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2020 – today
- 2024
[j52]Yuxiao Wei, Jin Cheng, Robert Burridge, Jianliang Qian
:
Hadamard integrator for time-dependent wave equations: Lagrangian formulation via ray tracing. J. Comput. Phys. 497: 112637 (2024)- [j51]Hao Liu, Shingyu Leung, Jianliang Qian:
Operator-Splitting/Finite Element Methods for the Minkowski Problem. SIAM J. Sci. Comput. 46(5): 3230- (2024) - [i8]Yuxiao Wei, Jin Cheng, Shingyu Leung, Robert Burridge, Jianliang Qian:
Hadamard integrators for wave equations in time and frequency domain: Eulerian formulations via butterfly algorithms. CoRR abs/2401.01423 (2024) - [i7]Jianliang Qian, Timo Sprekeler, Hung V. Tran, Yifeng Yu:
Optimal rate of convergence in periodic homogenization of viscous Hamilton-Jacobi equations. CoRR abs/2402.03091 (2024) - 2023
- [j50]Yang Liu, Jian Song, Robert Burridge, Jianliang Qian:
A Fast Butterfly-Compressed Hadamard-Babich Integrator for High-Frequency Helmholtz Equations in Inhomogeneous Media with Arbitrary Sources. Multiscale Model. Simul. 21(1): 269-308 (2023) - [i6]Hao Liu, Shingyu Leung, Jianliang Qian:
Operator Splitting/Finite Element Methods for the Minkowski Problem. CoRR abs/2307.16497 (2023) - [i5]Yuxiao Wei, Jin Cheng, Robert Burridge, Jianliang Qian:
Hadamard integrator for time-dependent wave equations: Lagrangian formulation via ray tracing. CoRR abs/2308.09232 (2023) - 2022
- [j49]Tak Shing Au Yeung, Ka Chun Cheung, Eric T. Chung, Shubin Fu, Jianliang Qian:
Learning rays via deep neural network in a ray-based IPDG method for high-frequency Helmholtz equations in inhomogeneous media. J. Comput. Phys. 465: 111380 (2022) - [i4]Hao Liu, Shingyu Leung, Jianliang Qian:
An Efficient Operator-Splitting Method for the Eigenvalue Problem of the Monge-Ampère Equation. CoRR abs/2205.05828 (2022) - [i3]Yang Liu, Jian Song, Robert Burridge, Jianliang Qian:
A Fast Butterfly-compressed Hadamard-Babich Integrator for High-Frequency Helmholtz Equations in Inhomogeneous Media with Arbitrary Sources. CoRR abs/2210.02698 (2022) - 2021
- [j48]Kaho Ho, Shingyu Leung, Jianliang Qian:
Fast Huygens Sweeping Methods for a Class of Nonlocal Schrödinger Equations. J. Sci. Comput. 88(3): 54 (2021) - [j47]Jianliang Qian, Jian Song, Wangtao Lu, Robert Burridge:
Hadamard-Babich Ansatz for Point-Source Elastic Wave Equations in Variable Media at High Frequencies. Multiscale Model. Simul. 19(1): 46-86 (2021) - [j46]Jianliang Qian, Chao Song:
Fast Multiscale Gaussian Beam Method for Three-Dimensional Elastic Wave Equations in Bounded Domains. SIAM J. Numer. Anal. 59(5): 2536-2570 (2021) - [j45]Shingyu Leung, Jianliang Qian, Jiangtao Hu:
A Level-Set Adjoint-State Method for Transmission Traveltime Tomography in Irregular Domains. SIAM J. Sci. Comput. 43(3): A2352-A2380 (2021) - [i2]Tak Shing Au Yeung, Ka Chun Cheung, Eric T. Chung, Shubin Fu, Jianliang Qian:
Learning Rays via Deep Neural Network in a Ray-based IPDG Method for High-Frequency Helmholtz Equations in Inhomogeneous Media. CoRR abs/2106.10523 (2021) - 2020
- [j44]Wenbin Li, Jianliang Qian:
A level-set algorithm for the inverse problem of full magnetic gradient tensor data. Appl. Math. Lett. 107: 106416 (2020) - [j43]Wenbin Li, Jianliang Qian:
Newton-type Gauss-Seidel Lax-Friedrichs high-order fast sweeping methods for solving generalized eikonal equations at large-scale discretization. Comput. Math. Appl. 79(4): 1222-1239 (2020) - [j42]Boxi Xu, Jin Cheng, Shingyu Leung, Jianliang Qian:
Efficient Algorithms for Computing Multidimensional Integral Fractional Laplacians via Spherical Means. SIAM J. Sci. Comput. 42(5): A2910-A2942 (2020) - [i1]Roland Glowinski, Shingyu Leung, Hao Liu, Jianliang Qian:
On the Numerical Solution of Nonlinear Eigenvalue Problems for the Monge-Ampère Operator. CoRR abs/2008.08103 (2020)
2010 – 2019
- 2019
- [j41]Roland Glowinski, Hao Liu, Shingyu Leung, Jianliang Qian:
