## Hou, Thomas Yizhao

Compute Distance To:
 Author ID: hou.thomas-yizhao Published as: Hou, Thomas Y.; Hou, T. Y.; Hou, Thomas Yizhao; Hou, Thomas; Hou, Th. Y.; Hou, T.-Y.; Hou, T. more...less Homepage: http://users.cms.caltech.edu/~hou/ External Links: MGP · Wikidata · dblp · GND · IdRef
 Documents Indexed: 169 Publications since 1988, including 1 Book 8 Contributions as Editor Biographic References: 1 Publication Co-Authors: 114 Co-Authors with 164 Joint Publications 5,339 Co-Co-Authors
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 Huang, De 4 Lei, Zhen 4 Wang, Shu 4 Zhou, Hao-Min 3 Chen, Yifan 3 Cheng, Mulin 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 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 Zhang, Ziyun 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, Zhenzhen 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. ...and 14 more Co-Authors
all top 5

### Serials

 26 Journal of Computational Physics 14 Multiscale Modeling & Simulation 13 Communications on Pure and Applied Mathematics 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 Physica D 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 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 1 SIAM Journal on Mathematics of Data Science
all top 5

### Fields

 111 Fluid mechanics (76-XX) 92 Partial differential equations (35-XX) 86 Numerical analysis (65-XX) 13 Information and communication theory, circuits (94-XX) 10 Mechanics of deformable solids (74-XX) 8 General and overarching topics; collections (00-XX) 8 Probability theory and stochastic processes (60-XX) 6 Statistics (62-XX) 4 Classical thermodynamics, heat transfer (80-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Computer science (68-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Biology and other natural sciences (92-XX) 1 History and biography (01-XX) 1 Potential theory (31-XX) 1 Approximations and expansions (41-XX) 1 Integral equations (45-XX) 1 Operator theory (47-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Mechanics of particles and systems (70-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Operations research, mathematical programming (90-XX)

