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Hou, Thomas Yizhao

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Author ID: hou.thomas-yizhao Recent zbMATH articles by "Hou, Thomas Yizhao"
Published as: Hou, Thomas Y.; Hou, T. Y.; Hou, Thomas Yizhao; Hou, Thomas; Hou, T.; Hou, Th. Y.; Hou, T.-Y.
Homepage: http://users.cms.caltech.edu/~hou/
External Links: MGP · Wikidata · dblp · GND · IdRef
Documents Indexed: 166 Publications since 1988, including 1 Book
8 Contributions as Editor
Biographic References: 1 Publication
all top 5

Co-Authors

12 single-authored
18 Shi, Zuoqiang
14 Efendiev, Yalchin R.
14 Lowengrub, John Samuel
7 Liu, Pengfei
7 Yu, Xinwei
6 Ceniceros, Hector D.
6 Deng, Jian
6 Li, Ruo
6 Wu, Xiaohui
6 Zhang, Zhiwen
5 Beale, J. Thomas
5 Li, Congming
5 Luo, Guo
5 Shelley, Michael J.
5 Yang, Danping
5 Zhang, Pengchuan
5 Zhang, Pingwen
4 Chen, Jiajie
4 Goodman, Jonathan B.
4 Lei, Zhen
4 Wang, Shu
4 Zhou, Hao-Min
3 Cheng, Mulin
3 Huang, De
3 Lam, Ka Chun
3 LeFloch, Philippe Gerard
3 Li, Qin
3 Luo, Wuan
3 Ran, Hongyu
3 Rozovskii, Boris L.
3 Tavallali, Peyman
3 Wetton, Brian T. R.
2 Aarnes, Jørg E.
2 Caflisch, Russel E.
2 Chan, Tony Fan-Cheong
2 Chen, Yifan
2 Dostert, Paul
2 Engquist, Bjorn E.
2 Ginting, Victor
2 Graham, Ivan G.
2 Hou, Anthony
2 Hu, Gang
2 Hu, Xin
2 Kim, Hongjoong
2 Liu, Chunguang
2 Liu, Wing Kam
2 Osher, Stanley Joel
2 Schaeffer, Hayden
2 Si, Helen
2 Stredie, V. G.
2 Tadmor, Eitan
2 Tang, Shaoqiang
2 Wu, Theodore Yaotsu
2 Yan, Mike
2 Zhao, Hongkai
1 Alber, Mark S.
1 Avellaneda, Marco
1 Cai, Zhiqiang
1 Chacón Rebollo, Tomás
1 Chan, Raymond Hon-Fu
1 Chen, Xinfu
1 Chen, Zhiming
1 Choi, Kyudong
1 Chung, Tsz Shun Eric
1 Ci, Maolin
1 Daubechies, Ingrid Chantal
1 E, Weinan
1 Ercolani, Nicholas M.
1 Ewing, Richard Edward
1 Fetecau, Razvan C.
1 Galvis, Juan
1 Glazier, James A.
1 Huang, Norden E.
1 Hwang, Fengnan
1 Jiang, Lijian
1 Jiang, Yi
1 Jin, Tianling
1 Kiselev, Alexander A.
1 Klapper, Isaac
1 Koumoutsakos, Petros D.
1 Krasny, Robert
1 Lakkis, Omar
1 Landis, Yelena
1 Lax, Peter David
1 Li, Zhilin
1 Liang, Dong
1 Lin, Guang
1 Lions, Pierre-Louis
1 Liu, Chun
1 Liu, Jianguo
1 Ma, Dingjiong
1 Merriman, Barry
1 Papanicolaou, George C.
1 Park, Peter J.
1 Rosakis, Phoebus
1 Scheichl, Robert
1 Shelly, M. J.
1 Strinopoulos, T.
1 Šverák, Vladimír
1 Tai, Xuecheng
...and 13 more Co-Authors
all top 5

Serials

26 Journal of Computational Physics
13 Communications on Pure and Applied Mathematics
13 Multiscale Modeling & Simulation
9 SIAM Journal on Numerical Analysis
8 Mathematics of Computation
7 Discrete and Continuous Dynamical Systems
5 Communications in Partial Differential Equations
4 Physics of Fluids
3 Methods and Applications of Analysis
3 Communications in Mathematical Sciences
3 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
2 Archive for Rational Mechanics and Analysis
2 Communications in Mathematical Physics
2 Journal of Computational Mathematics
2 Journal of Nonlinear Science
2 SIAM Journal on Scientific Computing
2 Applied and Computational Harmonic Analysis
2 Sibirskiĭ Zhurnal Vychislitel’noĭ Matematiki
2 Discrete and Continuous Dynamical Systems. Series B
2 Communications in Computational Physics
2 Advances in Adaptive Data Analysis
2 Science China. Mathematics
2 Information and Inference
2 Research in the Mathematical Sciences
1 Computer Methods in Applied Mechanics and Engineering
1 International Journal for Numerical Methods in Fluids
1 Journal of Fluid Mechanics
1 Nonlinearity
1 Advances in Mathematics
1 International Journal for Numerical Methods in Engineering
1 Numerische Mathematik
1 SIAM Journal on Scientific and Statistical Computing
1 Physica D
1 Applied Numerical Mathematics
1 RAIRO. Modélisation Mathématique et Analyse Numérique
1 Acta Mathematicae Applicatae Sinica. English Series
1 Computational Mechanics
1 Mathematical and Computer Modelling
1 Journal of Scientific Computing
1 Proceedings of the National Academy of Sciences of the United States of America
1 SIAM Journal on Applied Mathematics
1 SIAM Journal on Mathematical Analysis
1 SIAM Review
1 Documenta Mathematica
1 The Asian Journal of Mathematics
1 Computational Geosciences
1 HERMIS-\(\mu\pi\). Hellenic European Research on Mathematics and Informatics Science
1 International Journal of Computational Methods
1 Acta Numerica
1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
1 Bulletin of the Institute of Mathematics. Academia Sinica. New Series
1 Lecture Notes in Computational Science and Engineering
1 Surveys and Tutorials in the Applied Mathematical Sciences
1 Series in Contemporary Applied Mathematics CAM
1 Inverse Problems and Imaging
1 ICCM Notices
1 SIAM/ASA Journal on Uncertainty Quantification
1 Advances in Data Science and Adaptive Analysis

Publications by Year

Citations contained in zbMATH Open

148 Publications have been cited 4,286 times in 2,474 Documents Cited by Year
A multiscale finite element method for elliptic problems in composite materials and porous media. Zbl 0880.73065
Hou, Thomas Y.; Wu, Xiao-Hui
542
1997
Multiscale finite element methods. Theory and applications. Zbl 1163.65080
Efendiev, Yalchin; Hou, Thomas Y.
