book
- (with G. Bao) Maxwell's Equations in Periodic Structures, Series on Applied Mathematical Sciences, vol. 208, Science Press, Beijing/Springer, Singapore, 2022.
preprint
- (with H. Dong) Uniqueness of an inverse cavity scattering problem for the biharmonic wave equation, submitted, 2023.
- (with G. Bao and X. Yuan) Convergence of the PML method for the biharmonic wave scattering problem in periodic structures, submitted, 2023.
- (with X. Feng, Q. Yao, and X. Wang) An inverse source problem for the stochastic multi-term time-fractional diffusion-wave equation, submitted, 2023.
- (with J. Wang) Nonradiating sources of the biharmonic wave equation, submitted, 2023.
- (with X. Yuan) A highly efficient and accurate numerical method for the electromagnetic scattering problem with rectangular cavities, submitted, 2023.
- (with Y. Liang) Stability for inverse source problems of the stochastic Helmholtz equation with a white noise, submitted, 2023.
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journal
- (with X. Wang) Inverse scattering for the biharmonic wave equation with a random potential, SIAM J. Math. Anal., to appear.
- (with X. Yao and Y. Zhao) The scattering resonances for Schrodinger-type operators with unbounded potentials, SIAM J. Math. Anal., to appear.
- (with H. Dong) A novel boundary integral formulation for the biharmonic wave scattering problem, J. Sci. Comput., to appear.
- (with J. Yue) Numerical solution of the cavity scattering problem for flexural waves on thin plates: linear finite element methods, J. Comput. Phys., 497 (2024), 112606.
- (with D. Chen, N. Guan, and X. Zhong) A stochastic Galerkin method for the direct and inverse random source problems of the Helmholtz equation, Comm. Math. Sci., to appear.
- (with Y. Wang) Inverse scattering of periodic surfaces with a superlens, Optics Express, 31 (2023), 30894-30910.
- (with X. Feng and X. Wang) An inverse potential problem for the stochastic diffusion equation with a multiplicative white noise, Inverse Problems and Imaging, 18 (2024), 271-285.
- (with Y. Liang and Y. Wang) A data-assisted two-stage method for the inverse random source problem, SIAM J. Imaging Sci., 16 (2023), 1929-1952.
- (with J. Jia, Y. Wu, and D. Meng) Variational inverting network for statistical inverse problems of partial differential equations, J. Mach. Learn. Res., 24 (2023), 1-60.
- (with G. Bao, M. Zhang, X. Jiang, and X. Yuan) An adaptive finite element DtN method for Maxwell's equations, East Asian J. Appl. Math., 13 (2023), 610-645.
- (with J. Yue, X. Yuan, and X. Zhu) A diffraction problem for the biharmonic wave equation in one-dimensional periodic structures, Results Appl. Math., 17 (2023), 100350.
- (with J. Li and X. Wang) Inverse random potential scattering for elastic waves, Multiscale Model. Simul., 21 (2023), 426-447.
- (with J. Lai and H. Dong) A spectral boundary integral method for the elastic obstacle scattering problem in three dimensions, J. Comput. Phys., 469 (2022), 111546.
- (with J. Li and X. Wang) Inverse elastic scattering for a random potential, SIAM J. Math. Anal., 54 (2022), 5126-5159.
- (with J. Jia and D. Meng) Stein variational gradient descent on infinite-dimensional space and applications to statistical inverse problems, SIAM J. Numer. Anal., 60 (2022), 2225-2252.
- (with J. Li and X. Wang) Inverse source problems for the stochastic wave equations: far-field patterns, SIAM J. Appl. Math., 82 (2022), 1113-1134.
- (with X. Wang) An inverse random source problem for the biharmonic wave equation, SIAM/ASA J. Uncertainty Quantification, 10 (2022), 949-974.
- (with X. Yuan) An adaptive finite element DtN method for the elastic wave scattering problem, Numer. Math., 150 (2022), 993-1033.
