Wei, Yuxiao; Cheng, Jin; Burridge, Robert; Qian, Jianliang Hadamard integrator for time-dependent wave equations: Lagrangian formulation via ray tracing. (English) Zbl 07811323 J. Comput. Phys. 497, Article ID 112637, 36 p. (2024). MSC: 65Nxx 65Mxx 78Axx PDFBibTeX XMLCite \textit{Y. Wei} et al., J. Comput. Phys. 497, Article ID 112637, 36 p. (2024; Zbl 07811323) Full Text: DOI arXiv
Liu, Yang; Song, Jian; Burridge, Robert; Qian, Jianliang A fast butterfly-compressed Hadamard-Babich integrator for high-frequency Helmholtz equations in inhomogeneous media with arbitrary sources. (English) Zbl 1524.65193 Multiscale Model. Simul. 21, No. 1, 269-308 (2023). MSC: 65F50 35J05 65R10 65R20 PDFBibTeX XMLCite \textit{Y. Liu} et al., Multiscale Model. Simul. 21, No. 1, 269--308 (2023; Zbl 1524.65193) Full Text: DOI arXiv
Qian, Jianliang; Song, Jian; Lu, Wangtao; Burridge, Robert Truncated Hadamard-Babich ansatz and fast Huygens sweeping methods for time-harmonic elastic wave equations in inhomogeneous media in the asymptotic regime. (English) Zbl 1516.78001 Minimax Theory Appl. 8, No. 1, 171-212 (2023). MSC: 78A05 78A46 78M35 PDFBibTeX XMLCite \textit{J. Qian} et al., Minimax Theory Appl. 8, No. 1, 171--212 (2023; Zbl 1516.78001) Full Text: Link
Li, Wenbin; Qian, Jianliang Kantorovich-Rubinstein metric based level-set methods for inverting modulus of gravity-force data. (English) Zbl 1511.65116 Inverse Probl. Imaging 16, No. 6, 1643-1667 (2022). MSC: 65N21 65N06 65N80 35A01 35A02 35R30 35R60 86A22 PDFBibTeX XMLCite \textit{W. Li} and \textit{J. Qian}, Inverse Probl. Imaging 16, No. 6, 1643--1667 (2022; Zbl 1511.65116) Full Text: DOI
Yeung, Tak Shing Au; Cheung, Ka Chun; Chung, Eric T.; Fu, Shubin; Qian, Jianliang Learning rays via deep neural network in a ray-based IPDG method for high-frequency Helmholtz equations in inhomogeneous media. (English) Zbl 07561051 J. Comput. Phys. 465, Article ID 111380, 22 p. (2022). MSC: 65Nxx 78Axx 35Jxx PDFBibTeX XMLCite \textit{T. S. A. Yeung} et al., J. Comput. Phys. 465, Article ID 111380, 22 p. (2022; Zbl 07561051) Full Text: DOI arXiv
Qian, Jianliang; Song, Chao Fast multiscale Gaussian beam method for three-dimensional elastic wave equations in bounded domains. (English) Zbl 1479.65014 SIAM J. Numer. Anal. 59, No. 5, 2536-2570 (2021). Reviewer: Dana Černá (Liberec) MSC: 65M99 65M60 65M12 35L10 PDFBibTeX XMLCite \textit{J. Qian} and \textit{C. Song}, SIAM J. Numer. Anal. 59, No. 5, 2536--2570 (2021; Zbl 1479.65014) Full Text: DOI
Ho, Kaho; Leung, Shingyu; Qian, Jianliang Fast Huygens sweeping methods for a class of nonlocal Schrödinger equations. (English) Zbl 1502.65168 J. Sci. Comput. 88, No. 3, Paper No. 54, 26 p. (2021). MSC: 65M80 65T50 35Q55 35Q41 81Q20 PDFBibTeX XMLCite \textit{K. Ho} et al., J. Sci. Comput. 88, No. 3, Paper No. 54, 26 p. (2021; Zbl 1502.65168) Full Text: DOI