### Citations contained in zbMATH Open

151 Publications have been cited 4,617 times in 2,657 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
1997
Multiscale finite element methods. Theory and applications. Zbl 1163.65080
Efendiev, Yalchin; Hou, Thomas Y.
2009
Generalized multiscale finite element methods (GMsFEM). Zbl 1349.65617
Efendiev, Yalchin; Galvis, Juan; Hou, Thomas Y.
2013
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.
1996
Removing the stiffness from interfacial flows with surface tension. Zbl 0810.76095
Hou, Thomas Y.; Lowengrub, John S.; Shelley, Michael J.
1994
Global well-posedness of the viscous Boussinesq equations. Zbl 1274.76185
Hou, Thomas Y.; Li, Congming
2005
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
1999
A mixed multiscale finite element method for elliptic problems with oscillating coefficients. Zbl 1017.65088
Chen, Zhiming; Hou, Thomas Y.
2003
Convergence of a nonconforming multiscale finite element method. Zbl 0951.65105
Efendiev, Yalchin R.; Hou, Thomas Y.; Wu, Xiao-Hui
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
1997
Why nonconservative schemes converge to wrong solutions: Error analysis. Zbl 0809.65102
Hou, Thomas Y.; Le Floch, Philippe G.
1994
A new multiscale finite element method for high-contrast elliptic interface problems. Zbl 1202.65154
Chu, C.-C.; Graham, I. G.; Hou, T.-Y.
2010
Accurate multiscale finite element methods for two-phase flow simulations. Zbl 1158.76349
Efendiev, Y.; Ginting, V.; Hou, T.; Ewing, R.
2006
Adaptive multiscale model reduction with generalized multiscale finite element methods. Zbl 1349.76191
Chung, Eric; Efendiev, Yalchin; Hou, Thomas Y.
2016
Analysis of upscaling absolute permeability. Zbl 1162.65327
Wu, X. H.; Efendiev, Y.; Hou, T. Y.
2002
Computing nearly singular solutions using pseudo-spectral methods. Zbl 1310.76127
Hou, Thomas Y.; Li, Ruo
2007
Multiscale finite element methods for nonlinear problems and their applications. Zbl 1083.65105
Efendiev, Yalchin R.; Hou, Thomas Yizhao; Ginting, Victor
2004
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
2006
Boundary integral methods for multicomponent fluids and multiphase materials. Zbl 1046.76029
Hou, T. Y.; Lowengrub, J. S.; Shelley, M. J.
2001
The long-time motion of vortex sheets with surface tension. Zbl 1185.76545
Hou, T. Y.; Lowengrub, J. S.; Shelly, M. J.
1997
Growth rates for the linearized motion of fluid interfaces away from equilibrium. Zbl 0796.76041
Beale, J. Thomas; Hou, Thomas Y.; Lowengrub, John S.
1993
An efficient dynamically adaptive mesh for potentially singular solutions. Zbl 0986.65087
Ceniceros, Hector D.; Hou, Thomas Y.
2001
Dynamic depletion of vortex stretching and non-blowup of the 3-D incompressible Euler equations. Zbl 1370.76015
Hou, Thomas Y.; Li, Ruo
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
2004
Preconditioning Markov chain Monte Carlo simulations using coarse-scale models. Zbl 1111.65003
Efendiev, Yalchin R.; Hou, Thomas Yizhao; Luo, Wu An
2006
Convergence of the point vortex method for the 2-D Euler equations. Zbl 0694.76013
Goodman, Jonathan; Hou, Thomas Y.; Lowengrub, John
1990
Dynamic stability of the three-dimensional axisymmetric Navier-Stokes equations with swirl. Zbl 1138.35077
Hou, Thomas Y.; Li, Congming
2008
Geometric properties and nonblowup of 3D incompressible Euler flow. Zbl 1142.35549
Deng, Jian; Hou, Thomas Y.; Yu, Xinwei
2005
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
2013
Toward the finite-time blowup of the 3D axisymmetric Euler equations: a numerical investigation. Zbl 1316.35235
Luo, Guo; Hou, Thomas Y.
2014
Multiscale domain decomposition methods for elliptic problems with high aspect ratios. Zbl 1003.65142
Aarnes, Jørg; Hou, Thomas Y.
2002
Multiscale finite element methods for porous media flows and their applications. Zbl 1112.76046
Efendiev, Yalchin R.; Hou, Thomas Yizhao
2007
A mathematical framework of the bridging scale method. Zbl 1117.74056
Tang, Shaoqiang; Hou, Thomas Y.; Liu, Wing Kam
2006
Convergence of a boundary integral method for water waves. Zbl 0858.76046
Beale, J. Thomas; Hou, Thomas Y.; Lowengrub, John
1996
Improved geometric conditions for non-blowup of the 3D incompressible Euler equation. Zbl 1158.76305
Deng, Jian; Hou, Thomas Y.; Yu, Xinwei
2006
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
2017
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
2013
Global regularity of the 3D axi-symmetric Navier-Stokes equations with anisotropic data. Zbl 1146.76010
Hou, Thomas Y.; Lei, Zhen; Li, Congming
2008
On the stabilizing effect of convection in three-dimensional incompressible flows. Zbl 1171.35095
