Edit Profile (opens in new tab) Hou, Thomas Yizhao Compute Distance To: Compute 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) Publications by Year all cited Publications top 5 cited Publications 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 0880.73065Hou, Thomas Y.; Wu, Xiao-Hui 581 1997 Multiscale finite element methods. Theory and applications. Zbl 1163.65080Efendiev, Yalchin; Hou, Thomas Y. 298 2009 Generalized multiscale finite element methods (GMsFEM). Zbl 1349.65617Efendiev, Yalchin; Galvis, Juan; Hou, Thomas Y. 232 2013 A level set formulation of Eulerian interface capturing methods for incompressible fluid flows. Zbl 0847.76048Chang, Y. C.; Hou, T. Y.; Merriman, B.; Osher, S. 218 1996 Removing the stiffness from interfacial flows with surface tension. Zbl 0810.76095Hou, Thomas Y.; Lowengrub, John S.; Shelley, Michael J. 198 1994 Global well-posedness of the viscous Boussinesq equations. Zbl 1274.76185Hou, Thomas Y.; Li, Congming 190 2005 Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients. Zbl 0922.65071Hou, Thomas Y.; Wu, Xiao-Hui; Cai, Zhiqiang 188 1999 A mixed multiscale finite element method for elliptic problems with oscillating coefficients. Zbl 1017.65088Chen, Zhiming; Hou, Thomas Y. 142 2003 Convergence of a nonconforming multiscale finite element method. Zbl 0951.65105Efendiev, Yalchin R.; Hou, Thomas Y.; Wu, Xiao-Hui 107 2000 A hybrid method for moving interface problems with application to the Hele-Shaw flow. Zbl 0888.76067Hou, Thomas Y.; Li, Zhilin; Osher, Stanley; Zhao, Hongkai 103 1997 Why nonconservative schemes converge to wrong solutions: Error analysis. Zbl 0809.65102Hou, Thomas Y.; Le Floch, Philippe G. 95 1994 A new multiscale finite element method for high-contrast elliptic interface problems. Zbl 1202.65154Chu, C.-C.; Graham, I. G.; Hou, T.-Y. 91 2010 Accurate multiscale finite element methods for two-phase flow simulations. Zbl 1158.76349Efendiev, Y.; Ginting, V.; Hou, T.; Ewing, R. 85 2006 Adaptive multiscale model reduction with generalized multiscale finite element methods. Zbl 1349.76191Chung, Eric; Efendiev, Yalchin; Hou, Thomas Y. 83 2016 Analysis of upscaling absolute permeability. Zbl 1162.65327Wu, X. H.; Efendiev, Y.; Hou, T. Y. 74 2002 Computing nearly singular solutions using pseudo-spectral methods. Zbl 1310.76127Hou, Thomas Y.; Li, Ruo 73 2007 Multiscale finite element methods for nonlinear problems and their applications. Zbl 1083.65105Efendiev, Yalchin R.; Hou, Thomas Yizhao; Ginting, Victor 71 2004 Wiener chaos expansions and numerical solutions of randomly forced equations of fluid mechanics. Zbl 1095.76047Hou, Thomas Y.; Luo, Wuan; Rozovskii, Boris; Zhou, Hao-Min 69 2006 Boundary integral methods for multicomponent fluids and multiphase materials. Zbl 1046.76029Hou, T. Y.; Lowengrub, J. S.; Shelley, M. J. 65 2001 The long-time motion of vortex sheets with surface tension. Zbl 1185.76545Hou, T. Y.; Lowengrub, J. S.; Shelly, M. J. 64 1997 Growth rates for the linearized motion of fluid interfaces away from equilibrium. Zbl 0796.76041Beale, J. Thomas; Hou, Thomas Y.; Lowengrub, John S. 58 1993 An efficient dynamically adaptive mesh for potentially singular solutions. Zbl 0986.65087Ceniceros, Hector D.; Hou, Thomas Y. 57 2001 Dynamic depletion of vortex stretching and non-blowup of the 3-D incompressible Euler equations. Zbl 1370.76015Hou, Thomas Y.; Li, Ruo 53 2006 Removing the