- (with Y. Chen and Y. Gao) Analysis of the time-domain PML problem for the electromagnetic scattering by periodic structures, Comm. Math. Sci., 20 (2022), 1785-1813.
- (with G. Bao, X. Jiang, and X. Yuan) An adaptive finite element DtN method for the elastic wave scattering by biperiodic structures, ESAIM: Math. Model. Numer. Anal., 55 (2021) 2921-2947.
- (with X. Yao and Y. Zhao) Stability for an inverse source problem of the biharmonic operator, SIAM J. Appl. Math., 81 (2021), 2503-2525.
- (with G. Bao and X. Yuan) An adaptive finite element DtN method for the elastic wave scattering problem in three dimensions, SIAM J. Numer. Anal., 59 (2021), 2900-2925.
- (with X. Feng, M. Zhao, and X. Wang) An inverse source problem for the stochastic wave equation, Inverse Problems and Imaging, 16 (2022), 397-415.
- (with X. Yao and Y. Zhao) Stability of an inverse source problem for the damped biharmonic plate equation, Inverse Problems, 37 (2021), 085003.
- (with X. Jiang, J. Lv, Z. Wang, H. Wu, and W. Zheng) An adaptive edge finite element DtN method for Maxwell's equations in biperiodic structures, IMA J. Numer. Anal., 42 (2022), 2794-2828.
- (with H. Dong and J. Lai) A highly accurate boundary integral method for the elastic obstacle scattering problem, Math. Comp., 90 (2021), 2785-2814.
- (with Y. Chen, X. Jiang, and J. Lai) A fast algorithm for the electromagnetic scattering from a large rectangular cavity in three dimensions, J. Comput. Phys., 437 (2021), 110331.
- (with X. Wang) Regularity of distributional solutions to stochastic acoustic and elastic scattering problems, J. Differential Equations, 285 (2021), 640-662.
- (with Y. Gong, X. Wang, and X. Xu) Numerical solution of an inverse random source problem for the time fractional diffusion equation via PhaseLift, Inverse Problems, 37 (2021), 045001.
- (with X. Wang) Inverse random source scattering for the Helmholtz equation with attenuation, SIAM J. Appl. Math., 81 (2021), 485-506.
- (with J. Zhai and Y. Zhao) Lipschitz stability for an inverse source scattering problem at a fixed frequency, Inverse Problems, 37 (2021), 025003.
- (with X. Wang) An inverse random source problem for the one-dimensional Helmholtz equation with attenuation, Inverse Problems, 37 (2021), 015009.
- (with Y. Chen and X. Yuan) An adaptive finite element PML method for the open cavity scattering problems, Commun. Comput. Phys., 29 (2021), 1505-1540.
- (with G. Bao, M. Zhang, and B. Hu) An adaptive finite element DtN method for the three-dimensional acoustic wave scattering problem, Discrete Contin. Dyn. Syst. Ser. B, 26 (2021), 61-79.
- (with J. Zhai and Y. Zhao) Stability for the acoustic inverse source problem in inhomogeneous media, SIAM J. Appl. Math., 80 (2020), 2547-2559.
- (with X. Wang) An inverse random source problem for Maxwell's equations, Multiscale Model. Simul., 19 (2021), 25-45.
- (with X. Yuan and G. Bao) An adaptive finite element DtN method for the open cavity scattering problems, CSIAM Trans. Appl. Math., 1 (2020), 316-345.
- (with J. Li and T. Helin) Inverse random source problems for time-harmonic acoustic and elastic waves, Commun. Partial Differential Equations, 45 (2020), 1335-1380.
- (with S. Bugarija, P. Gibson, G. Hu, and Y. Zhao) Inverse scattering for the one-dimensional Helmholtz equation with piecewise constant wave speed, Inverse Problems, 36 (2020), 075008.
- (with G. Hu and Y. Zhao) Elastic scattering from rough surfaces in three dimensions, J. Differential Equations, 269 (2020), 4045-407.
- (with H. Dong and J. Lai) An inverse acoustic-elastic interaction problem with phased or phaseless far-field data, Inverse Problems, 36 (2020), 035014.
