PUBLICATIONS: SUBJECT CLASSIFICATION

A Posteriori Error Analysis and Adaptivity

  • General interests

  • Unfitted finite element method

  • Free boundary and phase transition

  • Electromagnetism

    • Reverse Time Migration for Inverse Scattering Problems

    Perfectly Matched Layer

    Multiscale Computation of Flow Transport in Porous Media

    Mathematical and Numerical Analysis for Free Boundary Problems

  • Superconductivity

  • Continuous casting

  • Phase transitions

    • Miscellaneous

    A Posteriori Error Analysis and Adaptivity

    Unfitted finite element method

    1. An arbitrarily high-order finite element method on arbitrarily shaped domains with automatic mesh generation (in Chinese), with Y. Liu, Sci. Sin. Math. 54 (2024), 1-18.

    2. An arbitrarily high order unfitted finite element method for elliptic interface problems with automatic mesh generation, with Y. Liu, J. Comput. Phys. 491 (2023) 112384 (24pp).

    3. An adaptive high-order unfitted finite element method for elliptic interface problems, with K. Li and X. Xiang, Numer. Math. 149 (2021), 507-548.

    General interests

    1. The adaptive immersed interface finite element method for elliptic and Maxwell interface problems, with Yuanming Xiao and Linbo Zhang, Journal of Computational Physics 228 (2009), 5000-5019.

    2. Sharp $L^1$ a posteriori error analysis for nonlinear convection-diffusion problems with G.H. Ji, Math. Comp. 75 (2006), 43-71.

    3. Uniform convergence of multigrid V-cycle on adaptively refined finite element meshes for second order elliptic problems,
      with H. Wu, Science in China: Series A Mathematics 49 (2006), 1405-1429.

    4. Adaptive computation for convection dominated diffusion problems,
      with G.H. Ji, Science in China (Series A) 47 (2004), Supp. 22-31.

    5. An adaptive finite element method with reliable and efficient error control for linear parabolic problems,
      with F. Jia, Math. Comp. 73 (2004), 1163-1197.

    6. On the efficiency of adaptive finite element methods for elliptic problems with discontinous coefficients,
      with S. Dai, SIAM J. Sci. Comput. 24 (2002), 443-462.

    Free boundary and phase transitions

    1. Adaptive Galerkin method with error control for a dynamical Ginzburg-Landau model in superconductivity,
      with S. Dai, SIAM J. Numer. Anal. 38 (2001), 1961-1985.

    2. A posteriori error control and adaptivity for a phase relaxation model,
      with R.H. Nochetto and A. Schmidt, Math. Model. Numer. Anal. 34 (2000), 775-797.

    3. An adaptive finite element method with error control for the continuous casting problem,
      with R.H. Nochetto and A. Schmidt, Computer Meth. Appl. Mech. Engrg. 189 (2000), 249-276

    4. Residual type a posteriori error estimates for elliptic obstacle problems,
      with R.H. Nochetto, Numer. Math. 84 (2000), 527-548

    Electromagnetism

    1. Detection and classification from electromagnetic induction data , with H. Ammari, J. Chen, D. Volkov, and H. Wang, Journal of Computational Physics, 301 (2015), 201-217.

    2. Target Detection and Characterization from Electromagnetic Induction Data, with H. Ammari, J. Chen, J. Garnier, and Volkov, J. Math. Pures Appl. 101 (2014), 54-75.

    3. ParAFEMCap: A parallel adaptive finite element method for 3-D VLSI Interconnect Capacitance Extraction with G. Chen, H. Zhu, T. Cui, X. Zeng, W. Cai, IEEE Transaction on Microwave Theory and Techniques 60 (2012), 218-231.

    4. An Adaptive Finite Element Method for the Eddy Current Model with Circuit/Field Couplings with Junqing Chen, Tao Cui and Linbo Zhang, SIAM J. Sci. Computing, 32 (2010), 1020-1042.

