A Slowness Matching Eulerian Method for Multivalued Solutions of Eikonal Equations. - William W. Symes; Jianliang Qian (J. Sci. Comput., 2003)

Simplex free adaptive tree fast sweeping and evolution methods for solving level set equations in arbitrary dimension. - Thomas C. Cecil; Stanley J. Osher; Jianliang Qian (J. Comput. Phys., 2006)

Fifth-Order Weighted Power-ENO Schemes for Hamilton-Jacobi Equations. - Susana Serna; Jianliang Qian (J. Sci. Comput., 2006)

High Order Fast Sweeping Methods for Static Hamilton-Jacobi Equations. - Yong-Tao Zhang; Hong-Kai Zhao; Jianliang Qian (J. Sci. Comput., 2006)

Approximations for Viscosity Solutions of Hamilton-Jacobi Equations With Locally Varying Time and Space Grids. - Jianliang Qian (SIAM J. Numer. Anal., 2006)

A Local Level Set Method for Paraxial Geometrical Optics. - Jianliang Qian; Shingyu Leung (SIAM J. Sci. Comput., 2006)

A Fast Sweeping Method for Static Convex Hamilton-Jacobi Equations. - Jianliang Qian; Yong-Tao Zhang; Hong-Kai Zhao (J. Sci. Comput., 2007)

Mountain Waves and Gaussian Beams. - Nicolay M. Tanushev; Jianliang Qian; James Ralston (Multiscale Model. Simul., 2007)

Fast Sweeping Methods for Eikonal Equations on Triangular Meshes. - Jianliang Qian; Yong-Tao Zhang; Hong-Kai Zhao (SIAM J. Numer. Anal., 2007)

Legendre-transform-based fast sweeping methods for static Hamilton-Jacobi equations on triangulated meshes. - Chiu-Yen Kao; Stanley J. Osher; Jianliang Qian (J. Comput. Phys., 2008)

Essentially Non-Oscillatory Adaptive Tree Methods. - Thomas C. Cecil; Stanley J. Osher; Jianliang Qian (J. Sci. Comput., 2008)

Eulerian Gaussian beams for Schrödinger equations in the semi-classical regime. - Shingyu Leung; Jianliang Qian (J. Comput. Phys., 2009)

The backward phase flow and FBI-transform-based Eulerian Gaussian beams for the Schrödinger equation. - Shingyu Leung; Jianliang Qian (J. Comput. Phys., 2010)

Fast Gaussian wavepacket transforms and Gaussian beams for the Schrödinger equation. - Jianliang Qian; Lexing Ying (J. Comput. Phys., 2010)

Fast Multiscale Gaussian Wavepacket Transforms and Multiscale Gaussian Beams for the Wave Equation. - Jianliang Qian; Lexing Ying (Multiscale Model. Simul., 2010)

Optimal Convergence of the Original DG Method on Special Meshes for Variable Transport Velocity. - Bernardo Cockburn; Bo Dong; Johnny Guzmán; Jianliang Qian (SIAM J. Numer. Anal., 2010)

Factored singularities and high-order Lax-Friedrichs sweeping schemes for point-source traveltimes and amplitudes. - Songting Luo; Jianliang Qian (J. Comput. Phys., 2011)

An Efficient Neumann Series-Based Algorithm for Thermoacoustic and Photoacoustic Tomography with Variable Sound Speed. - Jianliang Qian; Plamen Stefanov; Gunther Uhlmann; Hongkai Zhao (SIAM J. Imaging Sci., 2011)

Fast Sweeping Methods for Factored Anisotropic Eikonal Equations: Multiplicative and Additive Factors. - Songting Luo; Jianliang Qian (J. Sci. Comput., 2012)

Local a posteriori error estimates for time-dependent Hamilton-Jacobi equations. - Bernardo Cockburn; Ivan Merev; Jianliang Qian (Math. Comput., 2013)

Fast multiscale Gaussian beam methods for wave equations in bounded convex domains. - Gang Bao 004; Jun Lai; Jianliang Qian (J. Comput. Phys., 2014)

Fast Huygens sweeping methods for Helmholtz equations in inhomogeneous media in the high frequency regime. - Songting Luo; Jianliang Qian; Robert Burridge (J. Comput. Phys., 2014)

