Faculty > Professors > LI Jingzhi

LI Jingzhi

Professor  Associate Chair (Undergrad Teaching)

http://faculty.sustech.edu.cn/lijz/en/

  • Brief Biography
  • Research
  • Teaching
  • Published Works

Research interests

◆ Scientific computing 

◆ Finite element methods 

◆ Inverse problems in mathematical physics 

◆ Shape optimization in differential forms, 

◆ Computational finance

Education

◆ PhD in Applied and Computational Mathematics, Chinese University of Hong Kong, 2009; 

◆ MS in Computer Science, Wuhan University, 2004; 

◆ BS in Mathematics, Wuhan University, 2001.

Professional Appointments

◆ Jan. 2020 - present, Professor, Department of Mathematics, Southern University of Science and Technology 

◆ June 2012 - Dec. 2019, Associate Professor, Department of Mathematics, Southern University of Science and Technology 

◆ Sept. 2011 - May 2012, Assistant Professor, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences 

◆ Sept. 2009 - Aug. 2011, Postdoctoral fellow, SAM, D-MATH, ETH, Zurich 

◆ Sept. 2004 - Aug.2009, Teaching assistant, Department of Mathematics, Chinese University of Hong Kong

Honors & Awards

◆ Career Award, Shenzhen, 2021

◆ Excellent Mentor Award, Shude Residential College, SUSTech, 2020

◆ Dual-excellence Award, Faculty of Science, SUSTech, 2020

◆ Highlight Award, Faculty of Science, SUSTech, 2019

◆ Excellent Research Award, SUSTech, 2016

◆ Excellent Mentor Award, SUSTech, 2016

◆ Peacock Award (Tier B), Shenzhen, 2013

◆ Best Doctoral Dissertation Award, Mathematical Society of Hong Kong, 2011


Selected publications(*Corresponding author)

49. Klibanov, M., Li, J.* & Zhang, W.

A globally convergent numerical method for a 3D coefficient inverse problem for a wave-like equation,

SIAM Journal on Scientific Computing, 2022, accepted.

48. Chen, H., Li, J. & Qiu, Weifeng

A C^0 Interior penalty method for mth-Laplace equation,

ESAIM: Mathematical Modelling and Numerical Analysis, 2022, accepted.

47. Ma, Y, Ma, F., Guo, Y, & Li, J.*

Computation of transmission eigenvalues by the regularized Schur complement for the boundary integral operators,

CSIAM Transactions on Applied Mathematics, 2022, accepted.

46. Cai, J., Li, J., Lu, X. & You, J.,

Sparse signal recovery from phaseless measurements via hard thresholding pursuit,

Applied and Computational Harmonic Analysis, 2022, 56, pp. 367–390.

45. Li, J.; Liu, H. & Ma, S.,

Determining a random schroedinger operator: both potential and source are random,

Communications in Mathematical Physics, 2021, 381, pp. 527–556.

44. Klibanov, M. V., Li, J.* & Zhang, W.,

Linear Lavrent’ev integral equation for the numerical solution of a nonlinear coefficient inverse problem,

SIAM Journal on Applied Mathematics, 2021, 81, pp. 1954-1978.

43. Xu, L.; Li, J.* & Chen, R.

A scalable parallel unstructured finite volume lattice Boltzmann method for three-dimensional incompressible flow simulations,

International Journal for Numerical Methods in Fluids, 2021, 93, pp.  2744–2762.

42. Li M.; Zhu L.; Li, J.*, Zhang K.,

Design optimization of interconnected porous structures using extended triply periodic minimal surfaces,

Journal of Computational Physics, 2021, 425, 109909 (24pp).

41. Zhang, D.; Wang, Y.; Guo, Y. & Li, J.*,

Uniqueness in inverse cavity scattering problems with phaseless near-field data,

Inverse Problems, 2020, 36, 025004 (10pp).

40. Hu, G. & Li, J.*,

Inverse source problems in an inhomogeneous medium with a single far-field pattern,

SIAM Journal on Mathematical Analysis, 2020, 52, pp. 5213-5231.

39. Klibanov, M. V.; Li, J.* & Zhang, W.,

Convexification for an inverse parabolic problem,

Inverse Problems, 2020, 36, 085008 (32pp).