cell resonance error in the multiscale finite element method via a Petrov-Galerkin formulation. Zbl 1085.65109Hou, Thomas Y.; Wu, Xiao-Hui; Zhang, Yu 51 2004 Preconditioning Markov chain Monte Carlo simulations using coarse-scale models. Zbl 1111.65003Efendiev, Yalchin R.; Hou, Thomas Yizhao; Luo, Wu An 50 2006 Convergence of the point vortex method for the 2-D Euler equations. Zbl 0694.76013Goodman, Jonathan; Hou, Thomas Y.; Lowengrub, John 47 1990 Dynamic stability of the three-dimensional axisymmetric Navier-Stokes equations with swirl. Zbl 1138.35077Hou, Thomas Y.; Li, Congming 47 2008 Geometric properties and nonblowup of 3D incompressible Euler flow. Zbl 1142.35549Deng, Jian; Hou, Thomas Y.; Yu, Xinwei 42 2005 A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations. I: Derivation and algorithms. Zbl 1297.65008Cheng, Mulin; Hou, Thomas Y.; Zhang, Zhiwen 40 2013 Toward the finite-time blowup of the 3D axisymmetric Euler equations: a numerical investigation. Zbl 1316.35235Luo, Guo; Hou, Thomas Y. 39 2014 Multiscale domain decomposition methods for elliptic problems with high aspect ratios. Zbl 1003.65142Aarnes, Jørg; Hou, Thomas Y. 35 2002 Multiscale finite element methods for porous media flows and their applications. Zbl 1112.76046Efendiev, Yalchin R.; Hou, Thomas Yizhao 34 2007 A mathematical framework of the bridging scale method. Zbl 1117.74056Tang, Shaoqiang; Hou, Thomas Y.; Liu, Wing Kam 32 2006 Convergence of a boundary integral method for water waves. Zbl 0858.76046Beale, J. Thomas; Hou, Thomas Y.; Lowengrub, John 30 1996 Improved geometric conditions for non-blowup of the 3D incompressible Euler equation. Zbl 1158.76305Deng, Jian; Hou, Thomas Y.; Yu, Xinwei 30 2006 On the finite-time blowup of a one-dimensional model for the three-dimensional axisymmetric Euler equations. Zbl 1377.35218Choi, Kyudong; Hou, Thomas Y.; Kiselev, Alexander; Luo, Guo; Sverak, Vladimir; Yao, Yao 30 2017 A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations. II: Adaptivity and generalizations. Zbl 1297.65007Cheng, Mulin; Hou, Thomas Y.; Zhang, Zhiwen 29 2013 Global regularity of the 3D axi-symmetric Navier-Stokes equations with anisotropic data. Zbl 1146.76010Hou, Thomas Y.; Lei, Zhen; Li, Congming 29 2008 On the stabilizing effect of convection in three-dimensional incompressible flows. Zbl 1171.35095Hou, Thomas Y.; Lei, Zhen 26 2009 Blowup or no blowup? the interplay between theory and numerics. Zbl 1143.76390Hou, Thomas Y.; Li, Ruo 24 2008 Multiscale finite element methods for stochastic porous media flow equations and application to uncertainty quantification. Zbl 1194.76112Dostert, P.; Efendiev, Y.; Hou, T. Y. 23 2008 Dispersive approximations in fluid dynamics. Zbl 0729.76065Hou, Thomas Y.; Lax, Peter D. 22 1991 Blow-up or no blow-up? A unified computational and analytic approach to 3D incompressible Euler and Navier-Stokes equations. Zbl 1422.76041Hou, Thomas Y. 21 2009 A pseudo-spectral multiscale method: interfacial conditions and coarse grid equations. Zbl 1089.65110Tang, Shaoqiang; Hou, Thomas Y.; Liu, Wing Kam 21 2006 Data-driven time-frequency analysis. Zbl 1336.94019Hou, Thomas Y.; Shi, Zuoqiang 20 2013 An efficient semi-implicit immersed boundary method for the Navier-Stokes equations. Zbl 1161.76048Hou, Thomas Y.; Shi, Zuoqiang 20 2008 Adaptive data analysis via sparse time-frequency representation. Zbl 1234.94015Hou, Thomas