Hou, Thomas Y.; Lei, Zhen
2009
Blowup or no blowup? the interplay between theory and numerics. Zbl 1143.76390
Hou, Thomas Y.; Li, Ruo
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.
2008
Dispersive approximations in fluid dynamics. Zbl 0729.76065
Hou, Thomas Y.; Lax, Peter D.
1991
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.
2009
A pseudo-spectral multiscale method: interfacial conditions and coarse grid equations. Zbl 1089.65110
Tang, Shaoqiang; Hou, Thomas Y.; Liu, Wing Kam
2006
Data-driven time-frequency analysis. Zbl 1336.94019
Hou, Thomas Y.; Shi, Zuoqiang
2013
An efficient semi-implicit immersed boundary method for the Navier-Stokes equations. Zbl 1161.76048
Hou, Thomas Y.; Shi, Zuoqiang
2008
Adaptive data analysis via sparse time-frequency representation. Zbl 1234.94015
Hou, Thomas Y.; Shi, Zuoqiang
2011
Homogenization of linear transport equations with oscillatory vector fields. Zbl 0759.35008
Hou, Thomas Y.; Xin, Xue
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
1993
Coarse-gradient Langevin algorithms for dynamic data integration and uncertainty quantification. Zbl 1146.76637
Dostert, P.; Efendiev, Y.; Hou, T. Y.; Luo, W.
2006
Numerical study of Hele-Shaw flow with suction. Zbl 1149.76335
Ceniceros, Hector D.; Hou, Thomas Y.; Si, Helen
1999
Removing the stiffness of curvature in computing 3-D filaments. Zbl 0917.76063
Hou, Thomas Y.; Klapper, Isaac; Si, Helen
1998
Computational method for propagating phase boundaries. Zbl 0855.73080
Zhong, Xiaoguang; Hou, Thomas Y.; LeFloch, Philippe G.
1996
Convergence of a non-stiff boundary integral method for interfacial flows with surface tension. Zbl 0905.76012
Ceniceros, Héctor D.; Hou, Thomas Y.
1998
A data-driven stochastic method for elliptic PDEs with random coefficients. Zbl 1290.60068
Cheng, Mulin; Hou, Thomas Y.; Yan, Mike; Zhang, Zhiwen
2013
Removing the stiffness of elastic force from the immersed boundary method for the 2D Stokes equations. Zbl 1294.76201
Hou, Thomas Y.; Shi, Zuoqiang
2008
Potentially singular solutions of the 3D axisymmetric Euler equations. Zbl 1431.35115
Luo, Guo; Hou, Thomas Y.
2014
Optimal local multi-scale basis functions for linear elliptic equations with rough coefficients. Zbl 1333.65131
Hou, Thomas Y.; Liu, Pengfei
2016
Geometry related convergence results for domain decomposition algorithms. Zbl 0724.65109
Chan, Tony F.; Hou, Thomas Y.; Lions, P. L.
1991
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.
1993
Self-similar singularity of a 1D model for the 3D axisymmetric Euler equations. Zbl 1320.35269
Hou, Thomas Y.; Liu, Pengfei
2015
Convergence of a boundary integral method for 3-D water waves. Zbl 1131.76339
Hou, Thomas Y.; Zhang, Pingwen
2002
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.
1992
Multiscale numerical methods for singularly perturbed convection-diffusion equations. Zbl 1182.76902
Park, Peter J.; Hou, Thomas Y.
2004
Convergence of a variable blob vortex method for the Euler and Navier- Stokes equations. Zbl 0727.76034
Hou, Thomas Y.
1990
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.
2006
Sparse operator compression of higher-order elliptic operators with rough coefficients. Zbl 1412.65215
Hou, Thomas Y.; Zhang, Pengchuan
2017
Convergence of the point vortex method for the 3-D Euler equations. Zbl 0856.76059
Hou, Thomas Y.; Lowengrub, John
1990
On the stability of the unsmoothed Fourier method for hyperbolic equations. Zbl 0791.65080
Goodman, Jonathan; Hou, Thomas; Tadmor, Eitan
1994
On the partial regularity of a 3D model of the Navier-Stokes equations. Zbl 1176.35130
Hou, Thomas Y.; Lei, Zhen
2009
On singularity formation of a 3D model for incompressible Navier-Stokes equations. Zbl 1252.35219
Hou, Thomas Y.; Shi, Zuoqiang; Wang, Shu
2012
Nonexistence of locally self-similar blow-up for the 3D incompressible Navier-Stokes equations. Zbl 1194.35307
Hou, Thomas Y.; Li, Ruo
2007
Dynamic generation of capillary waves. Zbl 1147.76354
Ceniceros, Hector D.; Hou, Thomas Y.
1999
A level-set approach to the computation of twinning and phase-transition dynamics. Zbl 0936.74052
Hou, Thomas Y.; Rosakis, Phoebus; LeFloch, Philippe
1999
Numerical solutions to free boundary problems. Zbl 0831.65137
Hou, Thomas Y.
1995
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
2014
The singular perturbation of surface tension in Hele-Shaw flows. Zbl 0991.76020
Ceniceros, Hector D.; Hou, Thomas Y.
2000
Convergence of a data-driven time-frequency analysis method. Zbl 1336.94020
Hou, Thomas Y.; Shi, Zuoqiang; Tavallali, Peyman
2014
Well-posedness of linearized motion for 3-D water waves far from equilibrium. Zbl 0874.76014