- (with X. Feng and X. Wang) An inverse random source problem for the time fractional diffusion equation driven by a fractional Brownian motion, Inverse Problems, 36 (2020), 045008.
- (with X. Ji and J. Sun) Computation of interior elastic transmission eigenvalues using a conforming finite element and the secant method, Results Appl. Math., 5 (2020), 100083.
- (with X. Yuan) Convergence of an adaptive finite element DtN method for the elastic wave scattering by periodic structures, Comput. Methods Appl. Mech. Engrg., 360 (2020), 112722.
- (with J. Li) Inverse elastic scattering for a random source,
SIAM J. Math. Anal., 51 (2019), 4570-4603.
- (with J. Lai) A framework for simulation of multiple elastic scattering in two-dimensions, SIAM J. Sci. Comput., 41 (2019), A3276-A3299.
- (with L. Zhang) Analysis of transient acoustic scattering by an elastic obstacle, Comm. Math. Sci., 17 (2019), 1671-1698.
- (with G. Bao and Y. Zhao) Stability for the inverse source problems in elastic and electromagnetic waves, J. Math. Pures Appl., 134 (2020), 122-178.
- (with J. Wang and L. Zhang) Inverse obstacle scattering for Maxwell's equations in an unbounded structure, Inverse Problems, 35 (2019), 095002.
- (with G. Bao, B. Hu, and J. Wang) Time domain scattering for elastic waves in a biperiodic structure, SCIENTIA SINICA Mathematica, 49 (2019), 1723-1748.
- (with G. Hu, Y. Kian, and Y. Zhao) Inverse moving source problems in electrodynamics, Inverse Problems, 35 (2019), 075001.
- (with G. Bao, H. Liu, and L. Zhang) Inverse obstacle scattering in an unbounded structure, Commun. Comput. Phys., 26 (2019), 1274-1306.
- (with H. Dong and J. Lai) Inverse obstacle scattering for elastic waves with phased or phaseless far-field data, SIAM J. Imaging Sci., 12 (2019), 809-838.
- (with G. Bao, B. Hu, and J. Wang) Analysis of time-domain Maxwell's equations in biperiodic structures, Discrete Contin. Dyn. Syst. Ser. B, 25 (2020), 259-286.
- (with Y. Gao and Y. Yang) On an inverse source problem for the Biot equations in electro-seismic imaging, Inverse Problems, 35 (2019), 095009.
- (with H.-A. Diao and X. Yuan) Inverse elastic surface scattering with far-field data, Inverse Problems and Imaging, 13 (2019), 721-744.
- (with X. Yuan) Inverse obstacle scattering for elastic waves in three dimensions, Inverse Problems and Imaging, 13 (2019), 545-573.
- (with J. Yue, M. Li, and X. Yuan) Numerical solution of an inverse obstacle scattering problem for elastic waves via the Helmholtz decomposition, Commun. Comput. Phys., 26 (2019), 809-837.
- (with G. Hu, X. Liu, and Y. Zhao) Inverse source problems in electrodynamics, Inverse Problems and Imaging, 12 (2018), 1411-1428.
- (with Y. Gao and Y. Li) Analysis of time-domain elastic scattering by an unbounded structure, Math. Meth. Appl. Sci., 41 (2018), 7032-7054.
- (with X. Jiang, J. Lv, and W. Zheng) Convergence of the PML solution for elastic wave scattering by biperiodic structures, Comm. Math. Sci., 16 (2018), 987-1014.
- (with G. Bao and Y. Gao) Time-domain analysis of an acoustic-elastic interaction problem, Arch. Ration. Mech. Anal., 229 (2018), 835-884.
- (with M. Li and C. Chen) Inverse random source scattering for the Helmholtz equation in inhomogeneous media, Inverse Problems, 34 (2018), 015003.
- (with Y. Zhao) Stability on the one-dimensional inverse source scattering problem in a two-layered medium, Applicable Analysis, 98 (2019), 682-692.