A Finite Element/Operator-Splitting Method for the Numerical Solution of the Two Dimensional Elliptic Monge-Ampère Equation. J. Sci. Comput. 79(1): 1-47 (2019) - [j40]Roland Glowinski, Hao Liu, Shingyu Leung, Jianliang Qian:
Correction to: A Finite Element/Operator-Splitting Method for the Numerical Solution of the Two Dimensional Elliptic Monge-Ampère Equation. J. Sci. Comput. 79(1): 48 (2019) - [j39]Hao Liu, Roland Glowinski, Shingyu Leung, Jianliang Qian:
A Finite Element/Operator-Splitting Method for the Numerical Solution of the Three Dimensional Monge-Ampère Equation. J. Sci. Comput. 81(3): 2271-2302 (2019) - [j38]Guanghui Huang, Jianliang Qian:
Analysis of Regularized Kantorovich-Rubinstein Metric and Its Application to Inverse Gravity Problems. SIAM J. Imaging Sci. 12(3): 1528-1560 (2019) - [j37]Chi Yeung Lam, Jianliang Qian:
Numerical Microlocal Analysis by Fast Gaussian Wave Packet Transforms and Application to High-Frequency Helmholtz Problems. SIAM J. Sci. Comput. 41(5): A2717-A2746 (2019) - 2018
- [j36]Jun Fang, Jianliang Qian, Leonardo Zepeda-Núñez, Hongkai Zhao:
A hybrid approach to solve the high-frequency Helmholtz equation with source singularity in smooth heterogeneous media. J. Comput. Phys. 371: 261-279 (2018) - [j35]Wangtao Lu, Jianliang Qian, Robert Burridge:
Extending Babich's Ansatz for Point-Source Maxwell's Equations Using Hadamard's Method. Multiscale Model. Simul. 16(2): 727-751 (2018) - [j34]Wangtao Lu, Ya Yan Lu, Jianliang Qian:
Perfectly Matched Layer Boundary Integral Equation Method for Wave Scattering in a Layered Medium. SIAM J. Appl. Math. 78(1): 246-265 (2018) - [j33]Roland Glowinski, Shingyu Leung, Jianliang Qian:
A Simple Explicit Operator-Splitting Method for Effective Hamiltonians. SIAM J. Sci. Comput. 40(1) (2018) - 2017
- [j32]Wingfai Kwan, Shingyu Leung, Xiao-Ping Wang, Jianliang Qian:
A fast Huygens sweeping method for capturing paraxial multi-color optical self-focusing in nematic liquid crystals. J. Comput. Phys. 348: 108-138 (2017) - [j31]Eric T. Chung, Chi Yeung Lam, Jianliang Qian:
A ray-based IPDG method for high-frequency time-domain acoustic wave propagation in inhomogeneous media. J. Comput. Phys. 348: 660-682 (2017) - 2016
- [j30]Wangtao Lu, Jianliang Qian, Robert Burridge:
Babich's expansion and the fast Huygens sweeping method for the Helmholtz wave equation at high frequencies. J. Comput. Phys. 313: 478-510 (2016) - [j29]Jianliang Qian, Lijun Yuan, Yuan Liu, Songting Luo, Robert Burridge:
Babich's Expansion and High-Order Eulerian Asymptotics for Point-Source Helmholtz Equations. J. Sci. Comput. 67(3): 883-908 (2016) - [j28]Jianliang Qian, Wangtao Lu, Lijun Yuan, Songting Luo, Robert Burridge:
Eulerian Geometrical Optics and Fast Huygens Sweeping Methods for Three-Dimensional Time-Harmonic High-Frequency Maxwell's Equations in Inhomogeneous Media. Multiscale Model. Simul. 14(2): 595-636 (2016) - [j27]Wangtao Lu, Jianliang Qian, Robert Burridge:
Babich-Like Ansatz for Three-Dimensional Point-Source Maxwell's Equations in an Inhomogeneous Medium at High Frequencies. Multiscale Model. Simul. 14(3): 1089-1122 (2016) - [j26]Roland Glowinski, Shingyu Leung, Jianliang Qian:
Operator-Splitting Based Fast Sweeping Methods for Isotropic Wave Propagation in a Moving Fluid. SIAM J. Sci. Comput. 38(2) (2016) - 2015
- [j25]Roland Glowinski, Shingyu Leung, Jianliang Qian:
A Penalization-Regularization-Operator Splitting Method for Eikonal Based Traveltime Tomography. SIAM J. Imaging Sci. 8(2): 1263-1292 (2015) - 2014
- [j24]Gang Bao, Jun Lai, Jianliang Qian:
Fast multiscale Gaussian beam methods for wave equations in bounded convex domains. J. Comput. Phys. 261: 36-64 (2014) - [j23]Songting Luo, Jianliang Qian, Robert Burridge:
Fast Huygens sweeping methods for Helmholtz equations in inhomogeneous media in the high frequency regime. J. Comput. Phys. 270: 378-401 (2014) - [j22]Songting Luo, Jianliang Qian, Plamen Stefanov:
Adjoint State Method for the Identification Problem in SPECT: Recovery of Both the Source and the Attenuation in the Attenuated X-Ray Transform. SIAM J. Imaging Sci. 7(2): 696-715 (2014) - [j21]Songting Luo, Jianliang Qian, Robert Burridge:
High-Order Factorization Based High-Order Hybrid Fast Sweeping Methods for Point-Source Eikonal Equations. SIAM J. Numer. Anal. 52(1): 23-44 (2014) - 2013
- [j20]Bernardo Cockburn, Ivan Merev, Jianliang Qian:
Local a posteriori error estimates for time-dependent Hamilton-Jacobi equations. Math. Comput. 82(281): 187-212 (2013) - 2012
- [j19]Songting Luo, Jianliang Qian:
Fast Sweeping Methods for Factored Anisotropic Eikonal Equations: Multiplicative and Additive Factors. J. Sci. Comput. 52(2): 360-382 (2012) - 2011
- [j18]Songting Luo, Jianliang Qian:
Factored singularities and high-order Lax-Friedrichs sweeping schemes for point-source traveltimes and amplitudes. J. Comput. Phys. 230(12): 4742-4755 (2011) - [j17]Jianliang Qian, Plamen Stefanov, Gunther Uhlmann, Hongkai Zhao:
An Efficient Neumann Series-Based Algorithm for Thermoacoustic and Photoacoustic Tomography with Variable Sound Speed. SIAM J. Imaging Sci. 4(3): 850-883 (2011) - 2010
- [j16]Jianliang Qian, Lexing Ying:
Fast Gaussian wavepacket transforms and Gaussian beams for the Schrödinger equation. J. Comput. Phys. 229(20): 7848-7873 (2010) - [j15]Shingyu Leung, Jianliang Qian:
The backward phase flow and FBI-transform-based Eulerian Gaussian beams for the Schrödinger equation. J. Comput. Phys. 229(23): 8888-8917 (2010) - [j14]Jianliang Qian, Lexing Ying:
Fast Multiscale Gaussian Wavepacket Transforms and Multiscale Gaussian Beams for the Wave Equation. Multiscale Model. Simul. 8(5): 1803-1837 (2010) - [j13]Bernardo Cockburn, Bo Dong, Johnny Guzmán, Jianliang Qian:
Optimal Convergence of the Original DG Method on Special Meshes for Variable Transport Velocity. SIAM J. Numer. Anal. 48(1): 133-146 (2010)
2000 – 2009
- 2009
- [j12]Shingyu Leung, Jianliang Qian:
Eulerian Gaussian beams for Schrödinger equations in the semi-classical regime. J. Comput. Phys. 228(8): 2951-2977 (2009) - 2008
- [j11]Chiu-Yen Kao, Stanley J. Osher, Jianliang Qian:
Legendre-transform-based fast sweeping methods for static Hamilton-Jacobi equations on triangulated meshes. J. Comput. Phys. 227(24): 10209-10225 (2008) - [j10]Thomas C. Cecil, Stanley J. Osher, Jianliang Qian:
Essentially Non-Oscillatory Adaptive Tree Methods. J. Sci. Comput. 35(1): 25-41 (2008) - 2007
- [j9]Jianliang Qian, Yong-Tao Zhang, Hong-Kai Zhao:
A Fast Sweeping Method for Static Convex Hamilton-Jacobi Equations. J. Sci. Comput. 31(1-2): 237-271 (2007) - [j8]Nicolay M. Tanushev, Jianliang Qian, James Ralston:
Mountain Waves and Gaussian Beams. Multiscale Model. Simul. 6(2): 688-709 (2007) - [j7]Jianliang Qian, Yong-Tao Zhang, Hong-Kai Zhao:
Fast Sweeping Methods for Eikonal Equations on Triangular Meshes. SIAM J. Numer. Anal. 45(1): 83-107 (2007) - 2006
- [j6]Thomas C. Cecil, Stanley J. Osher, Jianliang Qian:
Simplex free adaptive tree fast sweeping and evolution methods for solving level set equations in arbitrary dimension. J. Comput. Phys. 213(2): 458-473 (2006) - [j5]Yong-Tao Zhang, Hong-Kai Zhao, Jianliang Qian:
High Order Fast Sweeping Methods for Static Hamilton-Jacobi Equations. J. Sci. Comput. 29(1): 25-56 (2006) - [j4]Susana Serna, Jianliang Qian:
Fifth-Order Weighted Power-ENO Schemes for Hamilton-Jacobi Equations. J. Sci. Comput. 29(1): 57-81 (2006) - [j3]Jianliang Qian:
Approximations for Viscosity Solutions of Hamilton-Jacobi Equations With Locally Varying Time and Space Grids. SIAM J. Numer. Anal. 43(6): 2371-2401 (2006) - [j2]Jianliang Qian, Shingyu Leung:
A Local Level Set Method for Paraxial Geometrical Optics. SIAM J. Sci. Comput. 28(1): 206-223 (2006) - 2003
- [j1]William W. Symes, Jianliang Qian:
A Slowness Matching Eulerian Method for Multivalued Solutions of Eikonal Equations. J. Sci. Comput. 19(1-3): 501-526 (2003)
Coauthor Index
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