Hou, Thomas Y.; Teng, Zhenhuan; Zhang, Pingwen
1996
Multiscale modelling and computation of fluid flow. Zbl 1134.76386
Hou, Thomas Y.
2005
On global well-posedness of the Lagrangian averaged Euler equations. Zbl 1111.76006
Hou, Thomas Y.; Li, Congming
2006
Exploring the locally low dimensional structure in solving random elliptic PDEs. Zbl 1365.65015
Hou, Thomas Y.; Li, Qin; Zhang, Pengchuan
2017
An efficient boundary integral method for the Mullins-Sekerka problem. Zbl 0879.65092
Zhu, Jingyi; Chen, Xinfu; Hou, Thomas Y.
1996
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.
1994
Particle method approximation of oscillatory solutions to hyperbolic differential equations. Zbl 0675.65093
Engquist, Bjorn; Hou, Thomas Y.
1989
Convergence of a point vortex method for vortex sheets. Zbl 0799.76062
Hou, Thomas Y.; Lowengrub, John; Krasny, Robert
1991
New stability estimates for the 2-D vortex method. Zbl 0745.76061
Goodman, Jonathan; Hou, Thomas Y.
1991
On singularity formation of a nonlinear nonlocal system. Zbl 1241.35038
Hou, Thomas Y.; Li, Congming; Shi, Zuoqiang; Wang, Shu; Yu, Xinwei
2011
A heterogeneous stochastic FEM framework for elliptic PDEs. Zbl 1352.65510
Hou, Thomas Y.; Liu, Pengfei
2015
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
2019
Numerical approximations to multiscale solutions in partial differential equations. Zbl 1027.65154
Hou, Thomas Y.
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.
1991
Sparse + low-energy decomposition for viscous conservation laws. Zbl 1352.65413
Hou, Thomas Y.; Li, Qin; Schaeffer, Hayden
2015
Extracting a shape function for a signal with intra-wave frequency modulation. Zbl 1353.94017
Hou, Thomas Y.; Shi, Zuoqiang
2016
An accelerated method for nonlinear elliptic PDE. Zbl 1368.65004
Schaeffer, Hayden; Hou, Thomas Y.
2016
Finite difference approximations for partial differential equations with rapidly oscillating coefficients. Zbl 0755.65088
Avellaneda, M.; Hou, Th. Y.; Papanicolaou, G. C.
1991
A Lagrangian finite element method for the 2-D Euler equations. Zbl 0705.76059
Chacon-Rebollo, Tomas; Hou, Thomas Y.
1990
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
2012
Finite time blowup of 2D Boussinesq and 3D Euler equations with $$C^{1, \alpha}$$ velocity and boundary. Zbl 1485.35071
Chen, Jiajie; Hou, Thomas Yizhao
2021
Stable fourth-order stream-function methods for incompressible flows with boundaries. Zbl 1212.65318
Hou, Thomas Y.; Wetton, Brian R.
2009
Finite time blowup of 2D Boussinesq and 3D Euler equations with $$C^{1, \alpha}$$ velocity and boundary. Zbl 1485.35071
Chen, Jiajie; Hou, Thomas Yizhao
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
2021
Exponential convergence for multiscale linear elliptic PDEs via adaptive edge basis functions. Zbl 1473.65296
Chen, Yifan; Hou, Thomas Y.; Wang, Yixuan
2021
Function approximation via the subsampled Poincaré inequality. Zbl 1458.35008
Chen, Yifan; Hou, Thomas Y.
2021
A prototype knockoff filter for group selection with FDR control. Zbl 1471.62409
Chen, Jiajie; Hou, Anthony; Hou, Thomas Y.
2020
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
2019
Formation of finite-time singularities in the 3D axisymmetric Euler equations: a numerics guided study. Zbl 1427.35190
Luo, Guo; Hou, Thomas Y.
2019
A fast hierarchically preconditioned eigensolver based on multiresolution matrix decomposition. Zbl 1455.65053
Hou, Thomas Y.; Huang, De; Lam, Ka Chun; Zhang, Ziyun
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
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
2018
Potential singularity for a family of models of the axisymmetric incompressible flow. Zbl 1405.35150
Hou, Thomas Y.; Jin, Tianling; Liu, Pengfei
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
2017
Sparse operator compression of higher-order elliptic operators with rough coefficients. Zbl 1412.65215
Hou, Thomas Y.; Zhang, Pengchuan
2017
Exploring the locally low dimensional structure in solving random elliptic PDEs. Zbl 1365.65015
Hou, Thomas Y.; Li, Qin; Zhang, Pengchuan
2017
A sparse decomposition of low rank symmetric positive semidefinite matrices. Zbl 1386.65127
Hou, Thomas Y.; Li, Qin; Zhang, Pengchuan
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.
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
2017
Sparse time-frequency decomposition for multiple signals with same frequencies. Zbl 1378.94007
Hou, Thomas Y.; Shi, Zuoqiang
2017
Adaptive multiscale model reduction with generalized multiscale finite element methods. Zbl 1349.76191
Chung, Eric; Efendiev, Yalchin; Hou, Thomas Y.
2016