Ao, Wenqi; Li, Wenbin; Qian, Jianliang A data and knowledge driven approach for SPECT using convolutional neural networks and iterative algorithms. (English) Zbl 1473.92023 J. Inverse Ill-Posed Probl. 29, No. 4, 543-555 (2021). MSC: 92C55 65R32 68T07 PDFBibTeX XMLCite \textit{W. Ao} et al., J. Inverse Ill-Posed Probl. 29, No. 4, 543--555 (2021; Zbl 1473.92023) Full Text: DOI
Leung, Shingyu; Qian, Jianliang; Hu, Jiangtao A level-set adjoint-state method for transmission traveltime tomography in irregular domains. (English) Zbl 1469.78015 SIAM J. Sci. Comput. 43, No. 3, A2352-A2380 (2021). MSC: 78A46 78A05 78M35 PDFBibTeX XMLCite \textit{S. Leung} et al., SIAM J. Sci. Comput. 43, No. 3, A2352--A2380 (2021; Zbl 1469.78015) Full Text: DOI
Li, Wenbin; Qian, Jianliang Simultaneously recovering both domain and varying density in inverse gravimetry by efficient level-set methods. (English) Zbl 1482.65173 Inverse Probl. Imaging 15, No. 3, 387-413 (2021). Reviewer: Barani Balan Natesan (Thiruvarur) MSC: 65M32 65M06 65N06 65N21 65N80 65K10 65F20 86A22 86-08 49M41 15A18 35Q86 PDFBibTeX XMLCite \textit{W. Li} and \textit{J. Qian}, Inverse Probl. Imaging 15, No. 3, 387--413 (2021; Zbl 1482.65173) Full Text: DOI
Qian, Jianliang; Song, Jian; Lu, Wangtao; Burridge, Robert Hadamard-Babich ansatz for point-source elastic wave equations in variable media at high frequencies. (English) Zbl 1453.65415 Multiscale Model. Simul. 19, No. 1, 46-86 (2021). MSC: 65N30 65M60 PDFBibTeX XMLCite \textit{J. Qian} et al., Multiscale Model. Simul. 19, No. 1, 46--86 (2021; Zbl 1453.65415) Full Text: DOI
Glowinski, Roland; Leung, Shingyu; Liu, Hao; Qian, Jianliang On the numerical solution of nonlinear eigenvalue problems for the Monge-Ampère operator. (English) Zbl 1460.35183 ESAIM, Control Optim. Calc. Var. 26, Paper No. 118, 25 p. (2020). MSC: 35J96 65N25 65N30 PDFBibTeX XMLCite \textit{R. Glowinski} et al., ESAIM, Control Optim. Calc. Var. 26, Paper No. 118, 25 p. (2020; Zbl 1460.35183) Full Text: DOI arXiv
Li, Wenbin; Qian, Jianliang Newton-type Gauss-Seidel Lax-Friedrichs high-order fast sweeping methods for solving generalized eikonal equations at large-scale discretization. (English) Zbl 1443.65284 Comput. Math. Appl. 79, No. 4, 1222-1239 (2020). MSC: 65N06 35F21 35F30 PDFBibTeX XMLCite \textit{W. Li} and \textit{J. Qian}, Comput. Math. Appl. 79, No. 4, 1222--1239 (2020; Zbl 1443.65284) Full Text: DOI
Li, Wenbin; Qian, Jianliang A level-set algorithm for the inverse problem of full magnetic gradient tensor data. (English) Zbl 1444.78006 Appl. Math. Lett. 107, Article ID 106416, 5 p. (2020). MSC: 78A46 35Q60 35R30 49N45 78M20 PDFBibTeX XMLCite \textit{W. Li} and \textit{J. Qian}, Appl. Math. Lett. 107, Article ID 106416, 5 p. (2020; Zbl 1444.78006) Full Text: DOI
Huang, Guanghui; Qian, Jianliang Analysis of regularized Kantorovich-Rubinstein metric and its application to inverse gravity problems. (English) Zbl 07198480 SIAM J. Imaging Sci. 12, No. 3, 1528-1560 (2019). MSC: 65D17 PDFBibTeX XMLCite \textit{G. Huang} and \textit{J. Qian}, SIAM J. Imaging Sci. 12, No. 3, 1528--1560 (2019; Zbl 07198480) Full Text: DOI