38. Li, J.; Liu, H. & Sun, H.,

On an inverse elastic wave imaging scheme for nearly incompressible materials,

IMA Journal of Applied Mathematics, 2019, 84, pp. 229-257.

37. Li, J.; Liu, H. & Ma, S.,

Determining a random schroedinger equation with unknown source and potential,

SIAM Journal on Mathematical Analysis, 2019, 51, pp. 3465-3491.

36. Klibanov, M. V.; Li, J.* & Zhang, W.,

Convexification of electrical impedance tomography with restricted Dirichlet-to-Neumann map data,

Inverse Problems, 2019, 35, 035005 (33pp).

35. Klibanov, M. V.; Li, J.* & Zhang, W.,

Convexification for the inversion of a time dependent wave front in a heterogeneous medium,

SIAM Journal on Applied Mathematics, 2019, 79, pp. 1722-1747.

34. Wang, G.; Ma, F.; Guo, Y. & Li, J.,

Solving the multi-frequency electromagnetic inverse source problem by the Fourier method,

Journal of Differential Equations, 2018, 265, pp. 417-443.

33. Hao, Y.; Kang, F.; Li, J.* & Zhang, K.,

Computation of moments for Maxwell’s equations with random interfaces via pivoted low-rank approximation,

Journal of Computational Physics, 2018, 371, pp. 1-19.

32. Zhang, D.; Guo, Y.; Li, J. & Liu, H.

Retrieval of acoustic sources from multi-frequency phaseless data,

Inverse Problems, 2018, 34, 094001 (21pp).

31. Hiptmair, R. & Li, J.*,

Shape derivatives for scattering problems,

Inverse Problems, 2018, 34, 105001 (25pp).

30. Li, X.; Li, J.; Liu, H. & Wang, Y.,

Electromagnetic interior transmission eigenvalue problem for inhomogeneous media containing obstacles and its applications to near cloaking,

IMA Journal of Applied Mathematics, 2017, 82, pp. 1013-1042.

29. Li, J.; Liu, H. & Wang, Y.,

Recovering an electromagnetic obstacle by a few phaseless backscattering measurements,

Inverse Problems, 2017, 33, 035011 (20pp).

28. Wang, X.; Guo, Y.; Li, J. & Liu, H.,

Mathematical design of a novel input/instruction device using a moving acoustic emitter,

Inverse Problems, 2017, 33, 105009 (19pp).

27. Wang, Q.; Hou, Y. & Li, J.*,

Numerical design of FSHL-based approximate cloaks with arbitrary shapes,

Journal of Computational Physics, 2017, 333, pp. 142-159.

26. Guo, Y.; Hoemberg, D.; Hu, G.; Li, J.* & Liu, H.,

A time domain sampling method for inverse acoustic scattering problems,

Journal of Computational Physics , 2016, 314, pp. 647-660.

25. Jiang, X.; Li, J.*; Xia, T. & Yan, W.

Robust and efficient estimation with weighted composite quantile regression

Physica A, 2016, 457, pp. 413-423.

24. Chen, H.; Li, J. & Qiu, W.,

Robust a posteriori error estimates for HDG method of convection-diffusion equations,

IMA Journal of Numerical Analysis, 2016, 36, pp. 437-462.

23. Li, J.; Li, P.; Liu, H. & Liu, X.,

Recovering multiscale buried anomalies in a two-layered medium,

Inverse Problems, 2015, 31, 105006(26pp).

22. Li, H.; Li, J. & Liu, H.,

On quasi-static cloaking due to anomalous localized resonance in $R^3$,

SIAM Journal on Applied Mathematics, 2015, 75, pp. 1245-1260.

21. Li, J. & Liu, H.,

Recovering a convex polyhedral obstacle by a few backscattering measurements,

Journal of Differential Equations, 2015, 259, pp. 2101-2120.

20. Li, J.; Liu, H.; Rondi, L. & Uhlmann, G.,

Regularized transformation-optics cloaking for the Helmholtz equation: from partial cloak to full cloak,

Communications in Mathematical Physics, 2015, 335, pp. 671-712.

19. Hu, G.; Li, J.* & Liu, H., & Sun H.,

Inverse elastic scattering for multiscale rigid bodies with a single far-field pattern,

SIAM Journal on Imaging Sciences, 2014, 7, pp. 1799-1825.