270
2009
A level set formulation of Eulerian interface capturing methods for incompressible fluid flows. Zbl 0847.76048
Chang, Y. C.; Hou, T. Y.; Merriman, B.; Osher, S.
213
1996
Generalized multiscale finite element methods (GMsFEM). Zbl 1349.65617
Efendiev, Yalchin; Galvis, Juan; Hou, Thomas Y.
193
2013
Removing the stiffness from interfacial flows with surface tension. Zbl 0810.76095
Hou, Thomas Y.; Lowengrub, John S.; Shelley, Michael J.
188
1994
Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients. Zbl 0922.65071
Hou, Thomas Y.; Wu, Xiao-Hui; Cai, Zhiqiang
180
1999
Global well-posedness of the viscous Boussinesq equations. Zbl 1274.76185
Hou, Thomas Y.; Li, Congming
173
2005
A mixed multiscale finite element method for elliptic problems with oscillating coefficients. Zbl 1017.65088
Chen, Zhiming; Hou, Thomas Y.
132
2003
Convergence of a nonconforming multiscale finite element method. Zbl 0951.65105
Efendiev, Yalchin R.; Hou, Thomas Y.; Wu, Xiao-Hui
102
2000
A hybrid method for moving interface problems with application to the Hele-Shaw flow. Zbl 0888.76067
Hou, Thomas Y.; Li, Zhilin; Osher, Stanley; Zhao, Hongkai
98
1997
Why nonconservative schemes converge to wrong solutions: Error analysis. Zbl 0809.65102
Hou, Thomas Y.; Le Floch, Philippe G.
91
1994
Accurate multiscale finite element methods for two-phase flow simulations. Zbl 1158.76349
Efendiev, Y.; Ginting, V.; Hou, T.; Ewing, R.
83
2006
A new multiscale finite element method for high-contrast elliptic interface problems. Zbl 1202.65154
Chu, C.-C.; Graham, I. G.; Hou, T.-Y.
81
2010
Analysis of upscaling absolute permeability. Zbl 1162.65327
Wu, X. H.; Efendiev, Y.; Hou, T. Y.
68
2002
Multiscale finite element methods for nonlinear problems and their applications. Zbl 1083.65105
Efendiev, Yalchin R.; Hou, Thomas Yizhao; Ginting, Victor
67
2004
Adaptive multiscale model reduction with generalized multiscale finite element methods. Zbl 1349.76191
Chung, Eric; Efendiev, Yalchin; Hou, Thomas Y.
67
2016
Wiener chaos expansions and numerical solutions of randomly forced equations of fluid mechanics. Zbl 1095.76047
Hou, Thomas Y.; Luo, Wuan; Rozovskii, Boris; Zhou, Hao-Min
64
2006
Boundary integral methods for multicomponent fluids and multiphase materials. Zbl 1046.76029
Hou, T. Y.; Lowengrub, J. S.; Shelley, M. J.
62
2001
The long-time motion of vortex sheets with surface tension. Zbl 1185.76545
Hou, T. Y.; Lowengrub, J. S.; Shelly, M. J.
60
1997
Computing nearly singular solutions using pseudo-spectral methods. Zbl 1310.76127
Hou, Thomas Y.; Li, Ruo
60
2007
Growth rates for the linearized motion of fluid interfaces away from equilibrium. Zbl 0796.76041
Beale, J. Thomas; Hou, Thomas Y.; Lowengrub, John S.
58
1993
An efficient dynamically adaptive mesh for potentially singular solutions. Zbl 0986.65087
Ceniceros, Hector D.; Hou, Thomas Y.
56
2001
Dynamic depletion of vortex stretching and non-blowup of the 3-D incompressible Euler equations. Zbl 1370.76015
Hou, Thomas Y.; Li, Ruo
51
2006
Removing the cell resonance error in the multiscale finite element method via a Petrov-Galerkin formulation. Zbl 1085.65109
Hou, Thomas Y.; Wu, Xiao-Hui; Zhang, Yu
47
2004
Preconditioning Markov chain Monte Carlo simulations using coarse-scale models. Zbl 1111.65003
Efendiev, Yalchin R.; Hou, Thomas Yizhao; Luo, Wu An
45
2006
Convergence of the point vortex method for the 2-D Euler equations. Zbl 0694.76013
Goodman, Jonathan; Hou, Thomas Y.; Lowengrub, John
44
1990
Dynamic stability of the three-dimensional axisymmetric Navier-Stokes equations with swirl. Zbl 1138.35077
Hou, Thomas Y.; Li, Congming
42
2008
Geometric properties and nonblowup of 3D incompressible Euler flow. Zbl 1142.35549
Deng, Jian; Hou, Thomas Y.; Yu, Xinwei
40
2005
Toward the finite-time blowup of the 3D axisymmetric Euler equations: a numerical investigation. Zbl 1316.35235
Luo, Guo; Hou, Thomas Y.
36
2014
A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations. I: Derivation and algorithms. Zbl 1297.65008
Cheng, Mulin; Hou, Thomas Y.; Zhang, Zhiwen
36
2013
Multiscale finite element methods for porous media flows and their applications. Zbl 1112.76046
Efendiev, Yalchin R.; Hou, Thomas Yizhao
33
2007
Multiscale domain decomposition methods for elliptic problems with high aspect ratios. Zbl 1003.65142
Aarnes, Jørg; Hou, Thomas Y.