    5. The adaptive immersed interface finite element method for elliptic and Maxwell interface problems, with Yuanming Xiao and Linbo Zhang, Journal of Computational Physics 228 (2009), 5000-5019.

    6. An $hp$ Adaptive Uniaxial Perfectly Matched Layer Method for Helmholtz Scattering Problems with B.Q. Guo and Y.M. Xiao, Communications in Computational Physics 5 (2009), 546-564.

    7. On Maxwell Equations with the transparent boundary condition with J.-C. Nedelec, J. Comput. Math. 26 (2008), 284-296.

    8. An adaptive multilevel method for time-harmonic Maxwell equations with singularities,
      with L. Wang and W. Zheng, SIAM J. Sci. Comput., 29 (2007), 118-138.

    9. An adaptive finite element method for the ${\bf H}-\psi$ formulation of time-dependent eddy current problems,
      with W.Y. Zheng and L. Wang, Numer. Math. 103 (2006), 667-689.

    10. An adaptive finite element method for diffraction gratings,
      with G. Bao and H.J. Wu, Journal of the Optical Society of America A, 22 (2005), 1106-1114.

    11. Finite element methods with matching and non-matching meshes for Maxwell equations with discontinuous coefficients,
      with Q. Du and J. Zou, SIAM J. Numer. Anal. 37 (2000), 1524-1570

    Reverse Time Migration for Inverse Scattering Problems

    1. A Direct Imaging Method for Half-space Inverse Elastic Scattering Problems, with S. Zhou, Inverse Problems 35 (2019), 075004 (33pp)

    2. A Direct Imaging Method for the Half-space Inverse Scattering Problems with Phaseless Data, with G. Huang and S. Fang, Inverse Problems and Imaging 11 (2017), 901-916.

    3. A Direct Imaging Method for Electromagnetic Scattering Data without Phase Information, with G. Huang, SIAM J. Imaging Sciences 9 (2016), 1273-1297.

    4. Phaseless Imaging by Reverse Time Migration: Acoustic Waves, with G. Huang, Numer. Math. Theor. Meth. Appl. 10 (2017), 1-21.

    5. Reverse Time Migration for Reconstructing Extended Obstacles in the Half Space, with G. Huang, Inverse Problems 31 (2015) 055007 (19pp) .

    6. Reverse Time Migration for Extended Obstacles: Elastic Waves (in Chinese), with G. Huang Sci. Sin. Math. 45 (2015), 1103-1114, doi: 10.1360/N012014-00097.

    7. Reverse Time Migration for Reconstructing Extended Obstacles in Planar Acoustic Waveguides, with G. Huang, Science in China: Series A Mathematics 58 (2015), 1811-1834.

    8. Reverse Time Migration for Extended Obstacles: Electromagnetic Waves, with J. Chen and G. Huang, Inverse Problems 29 (2013) 085006 (17pp).

    9. Reverse Time Migration for Extended Obstacles: Acoustic Waves, with J. Chen and G. Huang, Inverse Problems 29 (2013) 085005 (17pp).

    Perfectly Matched Layer Method

    1. PML method for electromagnetic scattering problem in a two-layer medium, with W. Zheng, SIAM J. Numer. Anal. 55 (2017), 2050-2084.

    2. A Source Transfer Domain Decomposition Method for Time-harmonic Elastic Wave Equations, with T. Cui and X. Xiang, Scientia Sinica Informatics 46 (2016), 1359-1371. (in Chinese)

    3. Convergence of the PML Method for Elastic Wave Scattering Problems, with X. Xiang and X. Zhang, Math. Comp. 85 (2016). 2687-2714.

    4. A Source Transfer Domain Decomposition Method For Helmholtz Equations in Unbounded Domain, with X. Xiang, SIAM J. Numer. Anal. 51 (2013), 2331-2356.

    5. A Source Transfer Domain Decomposition Method For Helmholtz Equations in Unbounded Domain, Part II: Extensions, with X. Xiang, Numer. Math. Theor. Meth. Appl. 6 (2013), 538-555.

