Lu Zhang

Data-Driven Computational Inversion:

  1. K. Ren and L. Zhang. Data-driven joint inversions for PDE models, link
  2. W. Ding, K. Ren and L. Zhang. Coupling deep learning with full waveform inversion, link

High-order Accuracy Methods for Wave Propagation:

  1. K. Ren, L. Zhang, Y. Zhou. An energy-based discontinuous Galerkin method for the nonlinear Schrodinger equation with wave operator, link
  2. Q. Du, H. Li, M. Weinstein, L. Zhang. Discontinuous Galerkin methods for a first-order semi-linear hyperbolic continuum model of a topological resonator dimer array, link
  3. Q. Wang, L. Zhang. An ultraweak-local discontinuous Galerkin method for nonlinear biharmonic Schrödinger equations, link, to appear in ESAIM: M2AN
  4. L. Zhang. A local energy-based discontinuous Galerkin method for fourth order semilinear wave equations, link, to appear in IMA J. Numeri. Anal.
  5. D. Appelo, L. Zhang, T. Hagstrom and F. Li. An energy-based discontinuous Galerkin method with Tame CFL numbers for the wave equation, BIT Numer. Math., 63(1), 5, (2023), link
  6. L. Zhang and S. Wang. A high order finite difference method for the elastic wave equation in bounded anisotropic and discontinuous media, SIAM J. Numer. Anal., 60(3), 1516-1547 (2022), link
  7. T. Hagstrom, D. Appelo, and L. Zhang. Discontinuous Galerkin methods for electromagnetic waves in dispersive media, 2021 International Applied Computational Electromagnetics Society Symposium (ACES), pp.1-4(2021), link
  8. L. Zhang, D. Appelo and T. Hagstrom. Energy-based discontinuous Galerkin difference methods for second-order wave equations, Comm. Appl. Math. Comput. (2021), link
  9. L. Zhang, S. Wang and N.A. Petersson. Elastic wave propagation in curvilinear coordinates with mesh refinement interfaces by a fourth order finite difference method, SIAM J. Sci. Comput., 43(2), A1472-A1496 (2021), link
  10. D. Appelo, T. Hagstrom, Q. Wang and L. Zhang. An energy-based discontinuous Galerkin method for semilinear wave equations, J. Comput. Phys., 418(2020), link
  11. L. Zhang, T. Hagstrom and D. Appelo. An energy-based discontinuous Galerkin method for the wave equation with advection, SIAM J. Numer. Anal., 57(5), 2469-2492(2019), link
  12. Y. Du, L. Zhang and Z. Zhang. Convergence analysis of a discontinuous Galerkin method for wave equations in second-order form, SIAM J. Numer. Anal., 57(1), 238-265(2019), link

Mathematical Biology:

  1. N. Rodriguez, Q. Wang, and L. Zhang. Understanding the effects of on- and off-hotspot policing: Evidence of hotspot, oscillating and chaotic activities, SIAM J. Appl. Dyn. Syst.,20(4), 1882-1916 (2021), link
  2. J. A. Carrillo, X. Chen, Q. Wang, Z. Wang and L. Zhang. Phase transitions and bump solutions of the Keller-Segel model with volume exclusion, SIAM J. Appl. Math., 80(1), 232-261(2020), link
  3. Q. Wang, J. Yang, and L. Zhang. Time–periodic and stable patterns of two–competing Keller–Segel chemotaxis model: Effect of cellular growth, Discrete Contin. Dyn. Syst. Ser. B, 22(9), 3547-3574(2017), link
  4. Q. Wang, and L. Zhang. On the multi–dimensional advective Lotka–Volterra competition systems, Nonlinear Anal. Real World Appl., 37, 329-349(2017), link
  5. Q. Wang, L. Zhang, J. Yang and J. Hu. Global existence and steady states of a two competing species Keller–Segel chemotaxis model, Kinet. Relat. Models, 8(4), 777-807(2015), link