Optimal local multi-scale basis functions for linear elliptic equations with rough coefficients. Zbl 1333.65131
Hou, Thomas Y.; Liu, Pengfei
2016
Extracting a shape function for a signal with intra-wave frequency modulation. Zbl 1353.94017
Hou, Thomas Y.; Shi, Zuoqiang
2016
An accelerated method for nonlinear elliptic PDE. Zbl 1368.65004
Schaeffer, Hayden; Hou, Thomas Y.
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
2016
Sparse time-frequency decomposition based on dictionary adaptation. Zbl 1353.42016
Hou, Thomas Y.; Shi, Zuoqiang
2016
Adaptive data analysis: theory and applications. Theme issue. Zbl 1354.00073
2016
Self-similar singularity of a 1D model for the 3D axisymmetric Euler equations. Zbl 1320.35269
Hou, Thomas Y.; Liu, Pengfei
2015
A heterogeneous stochastic FEM framework for elliptic PDEs. Zbl 1352.65510
Hou, Thomas Y.; Liu, Pengfei
2015
Sparse + low-energy decomposition for viscous conservation laws. Zbl 1352.65413
Hou, Thomas Y.; Li, Qin; Schaeffer, Hayden
2015
Sparse time frequency representations and dynamical systems. Zbl 1346.37062
Hou, Thomas Y.; Shi, Zuoqiang; Tavallali, Peyman
2015
On the uniqueness of sparse time-frequency representation of multiscale data. Zbl 1357.94035
Liu, Chunguang; Shi, Zuoqiang; Hou, Thomas Y.
2015
Toward the finite-time blowup of the 3D axisymmetric Euler equations: a numerical investigation. Zbl 1316.35235
Luo, Guo; Hou, Thomas Y.
2014
Potentially singular solutions of the 3D axisymmetric Euler equations. Zbl 1431.35115
Luo, Guo; Hou, Thomas Y.
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
2014
Convergence of a data-driven time-frequency analysis method. Zbl 1336.94020
Hou, Thomas Y.; Shi, Zuoqiang; Tavallali, Peyman
2014
Extraction of intrawave signals using the sparse time-frequency representation method. Zbl 1380.94062
Tavallali, Peyman; Hou, Thomas Y.; Shi, Zuoqiang
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
2014
A multiscale model reduction method for partial differential equations. Zbl 1312.65206
Ci, Maolin; Hou, Thomas Y.; Shi, Zuoqiang
2014
Generalized multiscale finite element methods (GMsFEM). Zbl 1349.65617
Efendiev, Yalchin; Galvis, Juan; Hou, Thomas Y.
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
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
2013
Data-driven time-frequency analysis. Zbl 1336.94019
Hou, Thomas Y.; Shi, Zuoqiang
2013
A data-driven stochastic method for elliptic PDEs with random coefficients. Zbl 1290.60068
Cheng, Mulin; Hou, Thomas Y.; Yan, Mike; Zhang, Zhiwen
2013
Sparse time-frequency representation of nonlinear and nonstationary data. Zbl 1304.65282
Hou, Thomas Yizhao; Shi, Zuoqiang
2013
Multiscale modeling of incompressible turbulent flows. Zbl 1291.76241
Hou, T. Y.; Hu, X.; Hussain, F.
2013
On singularity formation of a 3D model for incompressible Navier-Stokes equations. Zbl 1252.35219
Hou, Thomas Y.; Shi, Zuoqiang; Wang, Shu
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
2012
Dynamic growth estimates of maximum vorticity for 3D incompressible Euler equations and the SQG model. Zbl 1237.76014
Hou, Thomas Y.; Shi, Zuoqiang
2012
Adaptive data analysis via sparse time-frequency representation. Zbl 1234.94015
Hou, Thomas Y.; Shi, Zuoqiang
2011
On singularity formation of a nonlinear nonlocal system. Zbl 1241.35038
Hou, Thomas Y.; Li, Congming; Shi, Zuoqiang; Wang, Shu; Yu, Xinwei
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.
2010
Multiscale finite element methods. Theory and applications. Zbl 1163.65080
Efendiev, Yalchin; Hou, Thomas Y.
2009
On the stabilizing effect of convection in three-dimensional incompressible flows. Zbl 1171.35095
Hou, Thomas Y.; Lei, Zhen
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.
2009
On the partial regularity of a 3D model of the Navier-Stokes equations. Zbl 1176.35130
Hou, Thomas Y.; Lei, Zhen
2009
Stable fourth-order stream-function methods for incompressible flows with boundaries. Zbl 1212.65318
Hou, Thomas Y.; Wetton, Brian R.
2009
Multiscale analysis for convection-dominated transport equations. Zbl 1163.76048
Hou, Thomas Y.; Liang, Dong
2009
Dynamic stability of the three-dimensional axisymmetric Navier-Stokes equations with swirl. Zbl 1138.35077
Hou, Thomas Y.; Li, Congming
2008
Global regularity of the 3D axi-symmetric Navier-Stokes equations with anisotropic data. Zbl 1146.76010
Hou, Thomas Y.; Lei, Zhen; Li, Congming
2008
Blowup or no blowup? the interplay between theory and numerics. Zbl 1143.76390
Hou, Thomas Y.; Li, Ruo
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.
2008
An efficient semi-implicit immersed boundary method for the Navier-Stokes equations. Zbl 1161.76048
Hou, Thomas Y.; Shi, Zuoqiang
