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Research Interests

1.      Computational electromagnetism

2.      Numerical simulation of semiconductor devices

3.      Computational magnetohydrodynamics

 

Publication

Submitted:

1.     Finite element error estimates for the nonlinear Schrodinger-Poisson model, with T. Cui, W. Lu, and N. Pan, submitted, 2023.

2.     A perfectly matched layer method for wave scattering problem by a step-like surface, with W. Lu and X. Zhu, submitted, 2023.

Published:

1.     A uniform preconditioner for a Newton algorithm for total-variation minimization and minimum-surface problems, with X. Tai, R. Winther, and X. Zhang, SIAM J. Numer. Anal., 61 (2023), pp. 2062-2083.

2.     A nonconvex perfectly matched layer method for the Helmholtz equation, with B. Li and Y. Li, SIAM J. Appl. Math., 83 (2023), pp. 666-694.

3.     A PML method for signal-propagation problems in axon, with X. Jiang, M. Lyu, and T. Yin, to SIAM J. Appl. Math., 83 (2023), pp. 1785-1805.

4.     An energy-stable finite element method for nonlinear Maxwell's equations, with L. Li and M. Lyu, Journal of Computational Physics, 486 (2023), 111125.

5.     A finite element method with energy-adaptive grids for the coupled Schrödinger-Poisson Drift-Diffusion model, with P. Mu and X. Wu, Journal of Computational Physics, 495 (2023), 112528.

6.     Uniform convergence of multigrid V-cycle on adaptively refined finite element meshes for elliptic problems with discontinuous coefficients, with H. Wu, Communications in Mathematical Research, 39 (2023), pp. 437-475.

7.     High-order characteristic finite element methods for moving interface problems, with C. Ma and T. Tian, J. Comput. Appl. Math., 425 (2023), 115028.

8.     A positivity-preserving finite element method for quantum drift-diffusion model, with P. Mu,  Journal of Computational Mathematics, 41 (2023), pp. 909-932.

9.     A fourth-order unfitted characteristic finite element method for free-boundary problems, with C. Ma, Journal of Computational Physics, 469 (2022), 111552.

10.    A fourth-order characteristic finite element method for the advection-diffusion equation on time-varying domains, with C. Ma and Q. Zhang,  SIAM J. Numer. Anal., 60 (2022), https://doi.org/10.1137/22M1483475.  (arXiv:2104.01870).

11.    An adaptive finite element DtN method for Maxwell's equations in biperiodic structures, with X. Jiang, P. Li, J. Lv, Z. Wang, and H. Wu, IMA Journal of Numerical Analysis, 42 (2022), pp. 2794-2828.

12.    A constrained transport divergence-free finite element method for incompressible MHD equations, with L. Li and D. Zhang, Journal of Computational Physics, Vol. 428, 1 March 2021, 109980.

13.    Monolithic multigrid for reduced magnetohydrodynamic equations, with X. Zhang, Journal of Computational Mathematics,  39 (2021), 453-470. (pdf)

14.    A CIP-FEM for high-frequency scattering problem with the truncated DtN boundary condition, with Y. Li and X. Zhu, CSIAM Transactions on Applied Mathematics, 1 (2020), 530-560. (pdf)

15.    High-order finite element methods for interface problems: theory and implementations, with Y. Xiao, F. Zhai, and L. Zhang, Book Chapter in High Order Methods for Partial Differential Equations, Editors: S.J. Sherwin, D. Moxey, J. Peiro, P.E. Vincent, and C. Schwarb, Lecture Notes in Computational Science and Engineering, Springer, 2020, 167-177.

16.    Drift Alfvén Energetic Particle Stability with Circulating Particles, with Y. Li, S. Hu, and Y. Xiao, Physics of Plasmas, 27 (6)，https://doi.org/10.1063/5.0005727 , 2020.

17.    Interface-penalty finite element methods for interface problems in H^1, H(curl), and H(div), with H. Liu, L. Zhang, and X. Zhang, Computer Methods in Applied Mechanics and Engineering, 367 (2020), 113137. (pdf)

18.    Exponential convergence of Cartesian PML method for Maxwell's equations in a two-layer medium, with X. Jiang and X. Duan, ESAIM: Math. Model. Numer. Anal. (M2AN), 54 (2020), 929-956.

