胡广辉 |
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教育经历工作经历2022.06-Now. Dean of Department of Scientific and Engineering Computing, NKU. 2022.01-Now Professor, School of Mathematical Sciences, Nankai University (NKU), Tianjin, China. 2020.05-2021.12 Associate Professor, School of Mathematical Sciences, Nankai University (NKU), Tianjin, China. 2017-2020 Assistant Professor, Beijing Computational Science Research Center (CSRC), Beijing, China. 2009-2017 Postdoctoral position, Weierstrass Institute, Berlin, Germany. 2006-2009 Institute of Applied Mathematics, Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences (CAS). PhD thesis: Inverse electromagnetic scattering problems by bounded obstacles and periodic structure (Supervisor: Prof. Bo Zhang). 个人简介We invite applications for Postdoctoral Research Positions in our group starting as early as possible. Applicants are expected to have a PhD degree in applied mathematics, computational mathematics or physics. Priority will be given to those with an intimate knowledge in one the following topics:
Research topics will be confined (but not limited to) to direct and inverse scattering problems for acoustic, elastic and electromagnetic waves in various background media. Specific tasks can be changed depending on the applicant’s research experience. The initial appointment is for three years. Non-Chinese applicants are encouraged to apply for the offered position through the Research Fund for International Young Scientists. Please send your CV together with at most three representative publications to Prof. Guanghui Hu (ghhu@nankai.edu.cn). Discussions on possible collaborations are welcome and a visit to Nankai University can be arranged (under request) before the interview. 硕士博士研究生招生信息： （一）计算数学 招生方向: 偏微分方程反问题的数值计算 研究内容: 1. 无界区域中求解时域和频域散射问题的高精度数值方法，例如有限元方法、差分方法、积分方程方法等。 2. 反散射问题的数值求解方法，即利用偏微分方程单个或多个解的部分信息重构模型系数或反演未知区域形状的数值计算方法 。 3. 对一些有具体应用背景的逆散射问题（如雷达成像、无损探伤、光学隐形）的数学建模及数值模拟 。 （二）应用数学 招生方向: 波散射问题的理论与应用 研究内容: 1.声波、弹性波和电磁波反散射问题的唯一性和稳定性分析 2.无界区域上（例如周期、波导结构等）的正散射问题的的适定性分析 研究领域Inverse problems for elliptic and hyperbolic equations
教学工作2020-2021 (Autumn) Linear Algebra (Spring) Difference Methods Inverse Problems for Partial Differential Equations 2022-2023 (Autumn) Difference Methods Partial Differential Equations Inverse Problems for Partial Differential Equations 科研项目2021-2024 General Program of NSFC: Inversion algorithms based on sample data and scattering model, 12071236. 2021-2023. Alexander von Humboldt Fellowship for Experienced Researchers 2017-2020 General Program of NSFC: Inverse medium scattering with fixed-direction incoming waves, 11671028.
论文专著Preprints: M. Zhao, S. Si and G. Hu, Uniqueness, stability and algorithm for an inverse wave-number-dependent source problems, arXiv: 2402.12088. G. Hu and A. Kirsch, Time-harmonic scattering by locally perturbed periodic structures with Dirichlet and Neumann boundary conditions, arXiv: 2402.11230. G. Hu, T. Wang, X. Xu and Y. Zhao, Time-harmonic elastic scattering by unbounded deterministic and random rough surfaces in three dimensions, arXiv: 2401.15581. H. Guo, G. Hu and G. Ma, Inverse wave-number-dependent source problems for the Helmholtz equation with partial information on radiating period, arXiv: 2401.07193. G. Hu, J. Zhang and L. Zhu, Finite element and integral equation methods to conical diffraction by imperfectly conducting gratings, arXiv: 2304.04434. 