Y.; Shi, Zuoqiang 20 2011 Homogenization of linear transport equations with oscillatory vector fields. Zbl 0759.35008Hou, Thomas Y.; Xin, Xue 17 1992 Multi-valued solutions and branch point singularities for nonlinear hyperbolic or elliptic systems. Zbl 0797.35007Caflisch, Russel E.; Ercolani, Nicholas; Hou, Thomas Y.; Landis, Yelena 17 1993 Coarse-gradient Langevin algorithms for dynamic data integration and uncertainty quantification. Zbl 1146.76637Dostert, P.; Efendiev, Y.; Hou, T. Y.; Luo, W. 17 2006 Numerical study of Hele-Shaw flow with suction. Zbl 1149.76335Ceniceros, Hector D.; Hou, Thomas Y.; Si, Helen 16 1999 Removing the stiffness of curvature in computing 3-D filaments. Zbl 0917.76063Hou, Thomas Y.; Klapper, Isaac; Si, Helen 15 1998 Computational method for propagating phase boundaries. Zbl 0855.73080Zhong, Xiaoguang; Hou, Thomas Y.; LeFloch, Philippe G. 14 1996 Convergence of a non-stiff boundary integral method for interfacial flows with surface tension. Zbl 0905.76012Ceniceros, Héctor D.; Hou, Thomas Y. 14 1998 A data-driven stochastic method for elliptic PDEs with random coefficients. Zbl 1290.60068Cheng, Mulin; Hou, Thomas Y.; Yan, Mike; Zhang, Zhiwen 14 2013 Removing the stiffness of elastic force from the immersed boundary method for the 2D Stokes equations. Zbl 1294.76201Hou, Thomas Y.; Shi, Zuoqiang 14 2008 Potentially singular solutions of the 3D axisymmetric Euler equations. Zbl 1431.35115Luo, Guo; Hou, Thomas Y. 14 2014 Optimal local multi-scale basis functions for linear elliptic equations with rough coefficients. Zbl 1333.65131Hou, Thomas Y.; Liu, Pengfei 13 2016 Geometry related convergence results for domain decomposition algorithms. Zbl 0724.65109Chan, Tony F.; Hou, Thomas Y.; Lions, P. L. 13 1991 Second-order convergence of a projection scheme for the incompressible Navier-Stokes equations with boundaries. Zbl 0776.76055Hou, Thomas Y.; Wetton, Brian T. R. 12 1993 Self-similar singularity of a 1D model for the 3D axisymmetric Euler equations. Zbl 1320.35269Hou, Thomas Y.; Liu, Pengfei 12 2015 Convergence of a boundary integral method for 3-D water waves. Zbl 1131.76339Hou, Thomas Y.; Zhang, Pingwen 12 2002 Convergence of a finite difference scheme for the Navier-Stokes equations using vorticity boundary conditions. Zbl 0749.76046Hou, Thomas Y.; Wetton, Brian T. R. 12 1992 Multiscale numerical methods for singularly perturbed convection-diffusion equations. Zbl 1182.76902Park, Peter J.; Hou, Thomas Y. 12 2004 Convergence of a variable blob vortex method for the Euler and Navier- Stokes equations. Zbl 0727.76034Hou, Thomas Y. 12 1990 Level set dynamics and the non-blowup of the 2D quasi-geostrophic equation. Zbl 1173.76006Deng, J.; Hou, T. Y.; Li, R.; Yu, X. 12 2006 Sparse operator compression of higher-order elliptic operators with rough coefficients. Zbl 1412.65215Hou, Thomas Y.; Zhang, Pengchuan 12 2017 Convergence of the point vortex method for the 3-D Euler equations. Zbl 0856.76059Hou, Thomas Y.; Lowengrub, John 11 1990 On the stability of the unsmoothed Fourier method for hyperbolic equations. Zbl 0791.65080Goodman, Jonathan; Hou, Thomas; Tadmor, Eitan 11 1994 On the partial regularity of a 3D model of the Navier-Stokes equations. Zbl 1176.35130Hou, Thomas Y.; Lei, Zhen 11 2009 On singularity formation of a 3D model for incompressible Navier-Stokes equations. Zbl 1252.35219Hou, Thomas Y.; Shi, Zuoqiang; Wang, Shu 11 