Research

Contents



Analysis of Electronic Structure Models


  1. The Kohn-Sham equation for deformed crystals (with W. E), Mem. Amer. Math. Soc., to appear [pdf]
  2. Asymptotic analysis of the quantum dynamics: Bloch-Wigner transform and Bloch dynamics (with W. E and X. Yang), Acta Math. Appl. Sin. Engl. Ser., to appear [pdf]
  3. Effective Maxwell equations from time-dependent density functional theory (with W. E and X. Yang), Acta Math. Sin. 32, 339-368 (2011) [pdf] [journal]
  4. The electronic structure of smoothly deformed crystals: Wannier functions and the Cauchy-Born rule (with W. E), Arch. Ration. Mech. Anal. 199, 407-433 (2011) [pdf] [journal]
  5. The electronic structure of smoothly deformed crystals: Cauchy-Born rule for the nonlinear tight-binding model (with W. E), Comm. Pure Appl. Math. 63, 1432-1468 (2010). [pdf] [journal]
  6. The elastic continuum limit of the tight binding model (with W. E), Chin. Ann. Math. Ser. B 28, 665-675 (2007). [pdf] [journal]


Algorithms for Density Functional Theory


  1. Optimized local basis function for Kohn-Sham density functional theory (with W. E, L. Lin, and L. Ying), J. Comput. Phys, to appear [pdf]
  2. Adaptive local basis set for Kohn-Sham density functional theory in a discontinuous Galerkin framework I: Total energy calculation (with W. E, L. Lin, and L. Ying), J. Comput. Phys, to apprear [pdf]
  3. A fast parallel algorithm for selected inversion of structured sparse matrix with application to 2D electronic structure calculations (with W. E, L. Lin, C. Yang, and L. Ying), SIAM J. Sci. Comput. 33, 1329-1351 (2011). [pdf] [journal]
  4. SelInv - an algorithm for selected inversion of a sparse symmetric matrix (with W. E, L. Lin, J. Meza, C. Yang, and L. Ying), ACM Trans. Math. Software, 37, article no. 40 (2011) [pdf] [journal]
  5. Localized basis of eigen-subspaces and operator compression (with W. E and T. Li), Proc. Natl. Acad. Sci. 107, 1273-1278 (2010). [pdf] [journal]
  6. Fast algorithm for extracting the diagonal of the inverse matrix with application to the electronic structure analysis of metallic systems (with R. Car, W. E, L. Lin, and L. Ying), Commun. Math. Sci. 7, 755-777 (2009). [pdf] [journal]
  7. Pole-based approximation of the Fermi-Dirac function (with W. E, L. Lin, and L. Ying), Chin. Ann. Math. Ser. B 30, 729-742 (2009). [pdf] [journal]
  8. Multipole representation of the Fermi opreator with application to the electronic structure analysis of metallic systems (with R. Car, W. E, and L. Lin), Phys. Rev. B 79, 115133 (2009). [pdf] [journal]
  9. A linear scaling subspace iteration algorithm with optimally localized non-orthogonal wave functions for Kohn-Sham density functional theory (with W. E, C.J. Garcia-Cervera, and Y. Xuan), Phys. Rev. B 79, 115110 (2009). [pdf] [journal]
  10. Asymptotics-based sub-linear scaling algorithms and application to the study of the electronic structure of materials (with W. E and C.J. Garcia-Cervera), Commun. Math. Sci. 5, 999-1024 (2007). [pdf] [journal]
  11. The continuum limit and QM-continuum approximation of quantum mechanical models of solids (with W. E), Commun. Math. Sci. 5, 679-696 (2007). [pdf] [journal]


Multiscale Modeling and Analysis


  1. Convergence of a force-based hybrid method for atomistic and continuum models in three dimension (with P.B. Ming), Comm. Pure Appl. Math, to appear [pdf]
  2. Multiscale Modeling (with W. E), invited mini-review, Scholarpedia 6(10):11527 (2011) http://www.scholarpedia.org/article/Multiscale_modeling
  3. Sequential multiscale modeling using sparse representation (with W. E, C.J. Garcia-Cervera, and W. Ren), Commun. Comput. Phys. 4, 1025-1033 (2008). [journal]
  4. Seamless multiscale modeling via dynamics on fiber bundles (with W. E), Commun. Math. Sci. 5, 649-663 (2007). [pdf] [journal]
  5. Uniform accuracy of the quasicontinuum method (with W. E and J.Z. Yang), Phys. Rev. B 74, 214115 (2006). [pdf] [journal]


Time-Frequency Analysis and High-Frequency Wave Propagation


  1. Convergence of frozen Gaussian approximation for high frequency wave propagation (with X. Yang), Comm. Pure Appl. Math., to appear [pdf]
  2. Frozen Gaussian approximation for general linear strictly hyperbolic system: formulation and Eulerian methods (with X. Yang), Multiscale Model. Simul., to appear [pdf]
  3. Frozen Gaussian approximation for high frequency wave propagation (with X. Yang), Commun. Math. Sci. 9, 663-683 (2011). [pdf] [journal]
  4. Synchrosqueezed wavelet transforms: an empirical mode decomposition-like tool (with I. Daubechies and H.-T. Wu), Appl. Comp. Harmonic Anal. 30, 243-261 (2011). [pdf] [journal]


Rare Events, Chemical Reactions, etc


  1. Markov state models based on milestoning (with F. Noe, M. Sarich, C. Schuette and E. Vanden-Eijnden), J. Chem. Phys. 134, 204105 (2011). [pdf] [journal]


Numerical Linear Algebra, Fast Algorithms, etc


  1. Fast construction of hierarchical matrix representation from matrix-vector multiplication (with L. Lin and L. Ying), J. Comput. Phys. 230, 4071--4087 (2011). [pdf] [journal]

Last update: Apr, 2012