- (with J. Lai, M. Li, and W. Li) A fast direct imaging method for the inverse obstacle scattering problem with nonlinear point scatterers, Inverse Problems and Imaging, 12 (2018), 635-665.
- A survey of open cavity scattering problems, J. Comp. Math., 36 (2018), 1-16.
- (with J. Zheng, J. Cheng, and S. Lu) Periodic surface identification with phase or phaseless near-field data, Inverse Problems, 33 (2017), 115004.
- (with G. Bao and C. Chen) Inverse random source scattering for elastic waves, SIAM J. Numer. Anal., 55 (2017), 2616-2643.
- (with Y. Gao and B. Zhang) Analysis of transient acoustic-elastic interaction in an unbounded structure, SIAM J. Math. Anal., 49 (2017), 3951-3972.
- (with X. Jiang) Inverse electromagnetic diffraction by biperiodic dielectric gratings, Inverse Problems, 33 (2017), 085004.
- (with Y. Gao) Electromagnetic scattering for time-domain Maxwell's equations in an unbounded structure, Math. Models Methods Appl. Sci., 27 (2017), 1843-1870.
- (with X. Jiang) An adaptive finite element PML method for the acoustic-elastic interaction in three dimensions, Commun. Comput. Phys., 22 (2017), 1486-1507.
- (with X. Jiang, J. Lv, and W. Zheng) An adaptive finite element PML method for the elastic wave scattering problem in periodic structures, ESAIM: Math. Model. Numer. Anal., 51 (2017), 2017-2047.
- (with G. Yuan) Increasing stability for the inverse source scattering problem with multi-frequencies, Inverse Problems and Imaging, 11 (2017), 745-759.
- (with X. Jiang, J. Lv, and W. Zheng) An adaptive finite element method for the wave scattering with transparent boundary condition, J. Sci. Comput., 72 (2017), 936-956.
- (with G. Yuan) Stability on the inverse random source scattering problem for the one-dimensional Helmholtz equation, J. Math. Anal. Appl., 450 (2017), 872-887.
- (with G. Zheng and W. Zheng) Maxwell's equations in an unbounded structure, Math. Meth. Appl. Sci., 40 (2017), 573-588.
- (with Y. Wang, Z. Wang, and Y. Zhao) Inverse obstacle scattering for elastic waves, Inverse Problems, 32 (2016), 115018.
- (with G. Bao and C. Chen) Inverse random source scattering problems in several dimensions, SIAM/ASA J. Uncertainty Quantification, 4 (2016), 1263-1287.
- (with Y. Gao) Analysis of time-domain scattering by periodic structures, J. Differential Equations, 261 (2016), 5094-5118.
- (with Y. Wang and Y. Zhao) Near-field imaging of biperiodic surfaces for elastic waves, J. Comput. Phys., 324 (2016), 1-23.
- (with G. Bao and Y. Wang) Near-field imaging with far-field data, Appl. Math. Lett., 60 (2016), 36-42.
- (with X. Jiang and W. Zheng) Eddy current model for nondestructive evaluation with thin cracks, SIAM J. Sci. Comput., 38 (2016), A973-A996.
- (with Y. Wang and Y. Zhao) Convergence analysis in near-field imaging for elastic waves, Applicable Analysis, 95 (2016), 2339-2360.
- (with J. Li, H. Liu, and X. Liu) Recovering multiscale buried anomalies in a two-layered medium, Inverse Problems, 31 (2015), 105006.
- (with G. Bao, J. Lin, and F. Triki) Inverse scattering problems with multi-frequencies, Inverse Problems, 31 (2015), 093001.
- (with Y. Wang) Near-field imaging of small perturbed obstacles for elastic waves, Inverse Problems, 31 (2015), 085010.
- (with L. Wang and A. Wood) Analysis of transient electromagnetic scattering from a three-dimensional open cavity, SIAM J. Appl. Math., 75 (2015), 1675-1699.