2012 Nonexistence of locally self-similar blow-up for the 3D incompressible Navier-Stokes equations. Zbl 1194.35307Hou, Thomas Y.; Li, Ruo 11 2007 Dynamic generation of capillary waves. Zbl 1147.76354Ceniceros, Hector D.; Hou, Thomas Y. 11 1999 A level-set approach to the computation of twinning and phase-transition dynamics. Zbl 0936.74052Hou, Thomas Y.; Rosakis, Phoebus; LeFloch, Philippe 10 1999 Numerical solutions to free boundary problems. Zbl 0831.65137Hou, Thomas Y. 10 1995 On finite time singularity and global regularity of an axisymmetric model for the 3D Euler equations. Zbl 1293.35228Hou, Thomas Y.; Lei, Zhen; Luo, Guo; Wang, Shu; Zou, Chen 10 2014 The singular perturbation of surface tension in Hele-Shaw flows. Zbl 0991.76020Ceniceros, Hector D.; Hou, Thomas Y. 9 2000 Convergence of a data-driven time-frequency analysis method. Zbl 1336.94020Hou, Thomas Y.; Shi, Zuoqiang; Tavallali, Peyman 9 2014 Well-posedness of linearized motion for 3-D water waves far from equilibrium. Zbl 0874.76014Hou, Thomas Y.; Teng, Zhenhuan; Zhang, Pingwen 8 1996 Multiscale modelling and computation of fluid flow. Zbl 1134.76386Hou, Thomas Y. 8 2005 On global well-posedness of the Lagrangian averaged Euler equations. Zbl 1111.76006Hou, Thomas Y.; Li, Congming 8 2006 Exploring the locally low dimensional structure in solving random elliptic PDEs. Zbl 1365.65015Hou, Thomas Y.; Li, Qin; Zhang, Pengchuan 8 2017 An efficient boundary integral method for the Mullins-Sekerka problem. Zbl 0879.65092Zhu, Jingyi; Chen, Xinfu; Hou, Thomas Y. 7 1996 Spatial and temporal stability issues for interfacial flows with surface tension. Zbl 0816.76050Beale, J. T.; Hou, T. Y.; Lowengrub, J. S.; Shelley, M. J. 7 1994 Particle method approximation of oscillatory solutions to hyperbolic differential equations. Zbl 0675.65093Engquist, Bjorn; Hou, Thomas Y. 7 1989 Convergence of a point vortex method for vortex sheets. Zbl 0799.76062Hou, Thomas Y.; Lowengrub, John; Krasny, Robert 7 1991 New stability estimates for the 2-D vortex method. Zbl 0745.76061Goodman, Jonathan; Hou, Thomas Y. 7 1991 On singularity formation of a nonlinear nonlocal system. Zbl 1241.35038Hou, Thomas Y.; Li, Congming; Shi, Zuoqiang; Wang, Shu; Yu, Xinwei 7 2011 A heterogeneous stochastic FEM framework for elliptic PDEs. Zbl 1352.65510Hou, Thomas Y.; Liu, Pengfei 7 2015 A model reduction method for multiscale elliptic PDEs with random coefficients using an optimization approach. Zbl 1420.35083Hou, Thomas Y.; Ma, Dingjiong; Zhang, Zhiwen 7 2019 Numerical approximations to multiscale solutions in partial differential equations. Zbl 1027.65154Hou, Thomas Y. 6 2003 Convergence of the grid-free point vortex method for the three-dimensional Euler equations. Zbl 0850.76489Cottet, Georges-Henri; Goodman, Jonathan; Hou, Thomas Y. 6 1991 Sparse + low-energy decomposition for viscous conservation laws. Zbl 1352.65413Hou, Thomas Y.; Li, Qin; Schaeffer, Hayden 6 2015 Extracting a shape function for a signal with intra-wave frequency modulation. Zbl 1353.94017Hou, Thomas Y.; Shi, Zuoqiang 6 2016 An accelerated method for nonlinear elliptic PDE. Zbl 1368.65004Schaeffer, Hayden; Hou, Thomas Y. 6 2016 Finite difference approximations for partial differential equations with rapidly oscillating coefficients. Zbl 0755.65088Avellaneda, M.; Hou, Th. Y.; Papanicolaou, G. C. 5 1991 A Lagrangian finite element method for the 2-D Euler