2024 H. Guo and G. Hu, Inverse wave-number-dependent source problems for the Helmholtz equation, SIAM J. Numer. Anal, 62 (2024): 1372-1393. G. Ma, H. Guo and G. Hu, Imaging a moving point source from multi-frequency data measured at one and sparse observation directions (part II): near-field case in 3D, SIAM Journal of Imaging Sciences, 17 (2024): 1377-1414. G. Hu and A. Rathsfeld, Radiation conditions for the Helmholtz equation in a half plane filled by inhomogeneous periodic material, J. Differential Equations, 388 (2024): 215-252. H. Guo and G. Hu, Well-posedness and convergence analysis of PML method for time-dependent acoustic scattering problems over a locally rough surface, Computational Methods in Applied Mathematics, 24 (2024): 21-48. L. Zhu and G. Hu, Stability of grating diffraction problems for plane wave incidence: explicit dependence on wavenumbers and incident angles, Journal of Mathematical Analysis and Applications, 531 (2024): 127781. G. Hu, X. Xu, X. Yuan and Y. Zhao, Stability for the inverse source problem in a two-layered medium separated by rough interface, Inverse Problems and Imaging. doi: 10.3934/ipi.2023047 2023 J. Xiang and G. Hu, Uniqueness in determining rectangular grating profiles with a single incoming wave (Part II): TM polarization case, Inverse Problems 39 (2023): 115005. H. Guo, G. Hu and M. Zhao, Direct sampling method to inverse wave-number-dependent source problems : determination of the support of a stationary source, Inverse Problems 39 (2023): 105008. H. Guo, G. Hu and G. Ma, Imaging a moving point source from multi-frequency data measured at one and sparse observation directions (part I): far-field case, SIAM Journal of Imaging Sciences, 16 (2023): 1535-1571. X. Xu, G. Hu, B. Zhang, and H. Zhang, Uniqueness in inverse diffraction grating problems with infinitely many plane waves at a fixed frequency, SIAM J. Appl. Math., 83 (2023):302-326. L. Li, G. Hu and J. Yang, Piecewise-analytic interfaces with weakly singular points of arbitrary order always scatter, Journal of Functional Analysis, 284 (2023): 109800. J. Xiang and G.Hu, Uniqueness in determining rectangular grating proles with a single incoming wave (Part I): TE polarization case, Inverse Problems, 39 (2023): 055004. 2022: X. Yu, G. Hu, W. Lu and A. Rathsfeld, PML and high-accuracy boundary integral equation solver for wave scattering by a locally defected periodic surface, SIAM Nume. Anal., 60 (2022): 2592-2625. G. Ma and G. Hu, Factorization method for inverse time-harmonic elastic scattering with a single plane wave, Discrete and Continuous Dynamical Systems - B, 2022, 27(12): 7469-7492. G. Ma and G. Hu, Factorization method with one plane wave: from model-driven and data-driven perspectives, Inverse Problems, 38 (2022): 015003. 2021: Z. Yang, X. Gui, J. Ming and G. Hu, Bayesian approach to inverse time-harmonic acoustic obstacle scattering with phaseless data generated by point source waves, Computer Methods in Applied Mechanics and Engineering，386 (2021): 114073. G. Hu, W. Lu and A.Rathsfeld, Time-harmonic acoustic scattering from locally perturbed periodic curves. SIAM J. Appl. Math., 81(2021), 2569–2595. Y.Liu, G.Hu and M.Yamamoto, Inverse moving source problem for time-fractional evolution equations: determination of profiles, Inverse Problems, 37(2021): 084001. M.Choulli, G.Hu and M.Yamamoto, Stability estimate for a semilinear elliptic inverse problem, Nodea-nonlinear Differential Equations and Applications, 28(2021): 37. G. Hu, M. Vashisth and J. Yang, Inverse time-harmonic electromagnetic scattering from coated polyhedral scatterers with a single far-field pattern, SIAM J. Appl. Math. 81 (2021), 25–46. I. B. Aïcha, G. Hu, M. Vashisth and J Zou, Uniqueness for time-dependent inverse problems with single dynamical data, Journal of Mathematical Analysis and Applications 497 (2021):124910. Y. Zhao, G. Hu and B. Yan, Uniqueness to inverse acoustic and electromagnetic scattering from locally perturbed rough surfaces, Appl. Anal., 100 (2021): 361-382. 