Jianfeng Lu

Jianfeng Lu
  • Professor of Mathematics
  • Associate Professor of Physics (Secondary)
  • Associate Professor of Chemistry (Secondary)
  • Associate Professor in Physics (Secondary)
External address: 242 Physics Bldg, 120 Science Drive, Durham, NC 27708
Internal office address: Mathematics Department, Duke University, Box 90320, Durham, NC 27708
Phone: (919) 660-2875

Research Areas and Keywords


electronic structure models, calculus of variations, semiclassical analysis

Computational Mathematics

electronic structure models, multiscale modeling and simulations, numerical analysis, rare events simulation, computational physics, time-frequency analysis, fast algorithms, stochastic numerical methods, kinetic equations, nonlinear Schrodinger equations, quantum chemistry, computational statistical mechanics, optimization, high frequency wave propagation

Mathematical Physics

electronic structure models, quantum chemistry, kinetic theory, quantum information

PDE & Dynamical Systems

multiscale modeling and simulations, numerical analysis, calculus of variations, kinetic equations, Schroedinger equations

Physical Modeling

electronic structure models, multiscale modeling and simulations, rare events simulation, computational physics, kinetic equations, nonlinear Schroedinger equations, quantum chemistry, computational statistical mechanics


rare events simulation, computational statistical mechanics, stochastic numerical methods

Signals, Images & Data

time-frequency analysis, fast algorithms, optimization, applied harmonic analysis

Jianfeng Lu is an applied mathematician interested in mathematical analysis and algorithm development for problems from computational physics, theoretical chemistry, materials science and other related fields.

More specifically, his current research focuses include:
Electronic structure and many body problems; quantum molecular dynamics; multiscale modeling and analysis; rare events and sampling techniques.

Education & Training
  • Ph.D., Princeton University 2009

E, Weinan, and Jianfeng Lu. “The Kohn-Sham equation for deformed crystals.” Memoirs of the American Mathematical Society, vol. 221, no. 1040, American Mathematical Society (AMS), 2012, pp. 1–1. Crossref, doi:10.1090/s0065-9266-2012-00659-9. Full Text

Daubechies, Ingrid, et al. “Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool.” Applied and Computational Harmonic Analysis, vol. 30, no. 2, Elsevier BV, Mar. 2011, pp. 243–61. Crossref, doi:10.1016/j.acha.2010.08.002. Full Text

Lin, Lin, et al. “SelInv---An Algorithm for Selected Inversion of a Sparse Symmetric Matrix.” Acm Transactions on Mathematical Software, vol. 37, no. 4, Association for Computing Machinery (ACM), Feb. 2011, pp. 1–19. Crossref, doi:10.1145/1916461.1916464. Full Text

E, Weinan, and Jianfeng Lu. “The Electronic Structure of Smoothly Deformed Crystals: Wannier Functions and the Cauchy–Born Rule.” Archive for Rational Mechanics and Analysis, vol. 199, no. 2, Springer Science and Business Media LLC, Feb. 2011, pp. 407–33. Crossref, doi:10.1007/s00205-010-0339-1. Full Text

Lu, J., and X. Yang. “Frozen Gaussian approximation for high frequency wave propagation.” Communications in Mathematical Sciences, vol. 9, no. 3, 2011, pp. 663–83. Open Access Copy

E, W., et al. “Effective Maxwell equations from time-dependent density functional theory.” Acta Math. Sin., vol. 32, 2011, pp. 339–339. Open Access Copy

Lin, L., et al. “Fast construction of hierarchical matrix representation from matrix-vector multiplication.” Journal of Computational Physics, vol. 230, no. 10, Jan. 2011, pp. 4071–87. Scopus, doi:10.1016/j.jcp.2011.02.033. Full Text Open Access Copy

Lin, Lin, et al. “A Fast Parallel Algorithm for Selected Inversion of Structured Sparse Matrices with Application to 2D Electronic Structure Calculations.” Siam Journal on Scientific Computing, vol. 33, no. 3, Society for Industrial & Applied Mathematics (SIAM), Jan. 2011, pp. 1329–51. Crossref, doi:10.1137/09077432x. Full Text

Noe, Frank, et al. “Markov state models based on milestoning.” J. Chem. Phys., vol. 134, 2011, p. 204105.

E, Weinan, and Jianfeng Lu. “Electronic structure of smoothly deformed crystals: Cauchy-born rule for the nonlinear tight-binding model.” Communications on Pure and Applied Mathematics, vol. 63, no. 11, Wiley, Nov. 2010, pp. 1432–68. Crossref, doi:10.1002/cpa.20330. Full Text