equations. Zbl 0705.76059Chacon-Rebollo, Tomas; Hou, Thomas Y. 5 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 5 2012 Finite time blowup of 2D Boussinesq and 3D Euler equations with \(C^{1, \alpha}\) velocity and boundary. Zbl 1485.35071Chen, Jiajie; Hou, Thomas Yizhao 5 2021 Stable fourth-order stream-function methods for incompressible flows with boundaries. Zbl 1212.65318Hou, Thomas Y.; Wetton, Brian R. 5 2009 Finite time blowup of 2D Boussinesq and 3D Euler equations with \(C^{1, \alpha}\) velocity and boundary. Zbl 1485.35071Chen, Jiajie; Hou, Thomas Yizhao 5 2021 On the finite time blowup of the de Gregorio model for the 3D Euler equations. Zbl 1469.35053Chen, Jiajie; Hou, Thomas Y.; Huang, De 3 2021 Exponential convergence for multiscale linear elliptic PDEs via adaptive edge basis functions. Zbl 1473.65296Chen, Yifan; Hou, Thomas Y.; Wang, Yixuan 3 2021 Function approximation via the subsampled Poincaré inequality. Zbl 1458.35008Chen, Yifan; Hou, Thomas Y. 1 2021 A prototype knockoff filter for group selection with FDR control. Zbl 1471.62409Chen, Jiajie; Hou, Anthony; Hou, Thomas Y. 1 2020 A model reduction method for multiscale elliptic PDEs with random coefficients using an optimization approach. Zbl 1420.35083Hou, Thomas Y.; Ma, Dingjiong; Zhang, Zhiwen 7 2019 Formation of finite-time singularities in the 3D axisymmetric Euler equations: a numerics guided study. Zbl 1427.35190Luo, Guo; Hou, Thomas Y. 3 2019 A fast hierarchically preconditioned eigensolver based on multiresolution matrix decomposition. Zbl 1455.65053Hou, Thomas Y.; Huang, De; Lam, Ka Chun; Zhang, Ziyun 3 2019 An adaptive fast solver for a general class of positive definite matrices via energy decomposition. Zbl 1391.65066Hou, Thomas Y.; Huang, De; Lam, Ka Chun; Zhang, PengChuan 4 2018 Global regularity for a family of 3D models of the axi-symmetric Navier-Stokes equations. Zbl 1393.35170Hou, Thomas Y.; Liu, Pengfei; Wang, Fei 3 2018 Potential singularity for a family of models of the axisymmetric incompressible flow. Zbl 1405.35150Hou, Thomas Y.; Jin, Tianling; Liu, Pengfei 2 2018 On the finite-time blowup of a one-dimensional model for the three-dimensional axisymmetric Euler equations. Zbl 1377.35218Choi, Kyudong; Hou, Thomas Y.; Kiselev, Alexander; Luo, Guo; Sverak, Vladimir; Yao, Yao 30 2017 Sparse operator compression of higher-order elliptic operators with rough coefficients. Zbl 1412.65215Hou, Thomas Y.; Zhang, Pengchuan 12 2017 Exploring the locally low dimensional structure in solving random elliptic PDEs. Zbl 1365.65015Hou, Thomas Y.; Li, Qin; Zhang, Pengchuan 8 2017 A sparse decomposition of low rank symmetric positive semidefinite matrices. Zbl 1386.65127Hou, Thomas Y.; Li, Qin; Zhang, Pengchuan 5 2017 Discrete maximum-norm stability of a linearized second-order finite difference scheme for Allen-Cahn equation. Zbl 1399.65211Hou, T.; Wang, K.; Xiong, Y.; Xiao, X.; Zhang, Sh. 4 2017 An iteratively adaptive multi-scale finite element method for elliptic PDEs with rough coefficients. Zbl 1380.65268Hou, Thomas Y.; Hwang, Feng-Nan; Liu, Pengfei; Yao, Chien-Chou 3 2017 Sparse time-frequency decomposition for multiple signals with same frequencies. Zbl 1378.94007Hou, Thomas Y.; Shi, Zuoqiang 1 2017 Adaptive multiscale model reduction with generalized multiscale finite element methods. Zbl 1349.76191Chung, Eric; Efendiev, Yalchin; Hou, Thomas Y. 83 2016 Optimal