32
2002
A mathematical framework of the bridging scale method. Zbl 1117.74056
Tang, Shaoqiang; Hou, Thomas Y.; Liu, Wing Kam
31
2006
Improved geometric conditions for non-blowup of the 3D incompressible Euler equation. Zbl 1158.76305
Deng, Jian; Hou, Thomas Y.; Yu, Xinwei
30
2006
Convergence of a boundary integral method for water waves. Zbl 0858.76046
Beale, J. Thomas; Hou, Thomas Y.; Lowengrub, John
30
1996
On the finite-time blowup of a one-dimensional model for the three-dimensional axisymmetric Euler equations. Zbl 1377.35218
Choi, Kyudong; Hou, Thomas Y.; Kiselev, Alexander; Luo, Guo; Sverak, Vladimir; Yao, Yao
28
2017
Global regularity of the 3D axi-symmetric Navier-Stokes equations with anisotropic data. Zbl 1146.76010
Hou, Thomas Y.; Lei, Zhen; Li, Congming
27
2008
A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations. II: Adaptivity and generalizations. Zbl 1297.65007
Cheng, Mulin; Hou, Thomas Y.; Zhang, Zhiwen
26
2013
On the stabilizing effect of convection in three-dimensional incompressible flows. Zbl 1171.35095
Hou, Thomas Y.; Lei, Zhen
24
2009
Dispersive approximations in fluid dynamics. Zbl 0729.76065
Hou, Thomas Y.; Lax, Peter D.
22
1991
Blowup or no blowup? the interplay between theory and numerics. Zbl 1143.76390
Hou, Thomas Y.; Li, Ruo
22
2008
Multiscale finite element methods for stochastic porous media flow equations and application to uncertainty quantification. Zbl 1194.76112
Dostert, P.; Efendiev, Y.; Hou, T. Y.
21
2008
A pseudo-spectral multiscale method: interfacial conditions and coarse grid equations. Zbl 1089.65110
Tang, Shaoqiang; Hou, Thomas Y.; Liu, Wing Kam
21
2006
Blow-up or no blow-up? A unified computational and analytic approach to 3D incompressible Euler and Navier-Stokes equations. Zbl 1422.76041
Hou, Thomas Y.
21
2009
An efficient semi-implicit immersed boundary method for the Navier-Stokes equations. Zbl 1161.76048
Hou, Thomas Y.; Shi, Zuoqiang
20
2008
Data-driven time-frequency analysis. Zbl 1336.94019
Hou, Thomas Y.; Shi, Zuoqiang
19
2013
Coarse-gradient Langevin algorithms for dynamic data integration and uncertainty quantification. Zbl 1146.76637
Dostert, P.; Efendiev, Y.; Hou, T. Y.; Luo, W.
17
2006
Adaptive data analysis via sparse time-frequency representation. Zbl 1234.94015
Hou, Thomas Y.; Shi, Zuoqiang
17
2011
Homogenization of linear transport equations with oscillatory vector fields. Zbl 0759.35008
Hou, Thomas Y.; Xin, Xue
16
1992
Multi-valued solutions and branch point singularities for nonlinear hyperbolic or elliptic systems. Zbl 0797.35007
Caflisch, Russel E.; Ercolani, Nicholas; Hou, Thomas Y.; Landis, Yelena
16
1993
Numerical study of Hele-Shaw flow with suction. Zbl 1149.76335
Ceniceros, Hector D.; Hou, Thomas Y.; Si, Helen
15
1999
Computational method for propagating phase boundaries. Zbl 0855.73080
Zhong, Xiaoguang; Hou, Thomas Y.; LeFloch, Philippe G.
14
1996
Removing the stiffness of curvature in computing 3-D filaments. Zbl 0917.76063
Hou, Thomas Y.; Klapper, Isaac; Si, Helen
14
1998
Geometry related convergence results for domain decomposition algorithms. Zbl 0724.65109
Chan, Tony F.; Hou, Thomas Y.; Lions, P. L.
13
1991
Convergence of a non-stiff boundary integral method for interfacial flows with surface tension. Zbl 0905.76012
Ceniceros, Héctor D.; Hou, Thomas Y.
13
1998
Removing the stiffness of elastic force from the immersed boundary method for the 2D Stokes equations. Zbl 1294.76201
Hou, Thomas Y.; Shi, Zuoqiang
13
2008
Multiscale numerical methods for singularly perturbed convection-diffusion equations. Zbl 1182.76902
Park, Peter J.; Hou, Thomas Y.
12
2004
Second-order convergence of a projection scheme for the incompressible Navier-Stokes equations with boundaries. Zbl 0776.76055
Hou, Thomas Y.; Wetton, Brian T. R.
12
1993
Convergence of a boundary integral method for 3-D water waves. Zbl 1131.76339
Hou, Thomas Y.; Zhang, Pingwen
12
2002
Level set dynamics and the non-blowup of the 2D quasi-geostrophic equation. Zbl 1173.76006
Deng, J.; Hou, T. Y.; Li, R.; Yu, X.
12
2006
Convergence of a finite difference scheme for the Navier-Stokes equations using vorticity boundary conditions. Zbl 0749.76046
Hou, Thomas Y.; Wetton, Brian T. R.
12
1992
Convergence of a variable blob vortex method for the Euler and Navier- Stokes equations. Zbl 0727.76034
Hou, Thomas Y.
12
1990
A data-driven stochastic method for elliptic PDEs with random coefficients. Zbl 1290.60068
Cheng, Mulin; Hou, Thomas Y.; Yan, Mike; Zhang, Zhiwen
12
2013
Self-similar singularity of a 1D model for the 3D axisymmetric Euler equations. Zbl 1320.35269
Hou, Thomas Y.; Liu, Pengfei
11
2015
Convergence of the point vortex method for the 3-D Euler equations. Zbl 0856.76059
Hou, Thomas Y.; Lowengrub, John
11
1990
On the partial regularity of a 3D model of the Navier-Stokes equations. Zbl 1176.35130
Hou, Thomas Y.; Lei, Zhen
11
2009
On singularity formation of a 3D model for incompressible Navier-Stokes equations. Zbl 1252.35219
Hou, Thomas Y.; Shi, Zuoqiang; Wang, Shu
11
2012
Dynamic generation of capillary waves. Zbl 1147.76354
Ceniceros, Hector D.; Hou, Thomas Y.