19.    High-order numerical quadratures in a tetrahedron with an implicitly defined curved interface, with T. Cui, W. Leng, H. Liu, and L. Zhang, ACM Transactions on Mathematical Software, 46 (2019), No.1, 1-18. (pdf)

20.    A charge-conservative finite element method for inductionless MHD equations. Part I: convergence, with L. Li and M. Ni, SIAM Journal on Scientific Computing, 41 (2019), B796-B815. (pdf)

21.    A charge-conservative finite element method for inductionless MHD equations. Part II: a robust solver, with L. Li and M. Ni, SIAM Journal on Scientific Computing, 41 (2019), B816-B842. (pdf)

22.    Finite element analysis for non-stationary magneto-heat coupling problem, with X. Jiang, D. Zhang, and L. Zhang, Comm. Comput. Phys., 26 (2019), 1471-1489.

23.    Convergence of the PML solution for elastic wave scattering by biperiodic structures, with X. Jiang, P. Li, and J. Lv, Communications in Mathematical Sciences, 16 (2018), 987-1016. (pdf)

24.    A fully divergence-free finite element method for magnetohydrodynamic equations, with R. Hiptmair, L. Li, and S. Mao, Mathematical Models and Methods in Applied Sciences (M3AS), 28 (2018), 659-695. (pdf)

25.    A robust solver for the finite element approximation of stationary incompressible MHD equations in 3D, with L. Li, J. Comput. Phys., 351 (2017), 254-270. (pdf)

26.    An adaptive finite element PML method for the elastic wave scattering problem in periodic structures, with X. Jiang, P. Li, and J. Lv, ESAIM: Math. Model. Numer. Anal. (M2AN), 51 (2017), 2017-2047. (pdf)

27.    An adaptive finite element method for the wave scattering with transparent boundary condition, with X. Jiang, P. Li, and J. Lv, Journal of Scientific Computing, 72 (2017), 936-956. (pdf)

28.    PML method for electromagnetic scattering problem in a two-layer medium, with Z. Chen, SIAM J. Numer. Anal., 55 (2017), 2050-2084. (pdf)

29.    On the magneto-heat coupling model for large power transformers, with X. Li, S. Mao, and K. Yang, Comm. Comput. Phys., 22 (2017), 683-711.

30.    Maxwell's equations in an unbounded structure, with P. Li and G. Zheng, Mathematical Methods in the Applied Sciences, 40 (2017), 573-588. (pdf)

31.    Anisotropic adaptive FEM for MHD flow at high Hartmann numbers, with J. Zhao and S. Mao, Applied Mathematics and Mechanics, 37 (2016), 1479-1500. (pdf)

32.    The toolbox PHG and its applications, with L. Zhang et al, SCIENTIA SINICA, 10 (2016), 1442-1464. (pdf)

33.    An adaptive FEM for a Maxwell interface problem, with H. Duan, S. Li, and R. Tan, Journal of Scientific Computing, 67(2016), 669-704. (pdf)

34.    Eddy current model for nondestructive evaluation with thin cracks, with X. Jiang and P. Li, SIAM Journal on Scientific Computing, 38(2016), 973–996. (pdf)

35.    An adaptive perfectly matched layer method for multiple cavity scattering problems, with X. Wu, Communications in Computational Physics, 19 (2016), 534-558. (pdf)

36.    FEMAG: A High Performance Parallel Finite Element Toolbox for Electromagnetic Computations, with T. Cui and X. Jing, International Journal of Energy and Power Engineering, 5(2016), 57-64.

37.    Subspace correction method for computing magnetic shields in large power transformers, with X. Chen, IEEE Transactions on Magnetics, 51 (2015), Issue 5, DOI: 10.1109/TMAG.2014.2346741. (pdf)

38.    Homogenization of quasi-static Maxwell's equations, with X. Jiang, Multiscal Modeling and Simulation: A SIAM Interdisciplinary Journal, 12(2014), 152-180. (pdf)

39.    An H-ψ formulation for the three-dimensional eddy current problem in laminated structures, with P. Li, Journal of Differential Equations, 254 (2013), 3476-3500.(pdf)