2020: G. Hu and J. Li, Uniqueness to inverse source problems in an inhomogeneous medium with a single far-field pattern, SIAM J. Math. Anal., 52(5), 5213–5231. G. Hu, A. Mantile, M. Sini and T. Yin, Direct and inverse time-harmonic elastic scattering from point-like and extended obstacles, Inverse Problem and Imaging,14 (2020):1025-1056. G. Hu and M. Vashisth, Uniqueness to inverse acoustic scattering from coated polygonal obstacles with a single incoming wave, Inverse Problems,36(2020):105004. G. Hu and Y. Kian, Uniqueness and stability for the recovery of a time-dependent source in elastodynamics, Inverse Problems and Imaging, 14 (2020): 463-487. G. Hu, P. Li and Y. Zhao, Elastic scattering from rough surfaces in three dimensions, Journal of Differential Equations 269 (2020): 4045-4078. S. Bugarija, P. Gibson, G. Hu, P. Li and Y. Zhao, Inverse scattering for the one-dimensional Helmholtz equation with piecewise constant wave speed, Inverse Problems, 36 (2020): 075008. Z. Yang, X. Gui, J. Ming and G. Hu, Bayesian approach to inverse time-harmonic acoustic scattering with phaseless far-field data, Inverse Problems 36 (2020): 065012. A. Alzaalig, G. Hu, X. Liu and J. Sun,Fast acoustic source imaging using multi_frequency sparse data, Inverse Problems，36 (2020): 025009. J. Elschner, G. Hu and M. Yamamoto, Single logarithmic conditional stability in determining unknown boundaries, Applicable Analysis, 99 (2020): 725-746. G. Hu, Y. Kian and Y. Zhao, Uniqueness to some inverse source problems for the wave equation in unbounded domains, Acta Mathematicae Applicatae Sinica, English Series, 36 (2020) 134–150. 2019: J. Elschner and G. Hu, Uniqueness and factorization method for inverseelastic scattering with a single incoming wave，Inverse Problems, 35 (2019), 094002 (A special volume dedicated to the memory of Armin Lechleiter). W. Lu and G. Hu, Time-harmonic acoustic scattering from a non-locally perturbed trapezoidal surface, SIAM J. Sci. Comput. 41-3 (2019): B522-B544.https://arxiv.org/abs/1903.07369 H. Zhou, G. Hu and L. Ma, Imaging internal defects with synthetic and experimental data, International Journal of Antennas and Propagation, vol. 2019,Article ID 6956809, 13 pages. G. Hu, X. Liu, B.Zhang and H. Zhang, A non-iterative approach to inverse elastic scattering by unbounded rigid rough surfaces, Inverse Problems 35 (2019): 025007. G. Hu, L. Li and J. Zou, Unique determination of a penetrable scatterer of rectangular type for inverse Maxwell equations by a single incoming wave, Inverse Problems 35 (2019): 035006. G. Hu, Y. Kian, P. Li and Y. Zhao, Inverse moving source problems in electrodynamics, Inverse Problems 35 (2019): 075001. 2018: J. Elschner and G. Hu, Acoustic scattering from corners, edges and circular cones, Archive for Rational Mechanics and Analysis, 228 (2018): 653-690. G. Bao, G. Hu, Y. Kian and T. Yin, Inverse source problems in elastodynamics, Inverse Problems 34 (2018): 045009. G. Bao, G. Hu, J. Sun and T. Yin, Direct and inverse elastic scattering from anisotropic media, J. Math. Pures Appl. 117 (2018): 263-301. P. Gibson, G. Hu and Y. Zhao, Inverse medium scattering from periodic structures with fixed-direction incoming waves, Inverse Problems 34 (2018): 075011. L. Li, G. Hu and J. Yang, Interface with weakly singular points always scatter, Inverse Problems 34 (2018), 075002. G. Hu and Y. Kian, Determination of singular time-dependent coefficients for wave equations from full and partial data, Inverse Problems and Imaging, 12 (2018): 745-772. G. Hu,X. Yuan and Y. Zhao, Direct and inverse elastic scattering from a locally perturbed half-plane, Communications in Mathematical Sciences, 16 (2018): 1635-1658. G. Bao, G. Hu and T. Yin, Time-harmonic acoustic scattering from locally perturbed half-planes, SIAM J. Appl.Math., 78 (2018): 2672-2691. G. Hu, X. Liu, P. Li and Y. Zhao, Inverse source problems in electromagnetism, Inverse Problems and Imaging, 12 (2018): 1411-1428. G. Hu, Y. Liu and M. Yamamoto, Inverse moving source problem for fractional diffusion(-wave) equations: Determination of orbits,Inverse Problems and Related Topics, Conference proceedings of ICIP2: International Conference on Inverse Problems, eds. J. Cheng, S. Lu and M. Yamamoto, Shanghai, China, October 12–14, 2018, page 81-100. 