11
1999
Optimal local multi-scale basis functions for linear elliptic equations with rough coefficients. Zbl 1333.65131
Hou, Thomas Y.; Liu, Pengfei
11
2016
On finite time singularity and global regularity of an axisymmetric model for the 3D Euler equations. Zbl 1293.35228
Hou, Thomas Y.; Lei, Zhen; Luo, Guo; Wang, Shu; Zou, Chen
10
2014
Sparse operator compression of higher-order elliptic operators with rough coefficients. Zbl 1412.65215
Hou, Thomas Y.; Zhang, Pengchuan
10
2017
Nonexistence of locally self-similar blow-up for the 3D incompressible Navier-Stokes equations. Zbl 1194.35307
Hou, Thomas Y.; Li, Ruo
10
2007
Numerical solutions to free boundary problems. Zbl 0831.65137
Hou, Thomas Y.
10
1995
A level-set approach to the computation of twinning and phase-transition dynamics. Zbl 0936.74052
Hou, Thomas Y.; Rosakis, Phoebus; LeFloch, Philippe
10
1999
On the stability of the unsmoothed Fourier method for hyperbolic equations. Zbl 0791.65080
Goodman, Jonathan; Hou, Thomas; Tadmor, Eitan
10
1994
Potentially singular solutions of the 3D axisymmetric Euler equations. Zbl 1431.35115
Luo, Guo; Hou, Thomas Y.
10
2014
Convergence of a data-driven time-frequency analysis method. Zbl 1336.94020
Hou, Thomas Y.; Shi, Zuoqiang; Tavallali, Peyman
9
2014
The singular perturbation of surface tension in Hele-Shaw flows. Zbl 0991.76020
Ceniceros, Hector D.; Hou, Thomas Y.
9
2000
Well-posedness of linearized motion for 3-D water waves far from equilibrium. Zbl 0874.76014
Hou, Thomas Y.; Teng, Zhenhuan; Zhang, Pingwen
8
1996
Multiscale modelling and computation of fluid flow. Zbl 1134.76386
Hou, Thomas Y.
8
2005
On global well-posedness of the Lagrangian averaged Euler equations. Zbl 1111.76006
Hou, Thomas Y.; Li, Congming
8
2006
An efficient boundary integral method for the Mullins-Sekerka problem. Zbl 0879.65092
Zhu, Jingyi; Chen, Xinfu; Hou, Thomas Y.
7
1996
Convergence of a point vortex method for vortex sheets. Zbl 0799.76062
Hou, Thomas Y.; Lowengrub, John; Krasny, Robert
7
1991
A heterogeneous stochastic FEM framework for elliptic PDEs. Zbl 1352.65510
Hou, Thomas Y.; Liu, Pengfei
7
2015
Spatial and temporal stability issues for interfacial flows with surface tension. Zbl 0816.76050
Beale, J. T.; Hou, T. Y.; Lowengrub, J. S.; Shelley, M. J.
7
1994
Particle method approximation of oscillatory solutions to hyperbolic differential equations. Zbl 0675.65093
Engquist, Bjorn; Hou, Thomas Y.
7
1989
On singularity formation of a nonlinear nonlocal system. Zbl 1241.35038
Hou, Thomas Y.; Li, Congming; Shi, Zuoqiang; Wang, Shu; Yu, Xinwei
7
2011
Numerical approximations to multiscale solutions in partial differential equations. Zbl 1027.65154
Hou, Thomas Y.
6
2003
Convergence of the grid-free point vortex method for the three-dimensional Euler equations. Zbl 0850.76489
Cottet, Georges-Henri; Goodman, Jonathan; Hou, Thomas Y.
6
1991
New stability estimates for the 2-D vortex method. Zbl 0745.76061
Goodman, Jonathan; Hou, Thomas Y.
6
1991
Sparse + low-energy decomposition for viscous conservation laws. Zbl 1352.65413
Hou, Thomas Y.; Li, Qin; Schaeffer, Hayden
6
2015
Exploring the locally low dimensional structure in solving random elliptic PDEs. Zbl 1365.65015
Hou, Thomas Y.; Li, Qin; Zhang, Pengchuan
6
2017
Extracting a shape function for a signal with intra-wave frequency modulation. Zbl 1353.94017
Hou, Thomas Y.; Shi, Zuoqiang
5
2016
Finite difference approximations for partial differential equations with rapidly oscillating coefficients. Zbl 0755.65088
Avellaneda, M.; Hou, Th. Y.; Papanicolaou, G. C.
5
1991
A Lagrangian finite element method for the 2-D Euler equations. Zbl 0705.76059
Chacon-Rebollo, Tomas; Hou, Thomas Y.
5
1990
A model reduction method for multiscale elliptic PDEs with random coefficients using an optimization approach. Zbl 1420.35083
Hou, Thomas Y.; Ma, Dingjiong; Zhang, Zhiwen
5
2019
A sparse decomposition of low rank symmetric positive semidefinite matrices. Zbl 1386.65127
Hou, Thomas Y.; Li, Qin; Zhang, Pengchuan
5
2017
Numerical analysis of multiscale problems. Selected papers based on the presentations at the 91st London Mathematical Society symposium, Durham, UK, July 5–15, 2010. Zbl 1234.65007
4
2012
The convergence of an exact desingularization for vortex methods. Zbl 0769.76045
Hou, T. Y.; Lowengrub, J.; Shelley, M. J.
4
1993
Extraction of intrawave signals using the sparse time-frequency representation method. Zbl 1380.94062
Tavallali, Peyman; Hou, Thomas Y.; Shi, Zuoqiang
4
2014
Finite time blowup of 2D Boussinesq and 3D Euler equations with \(C^{1, \alpha}\) velocity and boundary. Zbl 07340014
Chen, Jiajie; Hou, Thomas Yizhao
4
2021
On the finite time blowup of the de Gregorio model for the 3D Euler equations. Zbl 1469.35053
Chen, Jiajie; Hou, Thomas Y.; Huang, De
1
2021
A model reduction method for multiscale elliptic PDEs with random coefficients using an optimization approach. Zbl 1420.35083
Hou, Thomas Y.; Ma, Dingjiong; Zhang, Zhiwen
5
2019
Formation of finite-time singularities in the 3D axisymmetric Euler equations: a numerics guided study. Zbl 1427.35190
Luo, Guo; Hou, Thomas Y.