18. Li, J.* Liu, H., & Wang, Q.,

Ground detection by a single electromagnetic far-field measurement,

Journal of Computational Physics, 2014, 273, pp. 472-487.

17. Hu, G.; Li, J.* & Liu, H.,

Recovering complex elastic scatterers by a single far-fielded pattern,

Journal of Differential Equations, 2014, 257, pp. 469-489.

16. Li, J.; Liu, H. & Zou, J.,

Locating multiple multiscale acoustic scatterers,

Multiscale Modeling and Simulations, 2014, 12, pp. 927-952.

15. Li, J., Liu, H. & Wang, Q.,

Enhanced multilevel linear sampling methods for inverse scattering problems,

Journal of Computational Physics, 2014, 257, pp. 554-571.

14. Li, J., Liu, H., Shang, Z. & Sun, H.,

Two single-shot methods for locating multiple electromagnetic scatterers,

SIAM Journal on Applied Mathematics, 2013, 73(4), pp. 1721-1746.

13. Li, J., Liu, H. & Wang, Q.,

Multiscale one-shot method for inverse scattering problems,

SIAM Journal on Imaging Sciences, 2013, 6, pp. 2285-2309.

12. Harbrecht, H. & Li, J.*,

First order second moment analysis for stochastic interface problems based on low-rank approximation,

ESAIM: Mathematical Modelling and Numerical Analysis, 2013, 47, pp. 1533-1552.

11. Hiptmair, R. & Li, J.*,

Shape derivatives in differential forms I: an intrinsic perspective,

Annali di Matematica Puraed Applicata, 2013, 192, pp. 1077-1098.

10. Hiptmair, R., Li, J.* & Zou, J.,

Universal extension for Sobolev spaces of differential forms and applications,

Journal of Functional Analysis, 2012, 263(2), pp. 364-382.

9. Hiptmair, R., Li, J. & Zou, J..

Convergence analysis of finite element methods for H(curl; Omega)-elliptic interface problems,

Numerische Mathematik, 2012, 122(3), pp. 557-578.

8. Hiptmair, R., Li, J. & Zou, J.,

Real interpolation of spaces of differential forms,

Mathematische Zeitschrift, 2012, 270(1), pp. 395-402.

7. Li, J., Liu, H. & Sun, H.,

Enhanced approximate cloaking by SH and FSH lining,

Inverse Problems, 2012, 28(7), 075011 (21pp), Selected as”Insights”article.

6. Li, J., Liu, H., Sun, H. & Zou, J.,

Reconstructing acoustic obstacles by planar and cylindrical waves,

Journal of Mathematical Physics, 2012, 53(10), 103705 (19pp), Selected as Cover article.

5. Li, J., Xie, J. & Zou, J.,

An adaptive finite element reconstruction of distributed fluxes,

Inverse Problems, 2011, 27(7), 075009 (25pp).

4. Li, J., Melenk, J. M., Wohlmuth, B. & Zou, J.,

Optimal a priori estimates for higher order finite elements for elliptic interface problems,

Applied Numerical Mathematics, 2010, 60(1-2), pp. 19-37.

3. Li, J., Liu, H. & Zou, J.,

Strengthened linear sampling method with a reference ball,

SIAM Journal on Scientific Computing, 2009, 31(6), pp. 4013-4040.

2. Li, J., Liu, H. & Zou, J.,

Multilevel linear sampling method for inverse scattering problems,

SIAM Journal on Scientific Computing, 2008, 30(3), pp. 1228-1250.

1. Li, J. & Zou, J.,

A multilevel model correction method for parameter identification,

Inverse Problems, 2007, 23(5), pp. 1759-1786.



Research Interests

My research primarily focuses on computational mathematics and related fields, including inverse problem theory and computational methods, shape optimization, unified theory of differential forms, scientific computing, and finite element methods. I have published over 70 high-quality papers in journals such as Inverse Problems, SIAM Journal on Mathematical Analysis, and Journal of Computational Physics.

Grants

I have been the principal investigator for 3 National Natural Science Foundation of China (NSFC) Young Scientists Fund projects, 2 Shenzhen Basic Research Projects, and 1 Shenzhen Excellent Science and Technology Innovation Talents Training Project.

