Publication

• H. Yang and L. Ying, Synchrosqueezed wave packet transform for 2D mode decomposition. Submitted.
  
• J. Hu, S. Fomel, L. Demanet, and L. Ying, A fast butterfly algorithm for the hyperbolic Radon transform. Submitted
  
• J. Hu and L. Ying, A fast algorithm for the energy space boson Boltzmann collision operator. Submitted.
  
• J. Poulson, B. Engquist, S. Li and L. Ying, A parallel sweeping preconditioner for heterogeneous 3D Helmholtz equations. Submitted.
• P. Schmitz and L. Ying, A fast multifrontal solver for 3D elliptic problems using hierarchical matrices. Submitted.

• X. Song, S. Fomel, and L. Ying, Lowrank finite-differences and lowrank Fourier finite-differences for seismic wave extrapolation. To appear in Geophysical Journal International.
• H. Zhang, G. Bao, J. Qian, and L. Ying, A convergent multiscale Gaussian-beam parametrix for wave equations. Communications in Partial Differential Equations 38 (2013).
  
• B. Engquist and L. Ying, A fast algorithm for reiterated homogenization. Commun. Math. Sci.11 (2013).
  
• S. Fomel, L. Ying, and X. Song, Seismic wave extrapolation using lowrank symbol approximation. To appear in Geophysical Prospecting.
• L. Lin and L. Ying, Element orbitals for Kohn-Sham density functional theory. Physical Review B 85 (2012).
  
• I. Lashuk, A. Chandramowlishwaran, H. Langston, T. Nguyen, R. Sampath, A. Shringarpure, R. Vuduc, L. Ying, D. Zorin, and G. Biros, A massively parallel adaptive fast multipole method on heterogeneous architectures. Communications of the ACM 55 (2012).
  
• L. Lin, J. Lu, L. Ying, and W. E, Optimized local basis set for Kohn-Sham density functional theory. Journal of Computational Physics 231 (2012).
• H. Yang and L. Ying, A fast algorithm for multilinear operators. Applied and Computational Harmonic Analysis 33 (2012).
• L. Ying, A pedestrian introduction to fast multipole methods. Science China Mathematics 55 (2012).
  
• L. Demanet and L. Ying. Fast wave computation via Fourier integral operators. Mathematics of Computation 81 (2012).
  
• P. Tsuji, B. Engquist, and L. Ying, A sweeping preconditioner for time-harmonic Maxwell's equations with finite elements. Journal of Computational Physics 231 (2012).
• P. Tsuji and L. Ying. A sweeping preconditioner for Yee’s finite difference approximation of time-harmonic Maxwell’s equations. Frontiers of Mathematics in China 7 (2012).
• L. Lin, J. Lu, L. Ying, and W. E, Adaptive local basis set for Kohn-Sham density functional theory in a discontinuous Galerkin framework I: Total energy calculation. Journal of Computational Physics 231 (2012).
• L. Demanet, M. Ferrara, N. Maxwell, J. Poulson, and L. Ying. A butterfly algorithm for synthetic aperture radar imaging. SIAM Journal on Imaging Sciences 5 (2012).
  
• J. Hu and L. Ying, A fast spectral algorithm for the quantum Boltzmann collision operator. Commun. Math. Sci 10 (2012).
• P. Schmitz and L. Ying, A fast direct solver for elliptic problems on general meshes in 2D. Journal of Computational Physics 231 (2012).
• S. Jiang, B. Ren, P. Tsuji, and L. Ying. Second kind integral equations for the first kind Dirichlet problem of the biharmonic equation in three dimensions. Journal of Computational Physics 230 (2011).
  
• B. Engquist and L. Ying. Sweeping preconditioner for the Helmholtz equation: Moving perfectly matched layers. Multiscale Modeling and Simulation 9 (2011).
  
• L. Lin, C. Yang, J. Lu, L. Ying, and W. E. A fast parallel algorithm for selected inversion of structured sparse matrices with application to 2D electronic structure calculations. SIAM Journal on Scientific Computing 33 (2011).
  
