SIAM Journal on Scientific Computing, 39-5 (2017), pp. B840-B859. CODE. PDF

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• 18. X. Zhang, On positivity-preserving high order discontinuous Galerkin schemes for compressible Navier-Stokes equations, Journal of Computational Physics,  328 (2017): 301–343. DOI. PDF
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• 17. X. Zhang, A curved boundary treatment for discontinuous Galerkin schemes solving time dependent problems, Journal of Computational Physics, 308 (2016): 153-170. DOI.   PDF.

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• 16. X. Cai, X. Zhang and J. Qiu, Positivity-preserving high order finite volume HWENO schemes for compressible Euler equations, Journal of Scientific Computing, (2016) 68: 464. DOI.   PDF.
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• 15. X. Zhang and S. Tan, A simple and accurate discontinuous Galerkin scheme for modeling scalar-wave propagation in media with curved interfaces, GEOPHYSICS Mar 2015, Vol. 80, No. 2, pp. T83-T89. DOI.    PDF.
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• 14. L. Demanet and X. Zhang, Eventual linear convergence of the Douglas Rachford iteration for basis pursuit, Mathematics of Computation 85 (2016), 209-238. DOI.   PDF.
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• 13. Y. Xing and X. Zhang, Positivity-preserving well-balanced discontinuous Galerkin methods for the shallow water equations on unstructured triangular meshes, Journal of Scientific Computing, v57 (2013), pp. 19-41. DOI.   PDF.
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• 12. Y. Zhang, X. Zhang and C.-W. Shu, Maximum-principle-satisfying second order discontinuous Galerkin schemes for convection-diffusion equations on triangular meshes, Journal of Computational Physics, v234 (2013), pp. 295-316. DOI.   PDF.
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• 11. X. Zhang, Y.-Y. Liu and C.-W. Shu, Maximum-principle-satisfying high order finite volume WENO schemes for convection-diffusion equations, SIAM Journal on Scientific Computing, v34 (2012), pp.A627-A658. DOI.   PDF.
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• 10. X. Zhang and C.-W. Shu, Positivity-preserving high order finite difference WENO schemes for compressible Euler equations, Journal of Computational Physics, v231 (2012), pp.2245-2258. DOI.   PDF.
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• 9. X. Zhang and C.-W. Shu, A minimum entropy principle of high order schemes for gas dynamics equations, Numerische Mathematik, (2012) 121:545-563. DOI.   PDF.
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• 8. C. Wang, X. Zhang, C.-W. Shu and J. Ning, Robust high order discontinuous Galerkin schemes for two-dimensional gaseous detonations, Journal of Computational Physics, v231 (2012), pp.653-665. DOI.   PDF.
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• 7. X. Zhang and C.-W. Shu, Maximum-principle-satisfying and positivity-preserving high order schemes for conservation laws: Survey and new developments, Proceedings of the Royal Society A, v467 (2011), pp.2752-2776. DOI.   PDF.  See Appendix C in this paper for a correction to the proof of Lemma 1. 
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• 6. X. Zhang and C.-W. Shu, Positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations with source terms, Journal of Computational Physics, v230 (2011), pp.1238-1248. DOI.   PDF.

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• 5. X. Zhang, Y. Xia and C.-W. Shu, Maximum-principle-satisfying and positivity-preserving high order discontinuous Galerkin schemes for conservation laws on triangular meshes, Journal of Scientific Computing, v50 (2012), pp.29-62. DOI.   PDF.
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• 4. Y. Xing, X. Zhang and C.-W. Shu, Positivity preserving high order well balanced discontinuous Galerkin methods for the shallow water equations, Advances in Water Resources, v33 (2010), pp.1476-1493. DOI.   PDF.

• 3. X. Zhang and C.-W. Shu, On positivity preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes, Journal of Computational Physics, v229 (2010), pp.8918-8934. DOI.   PDF.
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• 2. X. Zhang and C.-W. Shu, On maximum-principle-satisfying high order schemes for scalar conservation laws, Journal of Computational Physics, v229 (2010), pp. 3091-3120. DOI.   PDF.  See Appendix C in this paper for a correction to the proof of Lemma 2.4.

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• 1. X. Zhang and C.-W. Shu, A genuinely high order total variation diminishing scheme for one-dimensional scalar conservation laws, SIAM Journal on Numerical Analysis, Volume 48, Issue 2 (2010), pp. 772-795. DOI.   PDF.

Publications in Refereed Book Chapters

• 1. Z. Xu and X. Zhang, Bound-preserving high order schemes, Volume 18, Handbook of Numerical Methods for Hyperbolic Problems: Applied and Modern Issues, R. Abgrall and C.-W. Shu, Editors, North-Holland, Elsevier, Amsterdam, 2017, pp. 81-102.  PDF

Conference Proceedings

• 1. M. Leinonen, R. J. Hewett, X. Zhang, L. Ying, L. Demanet, High-dimensional wave atoms and compression of seismic datasets, in Proc. SEG annual meeting, Houston, September 2013. DOI. PDF. 
• 2. X. Zhang and S. Tan, A simple and accurate discontinuous Galerkin scheme for modeling scalar-wave propagation in media with curved interfaces, in Proc. SEG annual meeting, Denver, October 2014. DOI
• 3. Wen Huang, Kyle A. Gallivan, Xiangxiong Zhang, Solving PhaseLift by Low-rank Riemannian Optimization Methods, International Conference on Computational Science 2016, ICCS 2016, 6-8 June 2016, San Diego, California, USA. Procedia Computer Science, Volume 80, 2016, Pages 1125-1134, ISSN 1877-0509, DOI