Liu, Hao; Glowinski, Roland; Leung, Shingyu; Qian, Jianliang A finite element/operator-splitting method for the numerical solution of the three dimensional Monge-Ampère equation. (English) Zbl 1433.35157 J. Sci. Comput. 81, No. 3, 2271-2302 (2019). MSC: 35J96 65N30 PDFBibTeX XMLCite \textit{H. Liu} et al., J. Sci. Comput. 81, No. 3, 2271--2302 (2019; Zbl 1433.35157) Full Text: DOI
Lam, Chi Yeung; Qian, Jianliang Numerical microlocal analysis by fast Gaussian wave packet transforms and application to high-frequency Helmholtz problems. (English) Zbl 1426.78004 SIAM J. Sci. Comput. 41, No. 5, A2717-A2746 (2019). MSC: 78A05 78A46 78M35 PDFBibTeX XMLCite \textit{C. Y. Lam} and \textit{J. Qian}, SIAM J. Sci. Comput. 41, No. 5, A2717--A2746 (2019; Zbl 1426.78004) Full Text: DOI
Fang, Jun; Qian, Jianliang; Zepeda-Núñez, Leonardo; Zhao, Hongkai A hybrid approach to solve the high-frequency Helmholtz equation with source singularity in smooth heterogeneous media. (English) Zbl 1415.65255 J. Comput. Phys. 371, 261-279 (2018). MSC: 65N30 35J05 65N15 PDFBibTeX XMLCite \textit{J. Fang} et al., J. Comput. Phys. 371, 261--279 (2018; Zbl 1415.65255) Full Text: DOI arXiv
Lu, Wangtao; Qian, Jianliang; Burridge, Robert Extending Babich’s ansatz for point-source Maxwell’s equations using Hadamard’s method. (English) Zbl 1448.65242 Multiscale Model. Simul. 16, No. 2, 727-751 (2018). MSC: 65N30 65M60 78A25 35Q61 78M10 PDFBibTeX XMLCite \textit{W. Lu} et al., Multiscale Model. Simul. 16, No. 2, 727--751 (2018; Zbl 1448.65242) Full Text: DOI
Glowinski, Roland; Leung, Shingyu; Qian, Jianliang A simple explicit operator-splitting method for effective Hamiltonians. (English) Zbl 1383.65089 SIAM J. Sci. Comput. 40, No. 1, A484-A503 (2018). MSC: 65M06 35F21 PDFBibTeX XMLCite \textit{R. Glowinski} et al., SIAM J. Sci. Comput. 40, No. 1, A484--A503 (2018; Zbl 1383.65089) Full Text: DOI
Fang, Jun; Qian, Jianliang; Zepeda-Núñez, Leonardo; Zhao, Hongkai Learning dominant wave directions for plane wave methods for high-frequency Helmholtz equations. (English) Zbl 1425.35016 Res. Math. Sci. 4, Paper No. 9, 35 p. (2017). MSC: 35J05 35J25 65N30 PDFBibTeX XMLCite \textit{J. Fang} et al., Res. Math. Sci. 4, Paper No. 9, 35 p. (2017; Zbl 1425.35016) Full Text: DOI arXiv
Chung, Eric T.; Lam, Chi Yeung; Qian, Jianliang A ray-based IPDG method for high-frequency time-domain acoustic wave propagation in inhomogeneous media. (English) Zbl 1380.65254 J. Comput. Phys. 348, 660-682 (2017). MSC: 65M60 35L05 PDFBibTeX XMLCite \textit{E. T. Chung} et al., J. Comput. Phys. 348, 660--682 (2017; Zbl 1380.65254) Full Text: DOI arXiv
Kwan, Wingfai; Leung, Shingyu; Wang, Xiao-Ping; Qian, Jianliang A fast Huygens sweeping method for capturing paraxial multi-color optical self-focusing in nematic liquid crystals. (English) Zbl 1380.78001 J. Comput. Phys. 348, 108-138 (2017). MSC: 78A10 78M25 PDFBibTeX XMLCite \textit{W. Kwan} et al., J. Comput. Phys. 348, 108--138 (2017; Zbl 1380.78001) Full Text: DOI