40.    Numerical solution of acoustic scattering by an adaptive DtN finite element method, with P. Li and X. Jiang, Communications in Computational Physics, 13 (2013), 1227-1244.(pdf)

41.    On hp-adpative  finite element methods for time-harmonic Maxwell's equations, with X. Jiang and L. Zhang, Communications in Computational Physics, 13 (2013), 559-582. (pdf)

42.    A delta-regularization finite element method for a double curl problem with divergence-free constraint, with H. Duan, S. Li, and R. Tan, SIAM Journal on Numerical Analysis, 50 (2012), 3208-3230. (pdf)

43.    An overfilled cavity problem for Maxwell's equations, with P. Li and H. Wu, Mathematical Methods in the Applied Sciences, 35 (2012), 1951-1979. (pdf)

44.    An efficient eddy current model for nonlinear Maxwell equations with laminated conductors, with X. Jiang, SIAM Journal on Applied Mathematics, 72 (2012), 1021-1040. (pdf)

45.    An Inner-Constrained Separation Technique for 3D Finite Element Modeling of GO Silicon Steel Laminations, with Z. Cheng, IEEE Transactions on Magnetics, Vol. 48, No. 8, 2012, 2277-2283. (pdf)

46.    Uniform convergence of adaptive multigrid methods for elliptic problems and Maxwell's equations, with R. Hiptmair and H. Wu, Numerical Mathematics: Theory, Methods and Applications, 5 (2012), 297-332. (pdf)

47.    Local multilevel methods for second-order elliptic problems with highly discontinuous coefficients, with H. Chen and X. Xu, Journal of Computational Mathematics, 30 (2012), 223-248. (pdf)

48.     Adaptive uniaxial perfectly matched layer method for multiple scattering problems, with X. Jiang, Comput. Methods Appl. Mech. Engrg., 201 (2012), 42-52. (pdf).

49.    Electromagnetic scattering by unbounded rough surfaces, With P. Li and H. Wu, SIAM J. Math. Anal., 43(2011), 1205-1231 (pdf).

50.    Convergence of the uniaxial perfectly matched layer method for time-harmonic scattering problems in layered media, With Z. Chen, SIAM J. Numer. Anal., 48 (2010), 2158-2185 (pdf).

51.    Local Multigrid in H(curl), With R. Hiptmair, J. Comp. Math., 27(2009), 573-603 (pdf).

52.    Adaptive finite element frequency domain method for eddy current problems, with F. Zhang, Comput. Methods Appl. Mech. Engrg., 197 (2008), 1233-1241 (pdf).

53.    An adaptive multilevel method for time-harmonic Maxwell equations with singularities, With Z. Chen and L. Wang, SIAM J. Sci. Comput., 29 (2007), 118-138. (pdf).

54.    An adaptive finite element method for the H--Ψ formulation of time-dependent eddy current problems, With Z. Chen and L. Wang, Numer. Math., 103(2006), 667-689 (pdf).

55.    On Friedrichs-Poincaré-type inequalities, J. Math. Anal. Appl., 304(2005), 542-551 (Page-1, the rest).

56.    On locking-free finite element scheme for three-dimensional elasticity, With Q. He and L. Wang, J. Comp. Math., 23(2005), 101-112 (pdf).

57.    Finite element approximations to the discrete spectrum of the Schrodinger operator with the Coulomb potential, With L. Ying, SIAM J. Numer. Anal., 42(2004), 49-74 (pdf).

58.    Finite element calculations for the helium atom, With L. Ying, Int. J. Quantum Chem., 97(2004), 659-669 (pdf).

59.    Numerical solutions of the Schrodinger equation for the ground lithium by the finite element method, With L. Ying and P. Ding, Appl. Math. Comp., 153(2004), 685-695 (Page-1, the rest).

60.    The approximate energies of the 1S2P-states of the Helium by the finite element method, With L. Ying, Chinese J. Comp. Phys., 20 (2003), 119-122.

61.    Solving nonhomogenous Dirichlet boundary problems in Domain with curved boundaries by like Wilson element method, With S. Chen, Numer. Math. Sinica, 25 (2003), 67-78.

62.    The application of the Hylleraas-Breit transformation to the Schroedinger equations of helium-like atoms, Chinese Journal of Atomic and Molecular physics, 19 (2002), 253-259 (pdf).