local multi-scale basis functions for linear elliptic equations with rough coefficients. Zbl 1333.65131Hou, Thomas Y.; Liu, Pengfei 13 2016 Extracting a shape function for a signal with intra-wave frequency modulation. Zbl 1353.94017Hou, Thomas Y.; Shi, Zuoqiang 6 2016 An accelerated method for nonlinear elliptic PDE. Zbl 1368.65004Schaeffer, Hayden; Hou, Thomas Y. 6 2016 A model reduction method for elliptic PDEs with random input using the heterogeneous stochastic FEM framework. Zbl 1341.65004Hou, Thomas Y.; Liu, Pengfei; Zhang, Zhiwen 3 2016 Sparse time-frequency decomposition based on dictionary adaptation. Zbl 1353.42016Hou, 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 1320.35269Hou, Thomas Y.; Liu, Pengfei 12 2015 A heterogeneous stochastic FEM framework for elliptic PDEs. Zbl 1352.65510Hou, Thomas Y.; Liu, Pengfei 7 2015 Sparse + low-energy decomposition for viscous conservation laws. Zbl 1352.65413Hou, Thomas Y.; Li, Qin; Schaeffer, Hayden 6 2015 Sparse time frequency representations and dynamical systems. Zbl 1346.37062Hou, Thomas Y.; Shi, Zuoqiang; Tavallali, Peyman 3 2015 On the uniqueness of sparse time-frequency representation of multiscale data. Zbl 1357.94035Liu, Chunguang; Shi, Zuoqiang; Hou, Thomas Y. 2 2015 Toward the finite-time blowup of the 3D axisymmetric Euler equations: a numerical investigation. Zbl 1316.35235Luo, Guo; Hou, Thomas Y. 39 2014 Potentially singular solutions of the 3D axisymmetric Euler equations. Zbl 1431.35115Luo, Guo; Hou, Thomas Y. 14 2014 On finite time singularity and global regularity of an axisymmetric model for the 3D Euler equations. Zbl 1293.35228Hou, Thomas Y.; Lei, Zhen; Luo, Guo; Wang, Shu; Zou, Chen 10 2014 Convergence of a data-driven time-frequency analysis method. Zbl 1336.94020Hou, Thomas Y.; Shi, Zuoqiang; Tavallali, Peyman 9 2014 Extraction of intrawave signals using the sparse time-frequency representation method. Zbl 1380.94062Tavallali, Peyman; Hou, Thomas Y.; Shi, Zuoqiang 4 2014 An adaptive ANOVA-based data-driven stochastic method for elliptic PDEs with random coefficient. Zbl 1388.65178Zhang, Zhiwen; Hu, Xin; Hou, Thomas Y.; Lin, Guang; Yan, Mike 4 2014 A multiscale model reduction method for partial differential equations. Zbl 1312.65206Ci, Maolin; Hou, Thomas Y.; Shi, Zuoqiang 2 2014 Generalized multiscale finite element methods (GMsFEM). Zbl 1349.65617Efendiev, Yalchin; Galvis, Juan; Hou, Thomas Y. 232 2013 A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations. I: Derivation and algorithms. Zbl 1297.65008Cheng, Mulin; Hou, Thomas Y.; Zhang, Zhiwen 40 2013 A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations. II: Adaptivity and generalizations. Zbl 1297.65007Cheng, Mulin; Hou, Thomas Y.; Zhang, Zhiwen 29 2013 Data-driven time-frequency analysis. Zbl 1336.94019Hou, Thomas Y.; Shi, Zuoqiang 20 2013 A data-driven stochastic method for elliptic PDEs with random coefficients. Zbl 1290.60068Cheng, Mulin; Hou, Thomas Y.; Yan, Mike; Zhang, Zhiwen 14 2013 Sparse time-frequency representation of nonlinear and nonstationary data. Zbl 1304.65282Hou, Thomas Yizhao; Shi, Zuoqiang 3 2013 Multiscale modeling of incompressible turbulent flows. Zbl 1291.76241Hou, T. Y.; Hu, X.; Hussain, F. 1 2013 On singularity formation of a 3D model for incompressible Navier-Stokes equations. Zbl 1252.35219Hou, 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 5 2012 Dynamic growth estimates of maximum vorticity for 3D incompressible Euler equations and the SQG model. Zbl 1237.76014Hou, Thomas Y.; Shi, Zuoqiang 1 2012 Adaptive data analysis via sparse time-frequency representation. Zbl 1234.94015Hou, Thomas Y.; Shi, Zuoqiang 20 2011 On singularity formation of a nonlinear nonlocal system. Zbl 1241.35038Hou, 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 1202.65154Chu, C.