Lu, Wangtao; Qian, Jianliang; Burridge, Robert Babich-like ansatz for three-dimensional point-source Maxwell’s equations in an inhomogeneous medium at high frequencies. (English) Zbl 1352.65527 Multiscale Model. Simul. 14, No. 3, 1089-1122 (2016). MSC: 65N30 65M60 PDFBibTeX XMLCite \textit{W. Lu} et al., Multiscale Model. Simul. 14, No. 3, 1089--1122 (2016; Zbl 1352.65527) Full Text: DOI
Lu, Wangtao; Qian, Jianliang; Burridge, Robert Babich’s expansion and the fast Huygens sweeping method for the Helmholtz wave equation at high frequencies. (English) Zbl 1349.65691 J. Comput. Phys. 313, 478-510 (2016). MSC: 65N99 35J25 PDFBibTeX XMLCite \textit{W. Lu} et al., J. Comput. Phys. 313, 478--510 (2016; Zbl 1349.65691) Full Text: DOI
Qian, Jianliang; Yuan, Lijun; Liu, Yuan; Luo, Songting; Burridge, Robert Babich’s expansion and high-order Eulerian asymptotics for point-source Helmholtz equations. (English) Zbl 1398.65320 J. Sci. Comput. 67, No. 3, 883-908 (2016). MSC: 65N35 35J05 PDFBibTeX XMLCite \textit{J. Qian} et al., J. Sci. Comput. 67, No. 3, 883--908 (2016; Zbl 1398.65320) Full Text: DOI
Qian, Jianliang; Lu, Wangtao; Yuan, Lijun; Luo, Songting; Burridge, Robert Eulerian geometrical optics and fast Huygens sweeping methods for three-dimensional time-harmonic high-frequency Maxwell’s equations in inhomogeneous media. (English) Zbl 1338.65251 Multiscale Model. Simul. 14, No. 2, 595-636 (2016). MSC: 65N30 65M60 PDFBibTeX XMLCite \textit{J. Qian} et al., Multiscale Model. Simul. 14, No. 2, 595--636 (2016; Zbl 1338.65251) Full Text: DOI
Glowinski, Roland; Leung, Shingyu; Qian, Jianliang Operator-splitting based fast sweeping methods for isotropic wave propagation in a moving fluid. (English) Zbl 1407.65104 SIAM J. Sci. Comput. 38, No. 2, A1195-A1223 (2016). Reviewer: Abdallah Bradji (Annaba) MSC: 65M06 65N06 35F21 PDFBibTeX XMLCite \textit{R. Glowinski} et al., SIAM J. Sci. Comput. 38, No. 2, A1195--A1223 (2016; Zbl 1407.65104) Full Text: DOI
Lu, Wangtao; Leung, Shingyu; Qian, Jianliang An improved fast local level set method for three-dimensional inverse gravimetry. (English) Zbl 1369.65134 Inverse Probl. Imaging 9, No. 2, 479-509 (2015). MSC: 65N21 37D20 53C21 65R32 PDFBibTeX XMLCite \textit{W. Lu} et al., Inverse Probl. Imaging 9, No. 2, 479--509 (2015; Zbl 1369.65134) Full Text: DOI
Glowinski, Roland; Leung, Shingyu; Qian, Jianliang A penalization-regularization-operator splitting method for eikonal based traveltime tomography. (English) Zbl 1325.65092 SIAM J. Imaging Sci. 8, No. 2, 1263-1292 (2015). MSC: 65K10 35F21 49J20 92C55 86A15 PDFBibTeX XMLCite \textit{R. Glowinski} et al., SIAM J. Imaging Sci. 8, No. 2, 1263--1292 (2015; Zbl 1325.65092) Full Text: DOI Link
Luo, Songting; Qian, Jianliang; Burridge, Robert Fast Huygens sweeping methods for Helmholtz equations in inhomogeneous media in the high frequency regime. (English) Zbl 1349.78051 J. Comput. Phys. 270, 378-401 (2014). MSC: 78A48 PDFBibTeX XMLCite \textit{S. Luo} et al., J. Comput. Phys. 270, 378--401 (2014; Zbl 1349.78051) Full Text: DOI