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
2008
Multiscale analysis and computation for the three-dimensional incompressible Navier-Stokes equations. Zbl 1248.76037
Hou, Thomas Y.; Yang, Danping; Ran, Hongyu
2008
Multiscale simulations of porous media flows in flow-based coordinate system. Zbl 1155.76050
Efendiev, Yalchin R.; Hou, Thomas Yizhao; Strinopoulos, T.
2008
Computing nearly singular solutions using pseudo-spectral methods. Zbl 1310.76127
Hou, Thomas Y.; Li, Ruo
2007
Multiscale finite element methods for porous media flows and their applications. Zbl 1112.76046
Efendiev, Yalchin R.; Hou, Thomas Yizhao
2007
Nonexistence of locally self-similar blow-up for the 3D incompressible Navier-Stokes equations. Zbl 1194.35307
Hou, Thomas Y.; Li, Ruo
2007
Mathematical modeling and simulation of aquatic and aerial animal locomotion. Zbl 1343.76074
Hou, T. Y.; Stredie, V. G.; Wu, T. Y.
2007
Accurate multiscale finite element methods for two-phase flow simulations. Zbl 1158.76349
Efendiev, Y.; Ginting, V.; Hou, T.; Ewing, R.
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
2006
Dynamic depletion of vortex stretching and non-blowup of the 3-D incompressible Euler equations. Zbl 1370.76015
Hou, Thomas Y.; Li, Ruo
2006
Preconditioning Markov chain Monte Carlo simulations using coarse-scale models. Zbl 1111.65003
Efendiev, Yalchin R.; Hou, Thomas Yizhao; Luo, Wu An
2006
A mathematical framework of the bridging scale method. Zbl 1117.74056
Tang, Shaoqiang; Hou, Thomas Y.; Liu, Wing Kam
2006
Improved geometric conditions for non-blowup of the 3D incompressible Euler equation. Zbl 1158.76305
Deng, Jian; Hou, Thomas Y.; Yu, Xinwei
2006
A pseudo-spectral multiscale method: interfacial conditions and coarse grid equations. Zbl 1089.65110
Tang, Shaoqiang; Hou, Thomas Y.; Liu, Wing Kam
2006
Coarse-gradient Langevin algorithms for dynamic data integration and uncertainty quantification. Zbl 1146.76637
Dostert, P.; Efendiev, Y.; Hou, T. Y.; Luo, W.
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.
2006
On global well-posedness of the Lagrangian averaged Euler equations. Zbl 1111.76006
Hou, Thomas Y.; Li, Congming
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.
2006
A framework for modeling subgrid effects for two-phase flows in porous media. Zbl 1127.76064
Hou, Thomas Y.; Westhead, Andrew; Yang, Danping
2006
Global well-posedness of the viscous Boussinesq equations. Zbl 1274.76185
Hou, Thomas Y.; Li, Congming
2005
Geometric properties and nonblowup of 3D incompressible Euler flow. Zbl 1142.35549
Deng, Jian; Hou, Thomas Y.; Yu, Xinwei
2005
Multiscale modelling and computation of fluid flow. Zbl 1134.76386
Hou, Thomas Y.
2005
A level set formulation for the 3D incompressible Euler equations. Zbl 1107.76011
Deng, Jian; Hou, Thomas Y.; Yu, Xinwei
2005
Multiscale finite element methods for nonlinear problems and their applications. Zbl 1083.65105
Efendiev, Yalchin R.; Hou, Thomas Yizhao; Ginting, Victor
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
2004
Multiscale numerical methods for singularly perturbed convection-diffusion equations. Zbl 1182.76902
Park, Peter J.; Hou, Thomas Y.
2004
Homogenization of incompressible Euler equations. Zbl 1104.76054
Hou, Thomas Y.; Yang, Danping; Wang, Ke
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
2004
Multiscale modelling and computation of incompressible flow. Zbl 1181.76096
Hou, Thomas Y.
2004
A mixed multiscale finite element method for elliptic problems with oscillating coefficients. Zbl 1017.65088
Chen, Zhiming; Hou, Thomas Y.
2003
Numerical approximations to multiscale solutions in partial differential equations. Zbl 1027.65154
Hou, Thomas Y.
2003
A nearly optimal existence result for slightly perturbed 3-D vortex sheets. Zbl 1094.76014
Hou, Thomas Y.; Hu, Gang
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
2003
Analysis of upscaling absolute permeability. Zbl 1162.65327
Wu, X. H.; Efendiev, Y.; Hou, T. Y.
2002
Multiscale domain decomposition methods for elliptic problems with high aspect ratios. Zbl 1003.65142
Aarnes, Jørg; Hou, Thomas Y.
2002
Convergence of a boundary integral method for 3-D water waves. Zbl 1131.76339
Hou, Thomas Y.; Zhang, Pingwen
2002
Singularity formation in three-dimensional vortex sheets. Zbl 1185.76172
Hou, Thomas Y.; Hu, Gang; Zhang, Pingwen
2002
Boundary integral methods for multicomponent fluids and multiphase materials. Zbl 1046.76029
Hou, T. Y.; Lowengrub, J. S.; Shelley, M. J.
2001
An efficient dynamically adaptive mesh for potentially singular solutions. Zbl 0986.65087
Ceniceros, Hector D.; Hou, Thomas Y.
2001
...and 51 more Documents
all top 5