    6. An Anisotropic Perfectly Matched Layer Method for Helmholtz Scattering Problems with Discontinuous Wave Number, with C. Liang and X. Xiang, Inverse Problems and Imaging 7 (2013), 663-678.

    7. Long-time Stability and Convergence of the Uniaxial Perfectly Matched Layer Method for Time-domain Acoustic Scattering Problems with Xinming Wu, SIAM J. Numer. Anal. 50 (2012), 2632-2655.

    8. An adaptive anisotropic perfectly matched layer method for 3-D time harmonic electromagnetic scattering problems with Tao Cui and Linbo Zhang, Numer. Math. 125 (2013), 639-677.

    9. Convergence of the uniaxial perfectly matched layer method for time-harmonic scattering problems in two-layered media with Weiying Zheng, SIAM J. Numer. Anal, 48 (2010), 2158-2185.

    10. Convergence of the time-domain perfectly matched layer method for acoustic problems International Journal of Numerical Analysis and Modeling, 6 (2009), 124-146.

    11. An adaptive uniaxial perfectly matched layer technique for Time-Harmonic Scattering Problems with X.M. Wu, Numerical Mathematics: Theory, Methods and Applications, 1 (2008), 113-137.

    12. An adaptive perfectly matched layer technique for 3-D time-harmonic electromagnetic scattering problems with J. Chen, Math. Comp. 77 (2008), 673-698.

    13. An Adaptive Perfectly Matched Layer Technique for Time-harmonic Scattering Problems,
      with X.Z. Liu, SIAM J. Numer. Anal. 43 (2005), 645-671.

    14. An Adaptive Finite Element Method with Perfectly Matched Absorbing Layers for the Wave Scattering by Periodic Structures,
      with H.J. Wu, SIAM J. Numer. Anal. 41 (2003), 799-826.

      Multiscale Computation of Flow Transport in Porous Media

      1. Upscaling of a class of nonlinear parabolic equations for the flow transport in heterogeneous porous media,
        with W.B. Deng and H. Ye, Communications in Mathematical Sciences 3 (2005), 493-515.

      2. A new upscaling method for the solute transport equations,
        with W.B. Deng and H. Ye, Continuous and Discrete Dynamical Systems 13 (2005), 941-962.

      3. Numerical homogenization of well singularities in the flow transport through heterogeneous porous media,
        with X.Y. Yue, Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal 1 (2003), 260-303.

      4. A mixed multiscale finite element method for elliptic problems with oscillating coefficients,
        with T.Y. Hou, Math. Comp. 72 (2002), 541-576.

      Mathematical and Numerical Analysis for Free Boundary Problems

      Superconductivity

      1. Adaptive Galerkin method with error control for a dynamical Ginzburg-Landau model in superconductivity,
        with S. Dai, SIAM J. Numer. Anal. 38 (2001), 1961-1985.

      2. An upwinding finite element method for a mean field model for superconducting vortices,
        with Q. Du, Math. Model. Numer. Anal. 34 (2000), 687-706.

      3. Numerical solutions of an optimal control problem governed by a Ginzburg-Landau model in superconductivity,
        with K.-H. Hoffmann, Numer. Funct. Anal. Optimiz. 19 (1998), 737-758.

      4. Justification of a two-dimensional evolutionary Ginzburg-Landau superconductivity model,
        with C.M. Elliott and Q. Tang, RAIRO Math. Model. Numer. Anal. 32 (1998), 25-50.

      5. Global classical solutions to a non-isothermal dynamical Ginzburg-Landau model in superconductivity,
        with K.-H. Hoffmann, Numer. Funct. Anal. Optimiz. 18 (1997), 901-920.

      6. On the Lawrence-Doniach model for layered superconductors,
        with K.-H. Hoffmann and L. Jiang, Euro. J. Appl. Math. 8 (1997), 369-387.

      7. Mixed finite element methods for a dynamical Ginzburg-Landau model in superconductivity,
        Numer. Math. 76 (1997), 323-353.

