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Research Interests

  • Numerical methods of partial differential equations and fractional differential equations

  • Computational methods and numerical analysis related to Plasma Physics and Magnetohydrodynamics

  • Deep learning

  • System optimization and image reconstruction for x-ray computed tomography

  • Optimization techniques for optical tomography

  • Inverse scattering problems

Selected Publications

  • Y.T. Mehraliyev, H. Yang and E.I. Azizbayov, Recovery of unknown coefficients in a two-dimensional hyperbolic equation with additional conditions, submitted.

  • I. Tekin and H. Yang, Determination of a time-dependent coefficient in the time-fractional wave equation with a non-classical boundary conditions, TWMS Journal of Applied and Engineering Mathematics, accepted.

  • I. Tekin and H. Yang, Inverse problem for the time-fractional Euler-Bernoulli beam equation, Mathematical Modelling and Analysis, vol.26, no.3 (2021), pp.503-518.

  • H. Yang, Conservative local discontinuous Galerkin methods for the cubic-quintic nonlinear Schrodinger equation, Optik, vol.226, no.1 (2021), Article ID 165821.

  • H. Yang and J. Liu, A qualitative deep learning method for inverse scattering problems, Applied Computational Electromagnetics Society Journal, vol.35, no.2 (2020), pp.153-160.

  • H. Yang, An inverse problem for the sixth-order linear Boussinesq-type equation, U.P.B. Scientfic Bulletin, Series A: Applied Mathematics and Physics, vol.82, no.2 (2020), pp.27-36.

  • H. Yang, Optimal error estimate of a decoupled conservative local discontinuous Galerkin method for the Klein-Gordon-Schrodinger equations, Journal of Korean Society of Industrial and Applied Mathematics, vol.24, no.1 (2020), pp.39-78.

  • H. Yang, Homotopy analysis method for the time-fractional Boussinesq equation, Universal Journal of Mathematics and Applications, vol.3, no.1 (2020), pp.12-18.

  • H. Yang, Error estimates for a class of energy- and Hamiltonian-preserving local discontinuous Galerkin methods for the Klein-Gordon-Schrodinger equations, Journal of Applied Mathematics and Computing, vol.62, no.1-2 (2020), pp.377-424.

  • H. Yang, A new high-order method for the time-fractional diffusion equation with a source, Journal of Fractional Calculus and Applications, vol.11, no.2 (2020), pp.111-129.

  • F. Jones and H. Yang, A comparative study of the numerical approximations of quenching time for a nonlinear reaction-diffusion equation, Fundamental Journal of Mathematics and Applications, vol.3, no.2 (2020), pp.144-152.

  • H. Yang, High-order energy and linear momentum conserving methods for the Klein-Gordon equation, Mathematics, vol.6, no.10 (2018), 200.

  • H. Yang, W.-X. Cong and G. Wang, Deep learning for dual-energy X-ray computed tomography, Proceedings of the 14th International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine (2017), pp.864-869.

  • H. Yang, H. Yu and G. Wang, Deep learning for the classification of lung nodules, arXiv preprint arXiv:1611.06651v2 (2017).

  • H. Yang and F. Li, Discontinuous Galerkin methods for relativistic Vlasov-Maxwell system, Journal of Scientific Computing, vol.73, no.2-3 (2017), pp.1216-1248.

  • C.-S. Chou, W. Sun, Y. Xing and H. Yang, Local discontinuous Galerkin methods for the Khokhlov-Zabolotskaya-Kuznetzov equation, Journal of Scientific Computing, vol.73, no.2-3 (2017), pp.593-616.

  • H. Yang, J. Guo and J.-H. Jung, Schwartz duality of the Dirac delta function for the Chebyshev collocation approximation to the fractional advection equation, Applied Mathematics Letters, vol.64, (2017), pp.205-212.

  • H. Yang and F. Li, Stability analysis and error estimates of an exactly divergence-free method for the magnetic induction equations, ESAIM: Mathematical Modelling and Numerical Analysis, vol.50, no.4 (2016), pp. 965-993.

  • E. Kemmerling, M. Wu, H. Yang, P. Maxim, B. Loo and R. Fahrig, Optimization of an on-board imaging system for extremely rapid radiation therapy, Medical Physics, vol. 42 (2015), pp. 6757-6767.

  • H. Yang and F. Li, Error estimates of Runge-Kutta discontinuous Galerkin methods for the Vlasov-Maxwell system, ESAIM: Mathematical Modelling and Numerical Analysis, vol.49, no.1 (2015), pp. 69-99.

  • L. Zhao, H. Yang, W.-X. Cong, G. Wang and X. Intes, Lp regularization for early gate fluorescence molecular tomography, Optics Letters, vol.39, no.14 (2014), pp. 4156-4159.

  • L. Zhao, H. Yang, W.-X. Cong, G. Wang and X. Intes, Comparison of Lp-regularization-based reconstruction methods for early time gates in time-domain fluorescen molecular tomography, Proceedings of SPIE, vol. 8937 (2014).

  • H. Yang, F. Li and J. Qiu, Dispersion and dissipation errors of two fully discrete discontinuous Galerkin methods, Journal of Scientific Computing, vol.55, no.3 (2013), pp. 552-574.

  • D. Duffy, H. Yang, et al., Medical ultrasound imaging, Proceedings of the Twenty-Sixth Workshop on Mathematical Problems in Industry (2010), 42 pages.