XIANGXIONG
ZHANG
Preprints and publications:
Publications and Accepted Papers in Refereed Journals:
- 49. B. Ren, B.S. Wang, X. Zhang and Z. Gao, Fourth Order
Positivity and Bound Preserving Well-Balanced Compact Finite
Difference Scheme for Ripa and Pollutant Transport Systems,
to appear in Computers and Mathematics with
Applications, PDF
- 48. 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
-
- 47. 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,
Volume 519, 113440, 2024. PDF arXiv
- 46. H. Li and X. Zhang, A monotone Q1 finite element
method for anisotropic elliptic equations, to appear in the
special issue in honor of Prof. Chi-Wang Shu’s 65th birthday
for the Beijing Journal of Pure and Applied Mathematics. PDF
arXiv
- 45. 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, to appear in Communications in
Computational Physics. PDF arXiv Demonstration
for how to run the code
- 44. 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. to appear on the
special Deep Learning for Inverse Problems in Journal
of Computational and Applied Mathematics. PDF
- 43. L. Cross and X. Zhang, On the monotonicity of Q3
spectral element method for Laplacian, Annals of Applied
Mathematics 40(2), 161–190 (2024). PDF arXiv:2010.07282
- 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, SIAM Journal on Scientific Computing, Volume:
46, Issue: 3, pp. A1373-C271. PDF
arXiv
- 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
- 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
-
- 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
- 38. C. Liu, Y. Gao and X. Zhang, Structure preserving
schemes for Fokker-Planck equations of irreversible
processes, Journal of Scientific Computing 98(1):4,
2024. arXiv
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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..
- 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
- 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
- 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
- 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..
- 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
- 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
- 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
- 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
- 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
- 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), . CODE.
PDF
- 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
- 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.
- 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.
- 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.
- 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.
-
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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: Mathematical, Physical and
Engineering Sciences, v467 (2011), pp.2752-2776. DOI.
PDF. See
Appendix C in this
paper for a correction to the proof of Lemma 1.
- 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.
- 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.
-
- 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.
- 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.
- 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.
- 5. X. Zhang, Recent Progress on Qk Spectral Element
Method: Accuracy, Monotonicity and Applications, to appear
in: Sehun Chun, Jae-Hun Jung, Eun-Jae Park, and Jie
Shen, editors, Spectral and High-Order Methods for
Partial Differential Equations ICOSAHOM 2023, volume 142 of
Lecture Notes in Computational Science and Engineering.
Springer, Cham, 2025. PDF
- 4. 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
- 3. Wen Huang, Kyle A. Gallivan, Xiangxiong Zhang,
Solving PhaseLift by Low-rank Riemannian Optimization
Methods, The 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
- 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
- 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.
- 1. 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.
- 2. 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
- 3. Y. Chen, D. Xiu and X. Zhang, On enforcing
non-negativity in polynomial approximations in high
dimensions. PDF
- arXiv
- 4. C. Liu, J. Hu, W. Taitano and X. Zhang, An
optimization-based positivity-preserving limiter in
semi-implicit discontinuous Galerkin schemes solving
Fokker–Planck equations. PDF arXiv
- 5. A. Anshika, D. Ghosh and X. Zhang, A Three-Operator
Splitting Scheme Derived from Three-Block ADMM, submitted
to MOPTA 24 special issue of Optimization and Engineering.
PDF arXiv
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