3
2019
A fast hierarchically preconditioned eigensolver based on multiresolution matrix decomposition. Zbl 1455.65053
Hou, Thomas Y.; Huang, De; Lam, Ka Chun; Zhang, Ziyun
1
2019
An adaptive fast solver for a general class of positive definite matrices via energy decomposition. Zbl 1391.65066
Hou, Thomas Y.; Huang, De; Lam, Ka Chun; Zhang, PengChuan
2
2018
Global regularity for a family of 3D models of the axi-symmetric Navier-Stokes equations. Zbl 1393.35170
Hou, Thomas Y.; Liu, Pengfei; Wang, Fei
1
2018
Potential singularity for a family of models of the axisymmetric incompressible flow. Zbl 1405.35150
Hou, Thomas Y.; Jin, Tianling; Liu, Pengfei
1
2018
On the finite-time blowup of a one-dimensional model for the three-dimensional axisymmetric Euler equations. Zbl 1377.35218
Choi, Kyudong; Hou, Thomas Y.; Kiselev, Alexander; Luo, Guo; Sverak, Vladimir; Yao, Yao
28
2017
Sparse operator compression of higher-order elliptic operators with rough coefficients. Zbl 1412.65215
Hou, Thomas Y.; Zhang, Pengchuan
10
2017
Exploring the locally low dimensional structure in solving random elliptic PDEs. Zbl 1365.65015
Hou, Thomas Y.; Li, Qin; Zhang, Pengchuan
6
2017
A sparse decomposition of low rank symmetric positive semidefinite matrices. Zbl 1386.65127
Hou, Thomas Y.; Li, Qin; Zhang, Pengchuan
5
2017
An iteratively adaptive multi-scale finite element method for elliptic PDEs with rough coefficients. Zbl 1380.65268
Hou, Thomas Y.; Hwang, Feng-Nan; Liu, Pengfei; Yao, Chien-Chou
3
2017
Discrete maximum-norm stability of a linearized second-order finite difference scheme for Allen-Cahn equation. Zbl 1399.65211
Hou, T.; Wang, K.; Xiong, Y.; Xiao, X.; Zhang, Sh.
2
2017
Sparse time-frequency decomposition for multiple signals with same frequencies. Zbl 1378.94007
Hou, Thomas Y.; Shi, Zuoqiang
1
2017
Adaptive multiscale model reduction with generalized multiscale finite element methods. Zbl 1349.76191
Chung, Eric; Efendiev, Yalchin; Hou, Thomas Y.
67
2016
Optimal local multi-scale basis functions for linear elliptic equations with rough coefficients. Zbl 1333.65131
Hou, Thomas Y.; Liu, Pengfei
11
2016
Extracting a shape function for a signal with intra-wave frequency modulation. Zbl 1353.94017
Hou, Thomas Y.; Shi, Zuoqiang
5
2016
An accelerated method for nonlinear elliptic PDE. Zbl 1368.65004
Schaeffer, Hayden; Hou, Thomas Y.
4
2016
A model reduction method for elliptic PDEs with random input using the heterogeneous stochastic FEM framework. Zbl 1341.65004
Hou, Thomas Y.; Liu, Pengfei; Zhang, Zhiwen
3
2016
Sparse time-frequency decomposition based on dictionary adaptation. Zbl 1353.42016
Hou, Thomas Y.; Shi, Zuoqiang
1
2016
Adaptive data analysis: theory and applications. Theme issue. Zbl 1354.00073
1
2016
Self-similar singularity of a 1D model for the 3D axisymmetric Euler equations. Zbl 1320.35269
Hou, Thomas Y.; Liu, Pengfei
11
2015
A heterogeneous stochastic FEM framework for elliptic PDEs. Zbl 1352.65510
Hou, Thomas Y.; Liu, Pengfei
7
2015
Sparse + low-energy decomposition for viscous conservation laws. Zbl 1352.65413
Hou, Thomas Y.; Li, Qin; Schaeffer, Hayden
6
2015
Sparse time frequency representations and dynamical systems. Zbl 1346.37062
Hou, Thomas Y.; Shi, Zuoqiang; Tavallali, Peyman
3
2015
On the uniqueness of sparse time-frequency representation of multiscale data. Zbl 1357.94035
Liu, Chunguang; Shi, Zuoqiang; Hou, Thomas Y.
2
2015
Toward the finite-time blowup of the 3D axisymmetric Euler equations: a numerical investigation. Zbl 1316.35235
Luo, Guo; Hou, Thomas Y.
36
2014
On finite time singularity and global regularity of an axisymmetric model for the 3D Euler equations. Zbl 1293.35228
Hou, Thomas Y.; Lei, Zhen; Luo, Guo; Wang, Shu; Zou, Chen
10
2014
Potentially singular solutions of the 3D axisymmetric Euler equations. Zbl 1431.35115
Luo, Guo; Hou, Thomas Y.
10
2014
Convergence of a data-driven time-frequency analysis method. Zbl 1336.94020
Hou, Thomas Y.; Shi, Zuoqiang; Tavallali, Peyman
9
2014
Extraction of intrawave signals using the sparse time-frequency representation method. Zbl 1380.94062
Tavallali, Peyman; Hou, Thomas Y.; Shi, Zuoqiang
4
2014
An adaptive ANOVA-based data-driven stochastic method for elliptic PDEs with random coefficient. Zbl 1388.65178
Zhang, Zhiwen; Hu, Xin; Hou, Thomas Y.; Lin, Guang; Yan, Mike
4
2014
A multiscale model reduction method for partial differential equations. Zbl 1312.65206
Ci, Maolin; Hou, Thomas Y.; Shi, Zuoqiang
2
2014
Generalized multiscale finite element methods (GMsFEM). Zbl 1349.65617
Efendiev, Yalchin; Galvis, Juan; Hou, Thomas Y.