Bao, Gang; Lai, Jun; Qian, Jianliang Fast multiscale Gaussian beam methods for wave equations in bounded convex domains. (English) Zbl 1349.65543 J. Comput. Phys. 261, 36-64 (2014). MSC: 65M99 35L20 PDFBibTeX XMLCite \textit{G. Bao} et al., J. Comput. Phys. 261, 36--64 (2014; Zbl 1349.65543) Full Text: DOI
Bao, Gang; Qian, Jianliang; Ying, Lexing; Zhang, Hai A convergent multiscale Gaussian-beam parametrix for the wave equation. (English) Zbl 1302.35485 Commun. Partial Differ. Equations 38, No. 1-3, 92-134 (2013). MSC: 35S05 35A27 35S30 47G30 PDFBibTeX XMLCite \textit{G. Bao} et al., Commun. Partial Differ. Equations 38, No. 1--3, 92--134 (2013; Zbl 1302.35485) Full Text: DOI
Luo, Songting; Qian, Jianliang Fast sweeping methods for factored anisotropic eikonal equations: multiplicative and additive factors. (English) Zbl 1255.65192 J. Sci. Comput. 52, No. 2, 360-382 (2012). MSC: 65N06 PDFBibTeX XMLCite \textit{S. Luo} and \textit{J. Qian}, J. Sci. Comput. 52, No. 2, 360--382 (2012; Zbl 1255.65192) Full Text: DOI
Luo, Songting; Qian, Jianliang Factored singularities and high-order Lax-Friedrichs sweeping schemes for point-source traveltimes and amplitudes. (English) Zbl 1220.78004 J. Comput. Phys. 230, No. 12, 4742-4755 (2011). MSC: 78A05 78M20 35F21 PDFBibTeX XMLCite \textit{S. Luo} and \textit{J. Qian}, J. Comput. Phys. 230, No. 12, 4742--4755 (2011; Zbl 1220.78004) Full Text: DOI
Leung, Shingyu; Qian, Jianliang The backward phase flow and FBI-transform-based Eulerian Gaussian beams for the Schrödinger equation. (English) Zbl 1282.81090 J. Comput. Phys. 229, No. 23, 8888-8917 (2010). MSC: 81Q20 65M75 PDFBibTeX XMLCite \textit{S. Leung} and \textit{J. Qian}, J. Comput. Phys. 229, No. 23, 8888--8917 (2010; Zbl 1282.81090) Full Text: DOI
Qian, Jianliang; Ying, Lexing Fast Gaussian wavepacket transforms and Gaussian beams for the Schrödinger equation. (English) Zbl 1197.65156 J. Comput. Phys. 229, No. 20, 7848-7873 (2010). MSC: 65M70 35Q40 PDFBibTeX XMLCite \textit{J. Qian} and \textit{L. Ying}, J. Comput. Phys. 229, No. 20, 7848--7873 (2010; Zbl 1197.65156) Full Text: DOI
Leung, Shingyu; Qian, Jianliang Eulerian Gaussian beams for Schrödinger equations in the semi-classical regime. (English) Zbl 1161.81370 J. Comput. Phys. 228, No. 8, 2951-2977 (2009). MSC: 81Q20 81Q05 81-08 PDFBibTeX XMLCite \textit{S. Leung} and \textit{J. Qian}, J. Comput. Phys. 228, No. 8, 2951--2977 (2009; Zbl 1161.81370) Full Text: DOI
Cecil, Thomas C.; Osher, Stanley J.; Qian, Jianliang Essentially non-oscillatory adaptive tree methods. (English) Zbl 1203.65219 J. Sci. Comput. 35, No. 1, 25-41 (2008). MSC: 65N06 PDFBibTeX XMLCite \textit{T. C. Cecil} et al., J. Sci. Comput. 35, No. 1, 25--41 (2008; Zbl 1203.65219) Full Text: DOI