### Cited by 3,648 Authors

 94 Chung, Tsz Shun Eric 76 Hou, Thomas Yizhao 69 Efendiev, Yalchin R. 36 Vasilyeva, Maria V. 29 Leung, Wingtat 29 Wu, Jiahong 27 Cui, Junzhi 23 Fu, Shubin 23 Lowengrub, John Samuel 22 Chae, Dongho 21 Hajibeygi, Hadi 20 Abdulle, Assyr 20 Galvis, Juan 20 Li, Zhilin 19 Jiang, Lijian 18 Gancedo, Francisco 17 Cordoba, Diego 16 Jenny, Patrick 16 Shelley, Michael J. 16 Valentin, Frédéric 15 Ceniceros, Hector D. 15 Tchelepi, Hamdi A. 14 Osher, Stanley Joel 14 Xu, Xiaojing 14 Zhang, Zhiwen 13 Ambrose, David M. 13 Cao, Liqun 13 Li, Shuwang 13 Peterseim, Daniel 13 Pun, Saimang 12 Hoang, Viet Ha 12 Li, Guanglian 12 Li, Qin 12 Målqvist, Axel 12 Presho, Michael 12 Shi, Zuoqiang 12 Wheeler, Mary Fanett 11 Babuška, Ivo 11 Cheung, Siu Wun 11 Ohlberger, Mario 11 Yang, Zhiqiang 11 Ye, Zhuan 11 Zabaras, Nicholas J. 10 Kim, Junseok 10 LeFloch, Philippe Gerard 10 Lin, Guang 10 Lin, Tao 10 Tang, Shaoqiang 10 Wang, Yating 9 Brown, Donald L. 9 Calo, Victor Manuel 9 Cao, Chongsheng 9 Chen, Jinru 9 Ginting, Victor 9 Heinlein, Alexander 9 Henning, Patrick 9 Lei, Zhen 9 Li, Ruo 9 Lie, Knut-Andreas 9 Liu, Jianguo 9 Lu, Jianfeng 9 Ma, Qiang 9 Nie, Qing 9 Owhadi, Houman 9 Wei, Guowei 9 Zhao, Hongkai 8 Castro, Ángel 8 Constantin, Peter 8 Deng, Weibing 8 Dong, Hao 8 Fedkiw, Ronald P. 8 He, Wenming 8 Jabin, Pierre-Emmanuel 8 Karniadakis, George Em 8 Kukavica, Igor 8 Le Bris, Claude 8 Liu, Chun 8 Madureira, Alexandre L. 8 Protas, Bartosz 8 Reusken, Arnold 8 Zhang, Pingwen 8 Zhao, Kun 7 Abreu, Eduardo 7 Beale, J. Thomas 7 Berthon, Christophe 7 Caflisch, Russel E. 7 Cottet, Georges-Henri 7 Du, Qiang 7 Gómez-Serrano, Javier 7 Ji, Haifeng 7 Kiselev, Alexander A. 7 Klawonn, Axel 7 Legoll, Frédéric 7 Lin, Ping 7 Liu, Wing Kam 7 Mu, Lin 7 Park, Eun-Jae 7 Rheinbach, Oliver 7 Sakajo, Takashi 7 Sarkis, Marcus V. ...and 3,548 more Authors
all top 5