- (with Y. Wang) Numerical solution of an inverse obstacle scattering problem with near-field data, J. Comput. Phys., 290 (2015), 157-168.
- (with Z. Wang, G. Bao, J. Li, and H. Wu) An adaptive finite element method for the diffraction grating problem with transparent boundary condition, SIAM J. Numer. Anal., 53 (2015), 1585-1607.
- (with Y. Wang and Y. Zhao) Inverse elastic surface scattering with near-field data, Inverse Problems, 31 (2015), 035009.
- (with Y. Wang) Near-field imaging of interior cavities, Commun. Comput. Phys., 17 (2015), 542-563.
- (with Y. Wang) Near-field imaging of obstacles, Inverse Problems and Imaging, 9 (2015), 189-210.
- (with Y. He and J. Shen) A new spectral method for numerical solution of the unbounded rough surface scattering problem, J. Comput. Phys., 275 (2014), 608-625.
- (with G. Bao) Convergence analysis in near-field imaging, Inverse Problems, 30 (2014), 085008.
- (with G. Bao) Near-field imaging of infinite rough surfaces in dielectric media, SIAM J. Imaging Sci., 7 (2014), 867-899.
- (with G. Bao, S.-N. Chow, and H. Zhou) An inverse random source problem for the Helmholtz equation, Math. Comp., 83 (2014), 215-233.
- (with G. Bao, K. Huang, and H. Zhao) A direct imaging method for
inverse scattering using the generalized Foldy-Lax formulation,
Contemp. Math., 615 (2014), 49-70.
- (with G. Bao and T. Cui) Inverse diffraction grating of Maxwell's equations in biperiodic structures, Optics Express, 22 (2014), 4799-4816.
- (with A. Wood) Electromagnetic scattering by multiple cavities embedded in the infinite 2D ground plane, ACES Journal, 29 (2014), 505-514.
- (with G. Bao) Near-field imaging of infinite rough surfaces, SIAM J. Appl. Math., 73 (2013), 2162-2187.
- (with T. Cheng and Y. Wang) Near-field imaging of perfectly conducting grating surfaces, J. Opt. Soc. Am. A, 30 (2013), 2473-2481.
- (with A. Wood) A two-dimensional Helmholtz equation solution for the multiple cavity scattering problem, J. Comput. Phys., 240 (2013), 100-120.
- (with W. Zheng) An H-\psi formulation for the three-dimensional eddy current problem in laminated structures, J. Differential Equations, 254 (2013), 3476-3500.
- (with G. Bao and J. Lv) Numerical solution of an inverse diffraction grating problem from phaseless data, J. Opt. Soc. Am. A, 30 (2013), 293-299.
- (with K. Huang and H. Zhao) An efficient algorithm for the generalized Foldy-Lax formulation, J. Comput. Phys., 234 (2013), 376-398.
- (with G. Bao and T. Ehlers) Radiogenic source identification for the Helium production-diffusion equation, Commun. Comput. Phys., 14 (2013), 1-20.
- (with X. Jiang and W. Zheng) Numerical solution of acoustic scattering by an adaptive DtN finite element method, Commun. Comput. Phys., 13 (2013), 1227-1244.
- (with J. Shen) Analysis of the scattering by an unbounded rough surface, Math. Meth. Appl. Sci., 35 (2012), 2166-2184.
- (with H. Wu and W. Zheng) An overfilled cavity problem for Maxwell's equations, Math. Meth. Appl. Sci., 35 (2012), 1951-1979.
- (with G. Bao and H. Wu) A computational inverse diffraction grating problem, J. Opt. Soc. Am. A, 29 (2012), 394-399.
- An inverse cavity problem for Maxwell's equations, J. Differential Equations, 252 (2012), 3209-3225.
- (with H. Wu and W. Zheng) Electromagnetic scattering by unbounded rough surfaces, SIAM J. Math. Anal., 43 (2011), 1205-1231.
- (with G. Bao and J. Gao) Analysis of direct and inverse cavity scattering problems, Numer. Math. Theor. Meth. Appl., 4 (2011), 335-358.