193
2013
A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations. I: Derivation and algorithms. Zbl 1297.65008
Cheng, Mulin; Hou, Thomas Y.; Zhang, Zhiwen
36
2013
A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations. II: Adaptivity and generalizations. Zbl 1297.65007
Cheng, Mulin; Hou, Thomas Y.; Zhang, Zhiwen
26
2013
Data-driven time-frequency analysis. Zbl 1336.94019
Hou, Thomas Y.; Shi, Zuoqiang
19
2013
A data-driven stochastic method for elliptic PDEs with random coefficients. Zbl 1290.60068
Cheng, Mulin; Hou, Thomas Y.; Yan, Mike; Zhang, Zhiwen
12
2013
Sparse time-frequency representation of nonlinear and nonstationary data. Zbl 1304.65282
Hou, Thomas Yizhao; Shi, Zuoqiang
3
2013
Multiscale modeling of incompressible turbulent flows. Zbl 1291.76241
Hou, T. Y.; Hu, X.; Hussain, F.
1
2013
On singularity formation of a 3D model for incompressible Navier-Stokes equations. Zbl 1252.35219
Hou, Thomas Y.; Shi, Zuoqiang; Wang, Shu
11
2012
Numerical analysis of multiscale problems. Selected papers based on the presentations at the 91st London Mathematical Society symposium, Durham, UK, July 5–15, 2010. Zbl 1234.65007
4
2012
Dynamic growth estimates of maximum vorticity for 3D incompressible Euler equations and the SQG model. Zbl 1237.76014
Hou, Thomas Y.; Shi, Zuoqiang
1
2012
Adaptive data analysis via sparse time-frequency representation. Zbl 1234.94015
Hou, Thomas Y.; Shi, Zuoqiang
17
2011
On singularity formation of a nonlinear nonlocal system. Zbl 1241.35038
Hou, Thomas Y.; Li, Congming; Shi, Zuoqiang; Wang, Shu; Yu, Xinwei
7
2011
A new multiscale finite element method for high-contrast elliptic interface problems. Zbl 1202.65154
Chu, C.-C.; Graham, I. G.; Hou, T.-Y.
81
2010
Multiscale finite element methods. Theory and applications. Zbl 1163.65080
Efendiev, Yalchin; Hou, Thomas Y.
270
2009
On the stabilizing effect of convection in three-dimensional incompressible flows. Zbl 1171.35095
Hou, Thomas Y.; Lei, Zhen
24
2009
Blow-up or no blow-up? A unified computational and analytic approach to 3D incompressible Euler and Navier-Stokes equations. Zbl 1422.76041
Hou, Thomas Y.
21
2009
On the partial regularity of a 3D model of the Navier-Stokes equations. Zbl 1176.35130
Hou, Thomas Y.; Lei, Zhen
11
2009
Stable fourth-order stream-function methods for incompressible flows with boundaries. Zbl 1212.65318
Hou, Thomas Y.; Wetton, Brian R.
4
2009
Multiscale analysis for convection-dominated transport equations. Zbl 1163.76048
Hou, Thomas Y.; Liang, Dong
3
2009
Dynamic stability of the three-dimensional axisymmetric Navier-Stokes equations with swirl. Zbl 1138.35077
Hou, Thomas Y.; Li, Congming
42
2008
Global regularity of the 3D axi-symmetric Navier-Stokes equations with anisotropic data. Zbl 1146.76010
Hou, Thomas Y.; Lei, Zhen; Li, Congming
27
2008
Blowup or no blowup? the interplay between theory and numerics. Zbl 1143.76390
Hou, Thomas Y.; Li, Ruo
22
2008
Multiscale finite element methods for stochastic porous media flow equations and application to uncertainty quantification. Zbl 1194.76112
Dostert, P.; Efendiev, Y.; Hou, T. Y.
21
2008
An efficient semi-implicit immersed boundary method for the Navier-Stokes equations. Zbl 1161.76048
Hou, Thomas Y.; Shi, Zuoqiang
20
2008
Removing the stiffness of elastic force from the immersed boundary method for the 2D Stokes equations. Zbl 1294.76201
Hou, Thomas Y.; Shi, Zuoqiang
13
2008
Multiscale analysis and computation for the three-dimensional incompressible Navier-Stokes equations. Zbl 1248.76037
Hou, Thomas Y.; Yang, Danping; Ran, Hongyu
4
2008
Multiscale simulations of porous media flows in flow-based coordinate system. Zbl 1155.76050
Efendiev, Yalchin R.; Hou, Thomas Yizhao; Strinopoulos, T.
3
2008
Computing nearly singular solutions using pseudo-spectral methods. Zbl 1310.76127
Hou, Thomas Y.; Li, Ruo
60
2007
Multiscale finite element methods for porous media flows and their applications. Zbl 1112.76046
Efendiev, Yalchin R.; Hou, Thomas Yizhao
33
2007
Nonexistence of locally self-similar blow-up for the 3D incompressible Navier-Stokes equations. Zbl 1194.35307
Hou, Thomas Y.; Li, Ruo
10
2007
Mathematical modeling and simulation of aquatic and aerial animal locomotion. Zbl 1343.76074
Hou, T. Y.; Stredie, V. G.; Wu, T. Y.
3
2007
Accurate multiscale finite element methods for two-phase flow simulations. Zbl 1158.76349
Efendiev, Y.; Ginting, V.; Hou, T.; Ewing, R.
83
2006
Wiener chaos expansions and numerical solutions of randomly forced equations of fluid mechanics. Zbl 1095.76047
Hou, Thomas Y.; Luo, Wuan; Rozovskii, Boris; Zhou, Hao-Min
64
2006
Dynamic depletion of vortex stretching and non-blowup of the 3-D incompressible Euler equations. Zbl 1370.76015
Hou, Thomas Y.; Li, Ruo
51
2006
Preconditioning Markov chain Monte Carlo simulations using coarse-scale models. Zbl 1111.65003
Efendiev, Yalchin R.; Hou, Thomas Yizhao; Luo, Wu An
45
2006
A mathematical framework of the bridging scale method. Zbl 1117.74056
Tang, Shaoqiang; Hou, Thomas Y.; Liu, Wing Kam
31
2006
Improved geometric conditions for non-blowup of the 3D incompressible Euler equation. Zbl 1158.76305
Deng, Jian; Hou, Thomas Y.; Yu, Xinwei
30
2006
A pseudo-spectral multiscale method: interfacial conditions and coarse grid equations. Zbl 1089.65110
Tang, Shaoqiang; Hou, Thomas Y.; Liu, Wing Kam
21
2006
Coarse-gradient Langevin algorithms for dynamic data integration and uncertainty quantification. Zbl 1146.76637
Dostert, P.; Efendiev, Y.; Hou, T. Y.; Luo, W.