      8. Modelling and numerical solutions of a gauge periodic time dependent Ginzburg-Landau model for type-II superconductors,
        J. Comput. Math. 15 (1997) 365-384.

      9. Optimal control of dynamical Ginzburg-Landau vortices in Superconductivity,
        with K.-H. Hoffmann, Numer. Funct. Anal. Optimiz. 17 (1996), 241-258.

      10. Numerical Studies of a non-stationary Ginzburg-Landau model for superconductivity,
        with K.-H. Hoffmann, Adv. Math. Sci. Appl. 5 (1995), 363-389.

      Continuous casting

      1. An adaptive finite element method with error control for the continuous casting problem,
        with R.H. Nochetto and A. Schmidt, Computer Meth. Appl. Mech. Engrg. 189 (2000), 249-276.

      2. Numerical methods for Stefan problems with prescribed convection and nonlinear flux,
        with T.M. Shih and Y.X.Yue, IMA J. Numer. Anal. 20 (2000), 81-98.

      3. Approximation of a two-phase continuous casting Stefan problems,
        with L. Jiang, J. Partial Differential Equations 11 (1998), 59-72.

      Phase transitions

      1. A posteriori error control and adaptivity for a phase relaxation model,
        with R.H. Nochetto and A. Schmidt, Math. Model. Numer. Anal. 34 (2000), 775-797.

      2. Asymptotic behaviors of Landau-Devonshire-Ginzburg model for structural phase transitions in shape memory alloys,
        with K.-H. Hoffmann, Adv. Math. Sci. Appl. 4 (1994), 209-226.

      3. On a one-dimensional nonlinear thermoviscoelastic model for structural phase transitions in shape memory alloys,
        with K.-H. Hoffmann, J. Diff. Equations 112 (1994), 325-350.

      4. An error estimate for a finite element scheme for a phase field model,
        with K.-H. Hoffmann, IMA J. Numer. Anal. 14 (1994), 243-255.

      5. Optimal boundary controls for a phase field model,
        IMA J. Math. Contr. Inform. 10 (1993), 157-176.

      Miscellaneous

      1. Stochastic convergence of regularized solutions and their finite element approximations to inverse source problems, with W. Zhang and J. Zou, SIAM J. Numer. Anal. 60 (2022), 751-780.

      2. A balanced oversampling finite element method for elliptic problems with observational boundary data, with R. Tuo and W. Zhang, J. Comput. Math. 38 (2020), 355-374.

      3. Stochastic convergence of a nonconforming finite element method for the thin plate spline smoother for observational data, with R. Tuo and W. Zhang, SIAM J. Numer. Anal. 56 (2018), 635-659.

      4. An adaptive immersed finite element method with arbitrary Lagrangian-Eulerian scheme for parabolic equations in time variable domains, with Z. Wu and Y. Xiao, International Journal of Numerical Analysis and Modeling 12 (2015), 567-591.

      5. Uniform convergence of multigrid V-cycle on adaptively refined finite element meshes for second order elliptic problems,
        with H. Wu, Science in China: Series A Mathematics 49 (2006), 1405-1429.

      6. On the efficiency of adaptive finite element methods for elliptic problems with discontinous coefficients,
        with S. Dai, SIAM J. Sci. Comput. 24 (2002), 443-462.

      7. On the augmented Lagrangian approach to Signorini elastic contact problem,
        Numer. Math. 88 (2001), 641-659.

      8. An augmented Lagrangian method for identifying discontinuous parameters in elliptic systems,
        with J. Zou, SIAM J. Control and Optimization 37 (1999), 892-910.

      9. Finite element methods and their convergence for elliptic and parabolic interface problems,
        with J. Zou, Numer. Math. 79 (1998), 175-202.

      10. A full-discretization moving FEM with optimal convergence rate,
        with G.P. Liang, Chinese J. Num. Math. \& Appl. 12 (1990), 91-111.