Adjoint State Method for the Identification Problem in SPECT: Recovery of Both the Source and the Attenuation in the Attenuated X-Ray Transform. - Songting Luo; Jianliang Qian; Plamen Stefanov (SIAM J. Imaging Sci., 2014)

High-Order Factorization Based High-Order Hybrid Fast Sweeping Methods for Point-Source Eikonal Equations. - Songting Luo; Jianliang Qian; Robert Burridge (SIAM J. Numer. Anal., 2014)

A Penalization-Regularization-Operator Splitting Method for Eikonal Based Traveltime Tomography. - Roland Glowinski; Shingyu Leung; Jianliang Qian (SIAM J. Imaging Sci., 2015)

Babich's expansion and the fast Huygens sweeping method for the Helmholtz wave equation at high frequencies. - Wangtao Lu; Jianliang Qian; Robert Burridge (J. Comput. Phys., 2016)

Babich's Expansion and High-Order Eulerian Asymptotics for Point-Source Helmholtz Equations. - Jianliang Qian; Lijun Yuan; Yuan Liu 018; Songting Luo; Robert Burridge (J. Sci. Comput., 2016)

Babich-Like Ansatz for Three-Dimensional Point-Source Maxwell's Equations in an Inhomogeneous Medium at High Frequencies. - Wangtao Lu; Jianliang Qian; Robert Burridge (Multiscale Model. Simul., 2016)

Eulerian Geometrical Optics and Fast Huygens Sweeping Methods for Three-Dimensional Time-Harmonic High-Frequency Maxwell's Equations in Inhomogeneous Media. - Jianliang Qian; Wangtao Lu; Lijun Yuan; Songting Luo; Robert Burridge (Multiscale Model. Simul., 2016)

Operator-Splitting Based Fast Sweeping Methods for Isotropic Wave Propagation in a Moving Fluid. - Roland Glowinski; Shingyu Leung; Jianliang Qian (SIAM J. Sci. Comput., 2016)

A ray-based IPDG method for high-frequency time-domain acoustic wave propagation in inhomogeneous media. - Eric T. Chung 001; Chi Yeung Lam; Jianliang Qian (J. Comput. Phys., 2017)

A fast Huygens sweeping method for capturing paraxial multi-color optical self-focusing in nematic liquid crystals. - Wingfai Kwan; Shingyu Leung; Xiao-Ping Wang 002; Jianliang Qian (J. Comput. Phys., 2017)

A hybrid approach to solve the high-frequency Helmholtz equation with source singularity in smooth heterogeneous media. - Jun Fang 004; Jianliang Qian; Leonardo Zepeda-Núñez; Hongkai Zhao (J. Comput. Phys., 2018)

Extending Babich's Ansatz for Point-Source Maxwell's Equations Using Hadamard's Method. - Wangtao Lu; Jianliang Qian; Robert Burridge (Multiscale Model. Simul., 2018)

Perfectly Matched Layer Boundary Integral Equation Method for Wave Scattering in a Layered Medium. - Wangtao Lu; Ya Yan Lu; Jianliang Qian (SIAM J. Appl. Math., 2018)

A Simple Explicit Operator-Splitting Method for Effective Hamiltonians. - Roland Glowinski; Shingyu Leung; Jianliang Qian (SIAM J. Sci. Comput., 2018)

A Finite Element/Operator-Splitting Method for the Numerical Solution of the Two Dimensional Elliptic Monge-Ampère Equation. - Roland Glowinski; Hao Liu 028; Shingyu Leung; Jianliang Qian (J. Sci. Comput., 2019)

Correction to: A Finite Element/Operator-Splitting Method for the Numerical Solution of the Two Dimensional Elliptic Monge-Ampère Equation. - Roland Glowinski; Hao Liu 028; Shingyu Leung; Jianliang Qian (J. Sci. Comput., 2019)

A Finite Element/Operator-Splitting Method for the Numerical Solution of the Three Dimensional Monge-Ampère Equation. - Hao Liu 028; Roland Glowinski; Shingyu Leung; Jianliang Qian (J. Sci. Comput., 2019)