• L. Lin, J. Lu, and L. Ying. Fast construction of hierarchical matrix representation from matrix-vector multiplication. Journal of Computational Physics 230 (2011).
• P. Tsuji and L. Ying. A fast directional algorithm for high-frequency electromagnetic scattering. Journal of Computational Physics 230 (2011).
• B. Engquist and L. Ying. Sweeping preconditioner for the Helmholtz equation: Hierarchical matrix representation. Communications in Pure and Applied Mathematics 64 (2011).
  
• L. Lin, C. Yang, J. Meza, J. Lu, L. Ying, and W. E. SelInv--an algorithm for selected inversion of a sparse symmetric matrix. ACM Trans. Math. Software 37 (2011).
  
• P. Tsuji, D. Xiu, and L. Ying. A fast method for high-frequency acoustic scattering from random scatterers. International Journal on Uncertainty Quantification 1 (2011).
  
• L. Demanet and L. Ying. Discrete symbol calculus. SIAM Rev. 53 (2011).
• J. Qian and L. Ying. Fast multiscale Gaussian wavepacket transforms and multiscale Gaussian beams for the wave equation. SIAM MMS 8 (2010).
  
• J. Qian and L. Ying. Fast Gaussian wavepacket transforms and Gaussian beams for the Schrodinger equation. J. Computational Physics 229 (2010).
• L. Demanet and L. Ying. Scattering in flatland: efficient representations via wave atoms. Found. of Comput. Math. 10 (2010).
• B. Engquist and L. Ying. Fast directional algorithms for the Helmholtz kernel. Journal of Computational and Applied Mathematics 234 (2010).
• L. Lin, J. Lu, L. Ying, and W. E. Pole-based approximation of the Fermi-Dirac function. Chinese Annals of Mathematics - Series B 30 (2009).
• L. Ying and S. Fomel. Fast computation of partial Fourier transforms. Multiscale Model. Simul 8 (2009).
• L. Lin, J. Lu, L. Ying, R. Car, and W. E. Fast algorithm for extracting the diagonal of the inverse matrix with application to the electronic structure analysis of metallic systems. Commun. Math. Sci. 7 (2009).
• E. Candes, L. Demanet and L. Ying. A fast butterfly algorithm for the computation of Fourier integral operators.  Multiscale Modeling and Simulation 7 (2009).
• B. Engquist and L. Ying. A fast directional algorithm for high frequency acoustic scattering in two dimensions. Communications in Mathematical Sciences 7 (2009).
• L. Demanet and L. Ying. Wave atoms and time upscaling of wave equations. Numerische Mathematik 113 (2009).
• L. Ying. Sparse Fourier transform via butterfly algorithm. SIAM Journal on Scientific Computing 31 (2009).
• L. Demanet, L. Ying. Wave atoms and sparsity of oscillatory patterns. Applied and Computational Harmonic Analysis 23 (2007). Implementation (Matlab).
• E. Candes, L. Demanet and L. Ying. Fast computation of Fourier integral operators. SIAM Journal on Scientific Computing 29 (2007).
• B. Engquist and L. Ying. Fast directional multilevel algorithms for oscillatory kernels. SIAM Journal on Scientific Computing 29 (2007).
• L. Ying, E. Candes. The phase flow method. Journal of Computational Physics 220 (2006).
• L. Ying, E. Candes. Fast geodesics computation with the phase flow method. Journal of Computational Physics 220 (2006).
• L. Ying, G. Biros, D. Zorin. A high-order 3D boundary integral equation solver for elliptic PDEs in smooth domains. Journal of Computational Physics 219 (2006).
• E. Candes, L. Demanet, D. Donoho, L. Ying. Fast discrete curvelet transforms. SIAM Journal on Multiscale Modeling and Simulation 5 (2006). Implementation (Matlab and C++).
• L. Ying. A kernel independent fast multipole algorithm for radial basis functions. Journal of Computational Physics 213 (2006).
• L. Ying, D. Zorin. A simple manifold-based construction of surfaces of arbitrary smoothness. ACM Transactions on Graphics 23 (2004) (SIGGRAPH 2004). Implementation (C++).
• L. Ying, G. Biros, D. Zorin. A kernel-independent adaptive fast multipole method in two and three dimensions. Journal of Computational Physics 196 (2004). Implementation (C++).
• G. Biros, L. Ying, D. Zorin. A fast solver for the Stokes equations with distributed forces in complex geometries. Journal of Computational Physics 194 (2004).
• L. Velho, K. Perlin, L. Ying, H. Biermann. Algorithmic shape modeling with subdivision surfaces. Computers and Graphics 26 (2002). 