2017: T. Abbas, H. Ammari, G. Hu,A. Wahab and J. C. Ye, Two-dimensional elastic scattering coefficients and enhancement of nearly elastic cloaking, J. Elasticity 128 (2017): 203--243. 2016: T. Yin, G. Hu and L. Xu, Near-field imaging point-like scatterers and extended elastic solid in a fluid, Commun. Comput. Phys. 19 (2016): 1317--1342. G. Hu, A. Rathsfeld and T Yin,Finite element method to fluid-solid interaction problems with unbounded periodic interfaces, Numer. Methods Partial Differential Equations, 32 (2016): 5-35. G. Hu, J. Li, H. Liu and Q. Wang, A numerical study of complex reconstruction in inverse elastic scattering, Commun. Comput. Phys. 19 (2016): 1265--1286. G. Hu, A. Kirsch and T. Yin, Factorization method in inverse interaction problems with bi-periodic interfaces between acoustic and elastic waves, Inverse Probl. Imaging 10 (2016): 103--129. Y. Guo, D. Hoemberg, G. Hu, J. Li, H. Liu, A time domain sampling method for inverse acoustic scattering problems, J. Comput. Phys. 314 (2016): 647--660. T. Yin, G. Hu, L. Xu, and B. Zhang, Near-field imaging of obstacles with the factorization method: fluid-solid interaction, Inverse Problems 32 (2016): 015003. G. Hu, M. Salo, E. V. Vesalainen, Shape identification in inverse medium scattering problems with a single far-field pattern, SIAM J. Math. Anal. 48 (2016): 152--165. 2015: J. Elschner, G. Hu and M. Yamamoto, Uniqueness in inverse elastic scattering from unbounded rigid surfaces of rectangular type, Inverse Problems and Imaging 9 (2015):127–141. G. Hu and M. Yamamoto, Hölder stability estimate of the Robin coefficient in corrosion detection problems with a single boundary measurement, Inverse Problems 31 (2015):115009. G. Hu and H. Liu, Nearly cloaking the elastic wave fields, J. Math. Pures Appl. (9),104 (2015): 1045–1074. J. Elschner and G. Hu, Corners and edges always scatter, Inverse Problems 31 (2015):015003. G. Hu, X. Liu, F. Qu and B. Zhang, Variational approach to rough surface scattering problems with Neumann and generalized impedance boundary conditions, Communications in Mathematical Sciences 13 (2015): 511–537. J. Elschner and G. Hu, Elastic scattering by unbounded rough surfaces: Solvability in weighted Sobolev spaces, Applicable Analysis 94 (2015): 251–278. G. Hu and A. Rathsfeld, Scattering of time-harmonic electromagnetic plane waves by perfectly conducting diffraction gratings, IMA Appl. Math. 80 (2015): 508-532. G. Hu, J. Li and H. Liu, Uniqueness in determining refractive indices by formallydetermined far-field data, Applicable Analysis 94 (2015): 1259-1269. 2014: D. P. Challa, G. Hu and M. Sini, Multiple scattering of electromagnetic waves by afinite number of point-like obstacles, Mathematical Model and Methods in Applied Sciences 24 (2014): 863–899. G. Hu, J. Li, H. Liu and H. Sun, Inverse elastic scattering for multiscale rigid bodies with a single far-field measurement, SIAM J. Imaging Sci. 6 (2014): 2285–2309. G. Hu, J. Li and H. Liu, Recovering complex elastic scatterers by a single far-field pattern, Journal of Differential Equations 257 (2014): 469–489. G. Hu and X. Liu, Unique determination of balls and polyhedral scatterers with a single point source wave, Inverse Problems 30 (2014): 065010. G. Hu, A. Mantile and M. Sini, Direct and inverse acoustic scattering by a collection of extended and point-like scatterers, SIAM Multiscale Modeling and Simulation, 12 (2014): 996–1027. G. Hu and A. Rathsfeld, Convergence analysis of the FEM coupled with Fourie rmode expansion for the electromagnetic scattering by biperiodic structures, Electronic Transactions on Numerical Analysis 41 (2014): 350-375. G. Hu, J. Yang, B. Zhang and H. Zhang, Near-field imaging of scattering obstacleswith the factorization method, Inverse Problems 30 (2014): 095005. 