### Cited in 278 Serials

 508 Journal of Computational Physics 147 Computer Methods in Applied Mechanics and Engineering 140 Journal of Computational and Applied Mathematics 82 Journal of Fluid Mechanics 77 Multiscale Modeling & Simulation 70 Journal of Scientific Computing 61 Computers and Fluids 59 Computational Geosciences 53 Physics of Fluids 48 Computers & Mathematics with Applications 47 Journal of Differential Equations 47 SIAM Journal on Scientific Computing 38 International Journal for Numerical Methods in Engineering 37 Physica D 37 Applied Numerical Mathematics 35 Archive for Rational Mechanics and Analysis 35 Applied Mathematics and Computation 32 Computational Mechanics 30 Mathematics of Computation 28 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 21 Advances in Computational Mathematics 21 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 20 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 20 Applied Mathematical Modelling 20 Discrete and Continuous Dynamical Systems 16 International Journal for Numerical Methods in Fluids 16 Engineering Analysis with Boundary Elements 16 Journal of Mathematical Fluid Mechanics 14 ZAMP. Zeitschrift für angewandte Mathematik und Physik 14 Mathematics and Computers in Simulation 12 Applicable Analysis 12 Journal of Mathematical Physics 12 Advances in Mathematics 12 Communications in Partial Differential Equations 12 SIAM/ASA Journal on Uncertainty Quantification 10 Journal of Statistical Physics 10 Numerical Methods for Partial Differential Equations 10 SIAM Journal on Mathematical Analysis 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 Mathematics Letters 9 Applied and Computational Harmonic Analysis 9 Mathematical Problems in Engineering 8 Journal of Engineering Mathematics 8 Nonlinearity 8 BIT 8 Journal of Functional Analysis 8 Numerical Algorithms 7 Mathematical Methods in the Applied Sciences 7 Chinese Annals of Mathematics. Series B 7 International Journal of Computer Mathematics 7 SIAM Review 7 Computational and Applied Mathematics 7 Archives of Computational Methods in Engineering 7 Comptes Rendus. Mathématique. Académie des Sciences, Paris 7 Science China. Mathematics 7 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 6 Computing and Visualization in Science 6 Chaos 6 European Journal of Mechanics. A. Solids 6 Annals of Mathematics. Second Series 6 International Journal of Computational Methods 6 Acta Mechanica Sinica 5 Computer Physics Communications 5 Communications on Pure and Applied Mathematics 5 Theoretical and Computational Fluid Dynamics 5 Journal of the American Mathematical Society 5 European Journal of Applied Mathematics 5 Journal de Mathématiques Pures et Appliquées. Neuvième Série 5 Proceedings of the National Academy of Sciences of the United States of America 5 SIAM Journal on Applied Mathematics 5 Communications in Nonlinear Science and Numerical Simulation 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 Acta Applicandae Mathematicae 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. B. Fluids 4 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 4 Computational Methods in Applied Mathematics 4 Acta Mathematica Scientia. Series B. (English Edition) 4 Sādhanā 4 Journal of Numerical Mathematics ...and 178 more Serials
all top 5

### Cited in 45 Fields

 1,428 Fluid mechanics (76-XX) 1,313 Numerical analysis (65-XX) 1,154 Partial differential equations (35-XX) 361 Mechanics of deformable solids (74-XX) 107 Probability theory and stochastic processes (60-XX) 107 Geophysics (86-XX) 89 Statistical mechanics, structure of matter (82-XX) 69 Statistics (62-XX) 69 Biology and other natural sciences (92-XX) 60 Classical thermodynamics, heat transfer (80-XX) 51 Dynamical systems and ergodic theory (37-XX) 38 Optics, electromagnetic theory (78-XX) 36 Calculus of variations and optimal control; optimization (49-XX) 35 Computer science (68-XX) 32 Information and communication theory, circuits (94-XX) 29 Ordinary differential equations (34-XX) 29 Harmonic analysis on Euclidean spaces (42-XX) 17 Real functions (26-XX) 17 Operations research, mathematical programming (90-XX) 16 Linear and multilinear algebra; matrix theory (15-XX) 16 Differential geometry (53-XX) 16 Systems theory; control (93-XX) 12 Integral equations (45-XX) 12 Mechanics of particles and systems (70-XX) 11 Approximations and expansions (41-XX) 10 Functions of a complex variable (30-XX) 10 Global analysis, analysis on manifolds (58-XX) 9 Quantum theory (81-XX) 7 Astronomy and astrophysics (85-XX) 5 Potential theory (31-XX) 5 Relativity and gravitational theory (83-XX) 4 Integral transforms, operational calculus (44-XX) 3 Operator theory (47-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 History and biography (01-XX) 2 Special functions (33-XX) 1 General and overarching topics; collections (00-XX) 1 Combinatorics (05-XX) 1 Algebraic geometry (14-XX) 1 Nonassociative rings and algebras (17-XX) 1 Topological groups, Lie groups (22-XX) 1 Functional analysis (46-XX) 1 Geometry (51-XX) 1 Manifolds and cell complexes (57-XX) 1 Mathematics education (97-XX)

### Wikidata Timeline

The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.