Kao, Chiu-Yen; Osher, Stanley; Qian, Jianliang Legendre-transform-based fast sweeping methods for static Hamilton-Jacobi equations on triangulated meshes. (English) Zbl 1152.65102 J. Comput. Phys. 227, No. 24, 10209-10225 (2008). MSC: 65N35 35F21 PDFBibTeX XMLCite \textit{C.-Y. Kao} et al., J. Comput. Phys. 227, No. 24, 10209--10225 (2008; Zbl 1152.65102) Full Text: DOI
Qian, Jianliang; Zhang, Yong-Tao; Zhao, Hong-Kai A fast sweeping method for static convex Hamilton-Jacobi equations. (English) Zbl 1115.70005 J. Sci. Comput. 31, No. 1-2, 237-271 (2007). MSC: 70-08 70H20 PDFBibTeX XMLCite \textit{J. Qian} et al., J. Sci. Comput. 31, No. 1--2, 237--271 (2007; Zbl 1115.70005) Full Text: DOI
Serna, Susana; Qian, Jianliang Fifth-order weighted power-ENO schemes for Hamilton-Jacobi equations. (English) Zbl 1149.70301 J. Sci. Comput. 29, No. 1, 57-81 (2006). MSC: 70-08 70H20 PDFBibTeX XMLCite \textit{S. Serna} and \textit{J. Qian}, J. Sci. Comput. 29, No. 1, 57--81 (2006; Zbl 1149.70301) Full Text: DOI
Zhang, Yong-Tao; Zhao, Hong-Kai; Qian, Jianliang High order fast sweeping methods for static Hamilton-Jacobi equations. (English) Zbl 1149.70302 J. Sci. Comput. 29, No. 1, 25-56 (2006). MSC: 70-08 70H20 PDFBibTeX XMLCite \textit{Y.-T. Zhang} et al., J. Sci. Comput. 29, No. 1, 25--56 (2006; Zbl 1149.70302) Full Text: DOI
Cecil, Thomas C.; Osher, Stanley J.; Qian, Jianliang Simplex free adaptive tree fast sweeping and evolution methods for solving level set equations in arbitrary dimension. (English) Zbl 1089.65084 J. Comput. Phys. 213, No. 2, 458-473 (2006). MSC: 65M06 35L60 65M12 PDFBibTeX XMLCite \textit{T. C. Cecil} et al., J. Comput. Phys. 213, No. 2, 458--473 (2006; Zbl 1089.65084) Full Text: DOI
Cockburn, Bernardo; Qian, Jianliang; Reitich, Fernando; Wang, Jing An accurate spectral/discontinuous finite-element formulation of a phase-space-based level set approach to geometrical optics. (English) Zbl 1066.78015 J. Comput. Phys. 208, No. 1, 175-195 (2005). MSC: 78M10 65M60 65M20 78A05 PDFBibTeX XMLCite \textit{B. Cockburn} et al., J. Comput. Phys. 208, No. 1, 175--195 (2005; Zbl 1066.78015) Full Text: DOI
Kao, Chiu Yen; Osher, Stanley; Qian, Jianliang Lax-Friedrichs sweeping scheme for static Hamilton-Jacobi equations. (English) Zbl 1053.65088 J. Comput. Phys. 196, No. 1, 367-391 (2004). MSC: 65N06 65N12 35F30 PDFBibTeX XMLCite \textit{C. Y. Kao} et al., J. Comput. Phys. 196, No. 1, 367--391 (2004; Zbl 1053.65088) Full Text: DOI
Qian, Jianliang; Leung, Shingyu A level set based Eulerian method for paraxial multivalued traveltimes. (English) Zbl 1052.65087 J. Comput. Phys. 197, No. 2, 711-736 (2004). MSC: 65M25 35L60 65Y20 PDFBibTeX XMLCite \textit{J. Qian} and \textit{S. Leung}, J. Comput. Phys. 197, No. 2, 711--736 (2004; Zbl 1052.65087) Full Text: DOI
Qian, Jianliang; Cheng, Li-Tien; Osher, Stanley A level set-based Eulerian approach for anisotropic wave propagation. (English) Zbl 1163.74426 Wave Motion 37, No. 4, 365-379 (2003). MSC: 74-XX 76-XX PDFBibTeX XMLCite \textit{J. Qian} et al., Wave Motion 37, No. 4, 365--379 (2003; Zbl 1163.74426) Full Text: DOI