2013: J. Elschner and G. Hu, Direct and inverse elastic scattering problems for diffraction gratings, Radon Series on Computational and Applied Mathematics 14 (2013): 101-134. G. Hu, Y. Lu and B. Zhang, The factorization method for inverse elastic scatteringfrom periodic structures, Inverse Problems 29 (2013): 115005. G. Hu, A. Kirsch and M. Sini, Some inverse problems arising from elastic scattering by rigid obstacles, Inverse Problems 29 (2013): 015009. G. Hu and M. Sini, Elastic scattering by finitely many point-like obstacles, J. Math.Phys. 54 (2013): 042901-16. 2012: J. Elschner and G. Hu, Elastic scattering by unbounded rough surfaces, SIAM J. Math. Anal. 6 (2012): 4101-4127. J. Elschner and G. Hu, An optimization method in inverse elastic scattering for one dimensional grating profiles, Communications in Computational Physics 12 (2012):1434-1460. G. Hu, Inverse wave scattering by unbounded obstacles: Uniqueness for the two dimensional Helmholtz equation, Appl. Anal. 91 (2012): 703-717. J. Elschner and G. Hu, Scattering of plane elastic waves by three-dimensional diffraction gratings, Mathematical Models and Methods in Applied Sciences 22 (2012):1150019. G. Hu, F. Qu and B. Zhang, A linear sampling method for inverse problems of diffraction gratings of mixed-type, Math. Methods Appl. Sci. 35 (2012): 1047-1066. 2011: J. Elschner and G. Hu, Uniqueness in inverse scattering of elastic waves by three-dimensional polyhedral diffraction gratings, Inverse Problems and Ill-posed Problems 19 (2011) 717-768 J. Elschner and G. Hu, Uniqueness in inverse transmission scattering problems for multilayered obstacles, Inverse Problems and Imaging 5 No. 4 (2011) 793-813 J. Elschner and G. Hu, Inverse scattering of elastic waves by periodic structures: Uniqueness under the third or fourth kind boundary conditions, Methods and Applications of Analysis 18 (2011) 215-244. G. Hu and B. Zhang, The linear sampling method for the inverse electromagnetic scattering by a partially coated bi-periodic structure, Math. Methods Appl. Sci., 34 (2011) 509-519. G. Hu, J. Yang and B. Zhang, Inverse electromagnetic scattering for a bi-periodic inhomogeneous layer on perfectly conducting plates, Appl. Anal., 90 (2011) 317-333. 2010: G. Hu, F. Qu and B. Zhang, Direct and inverse problems for electromagnetic scattering by a doubly periodic structure with a partially coated dielectric, Math. Methods Appl. Sci., 33 (2010) 147—156. X. Liu, B. Zhang and G.Hu, Uniqueness in the inverse scattering problem in a piecewise homogeneous medium, Inverse Problems, 26 (2010) 015002/1--015002/14. J. Elschner and G. Hu, Global uniqueness in determining polygonal periodic structures with a minimal number of incident plane waves, Inverse Problems, 26 (2010) 115002/1--115002/23. J. Elschner and G. Hu, Variational approach to scattering of plane elastic waves by diffraction gratings, Math. Methods Appl. Sci., 33 (2010) 1924—1941. 2009: G. Hu, X. Liu and B. Zhang, Unique determination of a perfectly conducting ball by a finite number of electric far field data, J. Math. Anal. Appl., 352 (2009) 861--871. Publications in Books: J. Elschner and G. Hu, Direct and inverse elastic scattering problems for diffraction gratings, Radon Series on Computational and Applied Mathematics 14 (2013), eds. by I. G. Graham, U. Langer, J. M. Melenk and M. Sini. Highlights: J. Elschner and G. Hu, Elastic Wave Scattering for Diffraction Gratings, Highlight of WIAS Annual Research Reports in 2012. Edited Conference Proceedings: D. Hoemberg and G. Hu (Eds), Electromagnetics-Modelling, Simulation, Control and Industrial Applications: Discrete and Continuous Dynamical Systems-Series S (DCDS-S) 8 (3), 2015. 学术交流荣誉奖励学术成果 |