• B. Engquist and L. Ying, Fast algorithms for high frequency wave propagation. To appear in Numerical Analysis of Multiscale Problems,  I. Graham, T. Hou, O. Lakkis and R. Scheichl (editors), Lecture Notes in Computational Science and Engineeering, Springer.
• L. Ying. Fast algorithms for boundary integral equations. In B. Engquist, O. Runborg, P. Lotstedt, editors, Multiscale Methods in Science and Engineering, pages 139-194, volume 66 of Lecture Notes in Computational Science and Engineering, Heidelberg, 2009. Springer Verlag.

• J. Hu, S. Fomel, L. Demanet, and L. Ying, A fast butterfly algorithm for the hyperbolic Radon transform. Submitted to 2012 SEG Annual Meeting.
  
• J. Poulson, B. Engquist, S. Li, and L. Ying, A parallel sweeping preconditioner for frequency-domain seismic wave propagation. Submitted to 2012 SEG Annual Meeting.
  
• X. Song, S. Fomel, L. Ying, and T. Ding, Lowrank finite-difference for wave extrapolation. To appear in Proceedings of the 2011 SEG Annaul Meeting.
• B. Engquist, J. Poulson, and L. Ying, Sweeping preconditioner for the 3D Helmholtz equation. To appear in Proceedings of the 2011 SEG Annaul Meeting.
• S. Fomel, L. Ying, and X. Song, Seismic wave extrapolation using lowrank symbol approximation. Proceedings of the 2010 SEG Annaul Meeting.
• I. Lashuk, A. Chandramowlishwaran, H. Langston, T. Nguyen, R. Sampath, A. Shringarpure, R. Vuduc, L. Ying, D. Zorin, and G. Biros. A massively parallel adaptive fast multipole method on heterogeneous architectures. To appear in Proceedings of  Proc. ACM/IEEE Conf. Supercomputing (SC), Portland, OR, USA, 2009. This paper is nominated for the Best Technical Paper Award.
• B. Engquist, K. Tran, and L. Ying. Fast hybrid algorithms for high frequency scattering Engquist. The 3rd Conference on Mathematical Modeling of Wave Phenomena and the 20th Nordic Conference on Radio Science and Communications. AIP Conference Proceedings, Volume 1106, pp. 3-17 (2009).
  
• L. Demanet and L. Ying. Curvelets and wave atoms for mirror-extended images.Proc. SPIE Wavelets XII conf, San Diego, August 2007 (Invited Paper). Implementation (Matlab).
  
• L. Ying, L. Demanet, E. Candes. 3D discrete curvelet transform. Proc. Wavelets XI conf., San Diego, July 2005 (Invited Paper).
• L. Ying, G. Biros, D. Zorin, H. Langston. A new parallel kernel-independent fast multipole method. Proceedings of the 2003 ACM/IEEE conference on Supercomputing, 14-29, 2003. This paper was awarded the Best Student Paper Award and nominated for the Gordon Bell Award and the Best Technical Paper Award.
• G. Biros, L. Ying, D. Zorin. The embedded boundary integral equation solver for the incompressible Navier-Stokes equations. International Association for Boundary Element Methods Symposium, 2002.
• L. Ying, D. Zorin. Nonmanifold subdivision. The 12th IEEE Visualization Conference, 2001.
• L. Ying, A. Hertzmann, H. Biermann, D. Zorin. Texture and shape synthesis on surfaces. The 12th Eurographics Workshop on Rendering, 2001.

• A. Gupta and L. Ying. A Fast Maximum-Weight-Bipartite-Matching Algorithm for Reducing Pivoting in Sparse Gaussian Elimination, Tech. Report RC 21576 (97320), IBM T. J. Watson Research Center, Yorktown Heights, NY, 1999.