- An inverse random source scattering problem in inhomogeneous media, Inverse Problems, 27 (2011), 035004.
- (with G. Bao, Y. Dou, T. Ehlers, Y. Wang, and Z. Xu) Quantifying tectonic and geomorphic interpretations of thermochronometer data: the reconstruction of mountain surface, Commun. Comput. Phys., 9 (2011), 129-146.
- (with K. Huang) A two-scale multiple scattering problem, Multiscale Model. Simul., 8 (2010), 1511-1534.
- (with G. Bao, S.-N. Chow, and H. Zhou) Numerical solution of an inverse medium scattering problem with a stochastic source, Inverse Problems, 26 (2010), 074014.
- Coupling of finite element and boundary integral method for electromagnetic scattering in a two-layered medium, J. Comput. Phys., 229 (2010), 481-497.
- (with G. Bao and H. Wu) An adaptive edge element method with perfectly matched absorbing layers for wave scattering by biperiodic structures, Math. Comp., 79 (2010), 1-34.
- (with G. Bao) Numerical solution of an inverse medium scattering problem for Maxwell's equations at fixed frequency, J. Comput. Phys., 228 (2009), 4638-4648.
- (with H. Johnston and R. Krasny) A Cartesian treecode for screened Coulomb interactions, J. Comput. Phys., 228 (2009), 3858-3868.
- Numerical simulations of global approach for photon scanning tunneling microscopy: coupling of finite-element and boundary integral methods, J. Opt. Soc. Am. A, 25 (2008), 1929-1936.
- (with G. Bao and S. Hou) Inverse scattering by a continuation method with initial guesses from a direct imaging algorithm, J. Comput. Phys., 227 (2007), 755-762.
- (with G. Bao) Numerical solution of inverse scattering for near-field optics, Optics Letters, 32 (2007), 1465-1467.
- (with G. Bao) Inverse medium scattering problems in near-field optics, J. Comp. Math., 25 (2007), 252-265.
- (with G. Bao) Inverse medium scattering for the Helmholtz equation at fixed frequency, Inverse Problems, 21 (2005), 1621-1641.
- (with G. Bao) Inverse medium scattering problems for electromagnetic waves, SIAM J. Appl. Math., 65 (2005), 2049-2066.
- (with J. Enders, W. Geng, M. Frazier, and D. Scholl) The shift-invariant discrete wavelet transform and application to speech waveform analysis, J. Acoust. Soc. Am., 117 (2005), 2122-2133.
- (with G. Bao) Inverse medium scattering for three-dimensional time harmonic Maxwell's equations, Inverse Problems, 20 (2004), L1-L7.
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book chapter
- (with Y. Gao and X. Yuan) Electromagnetic field enhancement in a subwavelength rectangular open cavity, Photons, Phonons, and PDEs in Partial Differential Equations and Applications, ed. by H. Ammari, H. Kang, and H. Zhang, Springer, 2021, 2:55, 1-51.
- (with G. Bao) Shape reconstruction of inverse medium scattering for the Helmholtz equation, Computational Methods for Applied Inverse Problems, ed. by Y. Wang, A. Yagola, and C. Yang, De Gruyter and Higher Education Press, Beijing, 2012, 283-306.
- (with G. Bao and S. Hou) Recent studies on inverse medium scattering problems, Modeling and Computations in Electromagnetics, Lecture Notes in Computational Science and Engineering, H. Ammari, eds., Volume 59, Springer-Verlag, Berlin, 2007, 165-186.
- (with G. Bao) Computational inverse medium scattering at fixed frequency, Advances in Applied and Computational Mathematics, Nova Sci. Publ., Hauppauge, New York, 2006, 1-9.
- (with G. Zhang) An inverse problem of derivative security pricing, in Recent Developments in Theories and Numerics, Proceedings of the International Conf. on Inverse Problems, ed. by Y. Hon, M. Yamamoto, J. Cheng, and J. Lee, World Sci., Hong Kong, 2003, 411-419.