17
2006
Level set dynamics and the non-blowup of the 2D quasi-geostrophic equation. Zbl 1173.76006
Deng, J.; Hou, T. Y.; Li, R.; Yu, X.
12
2006
On global well-posedness of the Lagrangian averaged Euler equations. Zbl 1111.76006
Hou, Thomas Y.; Li, Congming
8
2006
A 3D numerical method for studying vortex formation behind a moving plate. Zbl 1218.76034
Hou, T. Y.; Stredie, V. G.; Wu, T. Y.
4
2006
A framework for modeling subgrid effects for two-phase flows in porous media. Zbl 1127.76064
Hou, Thomas Y.; Westhead, Andrew; Yang, Danping
2
2006
Global well-posedness of the viscous Boussinesq equations. Zbl 1274.76185
Hou, Thomas Y.; Li, Congming
173
2005
Geometric properties and nonblowup of 3D incompressible Euler flow. Zbl 1142.35549
Deng, Jian; Hou, Thomas Y.; Yu, Xinwei
40
2005
Multiscale modelling and computation of fluid flow. Zbl 1134.76386
Hou, Thomas Y.
8
2005
A level set formulation for the 3D incompressible Euler equations. Zbl 1107.76011
Deng, Jian; Hou, Thomas Y.; Yu, Xinwei
2
2005
Multiscale finite element methods for nonlinear problems and their applications. Zbl 1083.65105
Efendiev, Yalchin R.; Hou, Thomas Yizhao; Ginting, Victor
67
2004
Removing the cell resonance error in the multiscale finite element method via a Petrov-Galerkin formulation. Zbl 1085.65109
Hou, Thomas Y.; Wu, Xiao-Hui; Zhang, Yu
47
2004
Multiscale numerical methods for singularly perturbed convection-diffusion equations. Zbl 1182.76902
Park, Peter J.; Hou, Thomas Y.
12
2004
Wiener chaos expansions and numerical solutions of randomly forced equations of fluid mechanics. Zbl 1130.76411
Hou, Thomas Y.; Kim, Hongjoong; Rozovskii, Boris; Zhou, Hao-Min
1
2004
Homogenization of incompressible Euler equations. Zbl 1104.76054
Hou, Thomas Y.; Yang, Danping; Wang, Ke
1
2004
Multiscale modelling and computation of incompressible flow. Zbl 1181.76096
Hou, Thomas Y.
1
2004
A mixed multiscale finite element method for elliptic problems with oscillating coefficients. Zbl 1017.65088
Chen, Zhiming; Hou, Thomas Y.
132
2003
Numerical approximations to multiscale solutions in partial differential equations. Zbl 1027.65154
Hou, Thomas Y.
6
2003
Wiener chaos expansions and numerical solutions of randomly forced equations of fluid mechanics. Zbl 1130.76410
Hou, Thomas Y.; Kim, Hongjoong; Rozovski, Boris; Zhou, Hao-Min
3
2003
A nearly optimal existence result for slightly perturbed 3-D vortex sheets. Zbl 1094.76014
Hou, Thomas Y.; Hu, Gang
3
2003
Analysis of upscaling absolute permeability. Zbl 1162.65327
Wu, X. H.; Efendiev, Y.; Hou, T. Y.
68
2002
Multiscale domain decomposition methods for elliptic problems with high aspect ratios. Zbl 1003.65142
Aarnes, Jørg; Hou, Thomas Y.
32
2002
Convergence of a boundary integral method for 3-D water waves. Zbl 1131.76339
Hou, Thomas Y.; Zhang, Pingwen
12
2002
Singularity formation in three-dimensional vortex sheets. Zbl 1185.76172
Hou, Thomas Y.; Hu, Gang; Zhang, Pingwen
4
2002
Boundary integral methods for multicomponent fluids and multiphase materials. Zbl 1046.76029
Hou, T. Y.; Lowengrub, J. S.; Shelley, M. J.
62
2001
An efficient dynamically adaptive mesh for potentially singular solutions. Zbl 0986.65087
Ceniceros, Hector D.; Hou, Thomas Y.
56
2001
Numerical study of interfacial problems with small surface tension. Zbl 1288.76050
Ceniceros, Hector D.; Hou, Thomas Y.
3
2001
Convergence of a nonconforming multiscale finite element method. Zbl 0951.65105
Efendiev, Yalchin R.; Hou, Thomas Y.; Wu, Xiao-Hui
102
2000
The singular perturbation of surface tension in Hele-Shaw flows. Zbl 0991.76020
Ceniceros, Hector D.; Hou, Thomas Y.
9
2000
...and 48 more Documents
all top 5

Cited by 3,403 Authors