Analysis of Regularized Kantorovich-Rubinstein Metric and Its Application to Inverse Gravity Problems. - Guanghui Huang; Jianliang Qian (SIAM J. Imaging Sci., 2019)

Numerical Microlocal Analysis by Fast Gaussian Wave Packet Transforms and Application to High-Frequency Helmholtz Problems. - Chi Yeung Lam; Jianliang Qian (SIAM J. Sci. Comput., 2019)

A level-set algorithm for the inverse problem of full magnetic gradient tensor data. - Wenbin Li 007; Jianliang Qian (Appl. Math. Lett., 2020)

Newton-type Gauss-Seidel Lax-Friedrichs high-order fast sweeping methods for solving generalized eikonal equations at large-scale discretization. - Wenbin Li 007; Jianliang Qian (Comput. Math. Appl., 2020)

On the Numerical Solution of Nonlinear Eigenvalue Problems for the Monge-Ampère Operator. - Roland Glowinski; Shingyu Leung; Hao Liu 028; Jianliang Qian (CoRR, 2020)

Efficient Algorithms for Computing Multidimensional Integral Fractional Laplacians via Spherical Means. - Boxi Xu; Jin Cheng; Shingyu Leung; Jianliang Qian (SIAM J. Sci. Comput., 2020)

Fast Huygens Sweeping Methods for a Class of Nonlocal Schrödinger Equations. - Kaho Ho; Shingyu Leung; Jianliang Qian (J. Sci. Comput., 2021)

Hadamard-Babich Ansatz for Point-Source Elastic Wave Equations in Variable Media at High Frequencies. - Jianliang Qian; Jian Song; Wangtao Lu; Robert Burridge (Multiscale Model. Simul., 2021)

Fast Multiscale Gaussian Beam Method for Three-Dimensional Elastic Wave Equations in Bounded Domains. - Jianliang Qian; Chao Song (SIAM J. Numer. Anal., 2021)

A Level-Set Adjoint-State Method for Transmission Traveltime Tomography in Irregular Domains. - Shingyu Leung; Jianliang Qian; Jiangtao Hu (SIAM J. Sci. Comput., 2021)

An Efficient Operator-Splitting Method for the Eigenvalue Problem of the Monge-Ampère Equation. - Hao Liu 028; Shingyu Leung; Jianliang Qian (CoRR, 2022)

Learning rays via deep neural network in a ray-based IPDG method for high-frequency Helmholtz equations in inhomogeneous media. - Tak Shing Au Yeung; Ka Chun Cheung; Eric T. Chung 001; Shubin Fu; Jianliang Qian (J. Comput. Phys., 2022)

A Fast Butterfly-Compressed Hadamard-Babich Integrator for High-Frequency Helmholtz Equations in Inhomogeneous Media with Arbitrary Sources. - Yang Liu 179; Jian Song; Robert Burridge; Jianliang Qian (Multiscale Model. Simul., 2023)

Hadamard integrators for wave equations in time and frequency domain: Eulerian formulations via butterfly algorithms. - Yuxiao Wei; Jin Cheng; Shingyu Leung; Robert Burridge; Jianliang Qian (CoRR, 2024)

A Linear-complexity Tensor Butterfly Algorithm for Compressing High-dimensional Oscillatory Integral Operators. - P. Michael Kielstra; Tianyi Shi; Hengrui Luo; Jianliang Qian; Yang Liu 179 (CoRR, 2024)

Optimal Rate of Convergence in Periodic Homogenization of Viscous Hamilton-Jacobi Equations. - Jianliang Qian; Timo Sprekeler; Hung V. Tran; Yifeng Yu (Multiscale Model. Simul., 2024)

Operator-Splitting/Finite Element Methods for the Minkowski Problem. - Hao Liu 028; Shingyu Leung; Jianliang Qian (SIAM J. Sci. Comput., 2024)

Hadamard integrator for time-dependent wave equations: Lagrangian formulation via ray tracing. - Yuxiao Wei; Jin Cheng; Robert Burridge; Jianliang Qian (J. Comput. Phys., 2024)

High-order accurate adjoint-state methods for three-dimensional high-resolution first-arrival traveltime tomography. - Bingqian Si; Aaron Philip; Yuxiao Wei; Jianliang Qian (J. Comput. Phys., 2025)