胡广辉
教授
个人简介
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). 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. 2012 -2015 Principal Investigator of the DFG Individual Program (Germany): Direct and inverse interaction problems with unbounded interfaces between acoustic, electromagnetic and elastic waves, HU2111. 2009 -2012 Project Researcher of the DFG Program (Germany): Direct and inverse scattering problems for elastic waves} (led by J. Elschner), EL584. 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
研究领域
Inverse problems for elliptic and hyperbolic equations Asymptotic analysis for point interactions Direct and inverse scattering from unbounded surfaces Integral equation and finite element methods for wave scattering problems Inverse moving source problems
近期论文
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. 2401. 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. H. Guo and G. Hu, Inverse wave-number-dependent source problems for the Helmholtz equation, to appear in: SIAM Nume. Anal. arXiv: 2305.07459. H. Guo, G. Hu and G. Ma, Imaging a moving point source from multi-frequency data measured at one and sparse observation directions (part II): near-field case in 3D, arXiv: 2304.12683. 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. 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. 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. 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, to appear in: Appl. Anal., 100(2021): 361-382. 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.SIAM. 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. 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.IJAP-ZHM-2019. 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. IP-HLZZ-2019. 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. 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.