81 Chung, Tsz Shun Eric
73 Hou, Thomas Yizhao
60 Efendiev, Yalchin R.
31 Vasilyeva, Maria V.
29 Wu, Jiahong
27 Cui, Junzhi
26 Leung, Wingtat
22 Lowengrub, John Samuel
21 Chae, Dongho
20 Galvis, Juan
20 Hajibeygi, Hadi
19 Abdulle, Assyr
19 Li, Zhilin
18 Fu, Shubin
18 Gancedo, Francisco
18 Jiang, Lijian
17 Cordoba, Diego
16 Jenny, Patrick
15 Ceniceros, Hector D.
15 Shelley, Michael J.
15 Valentin, Frédéric
14 Osher, Stanley Joel
14 Tchelepi, Hamdi A.
14 Xu, Xiaojing
14 Zhang, Zhiwen
13 Cao, Liqun
13 Peterseim, Daniel
12 Ambrose, David M.
12 Li, Qin
12 Målqvist, Axel
12 Presho, Michael
12 Shi, Zuoqiang
12 Wheeler, Mary Fanett
11 Li, Shuwang
11 Ohlberger, Mario
11 Yang, Zhiqiang
11 Ye, Zhuan
10 Babuška, Ivo
10 Hoang, Viet Ha
10 Kim, Junseok
10 LeFloch, Philippe Gerard
10 Lin, Tao
10 Tang, Shaoqiang
10 Zabaras, Nicholas J.
9 Brown, Donald L.
9 Calo, Victor Manuel
9 Cao, Chongsheng
9 Cheung, Siu Wun
9 Ginting, Victor
9 Henning, Patrick
9 Lei, Zhen
9 Li, Guanglian
9 Lie, Knut-Andreas
9 Liu, Jianguo
9 Ma, Qiang
9 Nie, Qing
9 Owhadi, Houman
9 Pun, Saimang
9 Wei, Guowei
9 Zhao, Hongkai
8 Castro, Ángel
8 Chen, Jinru
8 Constantin, Peter
8 Dong, Hao
8 Fedkiw, Ronald P.
8 He, Wenming
8 Jabin, Pierre-Emmanuel
8 Kukavica, Igor
8 Le Bris, Claude
8 Li, Ruo
8 Lu, Jianfeng
8 Reusken, Arnold
8 Zhang, Pingwen
7 Beale, J. Thomas
7 Cottet, Georges-Henri
7 Deng, Weibing
7 Du, Qiang
7 Gómez-Serrano, Javier
7 Heinlein, Alexander
7 Karniadakis, George Em
7 Kiselev, Alexander A.
7 Legoll, Frédéric
7 Lin, Ping
7 Liu, Chun
7 Liu, Wing Kam
7 Madureira, Alexandre L.
7 Protas, Bartosz
7 Sarkis, Marcus V.
7 Schaeffer, Hayden
7 Scheichl, Robert
7 Sethian, James A.
7 Shu, Chi-Wang
7 Sun, Yi
7 Tang, Huazhong
7 Titi, Edriss Saleh
7 Wang, Shu
7 Wang, Yating
7 Yotov, Ivan
7 Zhao, Kun
6 Abreu, Eduardo
...and 3,303 more Authors
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Cited in 260 Serials

466 Journal of Computational Physics
138 Computer Methods in Applied Mechanics and Engineering
131 Journal of Computational and Applied Mathematics
77 Journal of Fluid Mechanics
70 Multiscale Modeling & Simulation
61 Journal of Scientific Computing
59 Computers and Fluids
57 Computational Geosciences
53 Physics of Fluids
46 Journal of Differential Equations
44 SIAM Journal on Scientific Computing
43 Computers & Mathematics with Applications
38 International Journal for Numerical Methods in Engineering
35 Physica D
35 Applied Numerical Mathematics
34 Archive for Rational Mechanics and Analysis
33 Applied Mathematics and Computation
30 Computational Mechanics
29 Mathematics of Computation
27 Numerische Mathematik
26 Communications in Mathematical Physics
26 Journal of Mathematical Analysis and Applications
23 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
23 SIAM Journal on Numerical Analysis
23 Communications in Computational Physics
21 Journal of Nonlinear Science
20 Applied Mathematical Modelling
20 Advances in Computational Mathematics
19 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
19 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
18 Discrete and Continuous Dynamical Systems
16 International Journal for Numerical Methods in Fluids
14 Engineering Analysis with Boundary Elements
13 Mathematics and Computers in Simulation
13 Journal of Mathematical Fluid Mechanics
12 Journal of Mathematical Physics
12 Advances in Mathematics
12 Communications in Partial Differential Equations
12 SIAM/ASA Journal on Uncertainty Quantification
11 Applicable Analysis
10 Journal of Statistical Physics
10 ZAMP. Zeitschrift für angewandte Mathematik und Physik
10 Numerical Methods for Partial Differential Equations
10 Discrete and Continuous Dynamical Systems. Series S
10 GEM - International Journal on Geomathematics
9 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
9 Applied and Computational Harmonic Analysis
9 Mathematical Problems in Engineering
8 Applied Mathematics Letters
8 Numerical Algorithms
8 SIAM Journal on Mathematical Analysis
7 Mathematical Methods in the Applied Sciences
7 BIT
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7 Chinese Annals of Mathematics. Series B
7 SIAM Review
7 Archives of Computational Methods in Engineering
7 Comptes Rendus. Mathématique. Académie des Sciences, Paris
7 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
6 Journal of Engineering Mathematics
6 Nonlinearity
6 Computing and Visualization in Science
6 Chaos
6 International Journal of Computational Methods
6 Acta Mechanica Sinica
6 Science China. Mathematics
5 Computer Physics Communications
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5 Journal of the American Mathematical Society
5 Journal de Mathématiques Pures et Appliquées. Neuvième Série
5 Proceedings of the National Academy of Sciences of the United States of America
5 Computational and Applied Mathematics
5 Annals of Mathematics. Second Series
5 Nonlinear Analysis. Real World Applications
5 Discrete and Continuous Dynamical Systems. Series B
5 Boundary Value Problems
5 Research in the Mathematical Sciences
5 Annals of PDE
4 Wave Motion
4 Bulletin of Mathematical Biology
4 Applied Mathematics and Optimization
4 Inventiones Mathematicae
4 Quarterly of Applied Mathematics
4 European Journal of Applied Mathematics
4 International Journal of Computer Mathematics
4 SIAM Journal on Applied Mathematics
4 Calculus of Variations and Partial Differential Equations
4 Numerical Linear Algebra with Applications
4 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings
4 Abstract and Applied Analysis
4 European Journal of Mechanics. A. Solids
4 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics
4 Communications in Nonlinear Science and Numerical Simulation
4 Computational Methods in Applied Mathematics
4 Sādhanā
4 Journal of Numerical Mathematics
4 Communications on Pure and Applied Analysis
4 Acta Numerica
4 Mathematical Geosciences
...and 160 more Serials
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Cited in 45 Fields

1,339 Fluid mechanics (76-XX)
1,199 Numerical analysis (65-XX)
1,075 Partial differential equations (35-XX)
336 Mechanics of deformable solids (74-XX)
100 Geophysics (86-XX)
99 Probability theory and stochastic processes (60-XX)
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44 Dynamical systems and ergodic theory (37-XX)
36 Optics, electromagnetic theory (78-XX)
33 Calculus of variations and optimal control; optimization (49-XX)
31 Information and communication theory, circuits (94-XX)
28 Harmonic analysis on Euclidean spaces (42-XX)
26 Ordinary differential equations (34-XX)
26 Computer science (68-XX)
15 Linear and multilinear algebra; matrix theory (15-XX)
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7 Quantum theory (81-XX)
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