I have also led two NSFC General Projects:

Project Number: 11571161
Title: Theoretical and Algorithmic Research on Localization Procedures for Electromagnetic Inverse Scattering Problems
Duration: January 2016 - December 2019
Funding: 550,000 CNY
Funding Agency: NSFC

Project Number: 11971221
Title: Quantification Theory of Shape Uncertainty in Opto-electromagnetic Scattering and Research on Shape Inversion Reconstruction Algorithms
Duration: January 2020 - December 2023
Funding: 520,000 CNY
Funding Agency: NSFC

I have also participated in a key project funded by the NSFC, led by Academician Tang Tao:

Project Number: 11731006
Title: Adaptive Methods for Uncertainty Quantification and Their Applications in Environmental Science
Duration: January 2018 - December 2022
Funding: 2.5 million CNY

Funding Agency: NSFC


Publications

53. Klibanov, M.; Li, J.; Nguyen, L., Romanov, V. G. & Yang, Z.,
Convexification numerical method for a coefficient inverse problem for the Riemannian radiative transport equation,
SIAM Journal on Imaging Sciences, 2023,  16, pp. 1762–1790.
52. Klibanov, M.; Li, J.* & Zhang, W.,
Numerical solution of the 3-D travel time tomography problem,
Journal of Computational Physics, 2023, 476, 111910 (18pp).
51. Gu H.; M. Cai & Li, J.,
An iterative decoupled algorithm with unconditional stability for Biot model,
Mathematics of Computation, 2023, 92, pp. 1087–1108.
50. Klibanov, M.; Li, J.*; Nguyen, L. & Yang, Z.,
Convexification numerical method for a coefficient inverse problem for the radiative transport equation,
SIAM Journal on Imaging Sciences, 2023, 16, pp. 35-63.
49. Ma, Y.; Ma, F.; Guo, Y., & Li, J.*,
Computation of transmission eigenvalues by the regularized Schur complement for the boundary integral operators,
CSIAM Transactions on Applied Mathematics, 2023, 4, pp. 306–324.
48. Chen, H.; Li, J. & Qiu, W.,
A C^0 Interior penalty method for mth-Laplace equation,
ESAIM: Mathematical Modelling and Numerical Analysis, 2022, 56, pp. 2081–2103.
47. Klibanov, M.; Li, J.* & Zhang, W.,
A globally convergent numerical method for a 3D coefficient inverse problem for a wave-like equation,
SIAM Journal on Scientific Computing, 2022, 44, pp. A3341–A3365.
46. Cai, J.; Li, J.; Lu, X. & You, J.,
Sparse signal recovery from phaseless measurements via hard thresholding pursuit,
Applied and Computational Harmonic Analysis, 2022, 56, pp. 367–390.
45. Li, J.; Liu, H. & Ma, S.,
Determining a random schroedinger operator: both potential and source are random,
Communications in Mathematical Physics, 2021, 381, pp. 527–556.
44. Klibanov, M.; Li, J.* & Zhang, W.,
Linear Lavrent’ev integral equation for the numerical solution of a nonlinear coefficient inverse problem,
SIAM Journal on Applied Mathematics, 2021, 81, pp. 1954-1978.
43. Xu, L.; Li, J.* & Chen, R.,
A scalable parallel unstructured finite volume lattice Boltzmann method for three-dimensional incompressible flow simulations,
International Journal for Numerical Methods in Fluids, 2021, 93, pp.  2744–2762.
42. Li M.; Zhu L.; Li, J.* & Zhang K.,
Design optimization of interconnected porous structures using extended triply periodic minimal surfaces,
Journal of Computational Physics, 2021, 425, 109909 (24pp).
41. Zhang, D.; Wang, Y.; Guo, Y. & Li, J.*,
Uniqueness in inverse cavity scattering problems with phaseless near-field data,
Inverse Problems, 2020, 36, 025004 (10pp).
40. Hu, G. & Li, J.*,
Inverse source problems in an inhomogeneous medium with a single far-field pattern,
SIAM Journal on Mathematical Analysis, 2020, 52, pp. 5213-5231.
39. Klibanov, M.; Li, J.* & Zhang, W.,
Convexification for an inverse parabolic problem,
Inverse Problems, 2020, 36, 085008 (32pp).