-C.; Graham, I. G.; Hou, T.-Y. 91 2010 Multiscale finite element methods. Theory and applications. Zbl 1163.65080Efendiev, Yalchin; Hou, Thomas Y. 298 2009 On the stabilizing effect of convection in three-dimensional incompressible flows. Zbl 1171.35095Hou, Thomas Y.; Lei, Zhen 26 2009 Blow-up or no blow-up? A unified computational and analytic approach to 3D incompressible Euler and Navier-Stokes equations. Zbl 1422.76041Hou, Thomas Y. 21 2009 On the partial regularity of a 3D model of the Navier-Stokes equations. Zbl 1176.35130Hou, Thomas Y.; Lei, Zhen 11 2009 Stable fourth-order stream-function methods for incompressible flows with boundaries. Zbl 1212.65318Hou, Thomas Y.; Wetton, Brian R. 5 2009 Multiscale analysis for convection-dominated transport equations. Zbl 1163.76048Hou, Thomas Y.; Liang, Dong 3 2009 Dynamic stability of the three-dimensional axisymmetric Navier-Stokes equations with swirl. Zbl 1138.35077Hou, Thomas Y.; Li, Congming 47 2008 Global regularity of the 3D axi-symmetric Navier-Stokes equations with anisotropic data. Zbl 1146.76010Hou, Thomas Y.; Lei, Zhen; Li, Congming 29 2008 Blowup or no blowup? the interplay between theory and numerics. Zbl 1143.76390Hou, Thomas Y.; Li, Ruo 24 2008 Multiscale finite element methods for stochastic porous media flow equations and application to uncertainty quantification. Zbl 1194.76112Dostert, P.; Efendiev, Y.; Hou, T. Y. 23 2008 An efficient semi-implicit immersed boundary method for the Navier-Stokes equations. Zbl 1161.76048Hou, Thomas Y.; Shi, Zuoqiang 20 2008 Removing the stiffness of elastic force from the immersed boundary method for the 2D Stokes equations. Zbl 1294.76201Hou, Thomas Y.; Shi, Zuoqiang 14 2008 Multiscale analysis and computation for the three-dimensional incompressible Navier-Stokes equations. Zbl 1248.76037Hou, Thomas Y.; Yang, Danping; Ran, Hongyu 4 2008 Multiscale simulations of porous media flows in flow-based coordinate system. Zbl 1155.76050Efendiev, Yalchin R.; Hou, Thomas Yizhao; Strinopoulos, T. 3 2008 Computing nearly singular solutions using pseudo-spectral methods. Zbl 1310.76127Hou, Thomas Y.; Li, Ruo 73 2007 Multiscale finite element methods for porous media flows and their applications. Zbl 1112.76046Efendiev, Yalchin R.; Hou, Thomas Yizhao 34 2007 Nonexistence of locally self-similar blow-up for the 3D incompressible Navier-Stokes equations. Zbl 1194.35307Hou, Thomas Y.; Li, Ruo 11 2007 Mathematical modeling and simulation of aquatic and aerial animal locomotion. Zbl 1343.76074Hou, T. Y.; Stredie, V. G.; Wu, T. Y. 4 2007 Accurate multiscale finite element methods for two-phase flow simulations. Zbl 1158.76349Efendiev, Y.; Ginting, V.; Hou, T.; Ewing, R. 85 2006 Wiener chaos expansions and numerical solutions of randomly forced equations of fluid mechanics. Zbl 1095.76047Hou, Thomas Y.; Luo, Wuan; Rozovskii, Boris; Zhou, Hao-Min 69 2006 Dynamic depletion of vortex stretching and non-blowup of the 3-D incompressible Euler equations. Zbl 1370.76015Hou, Thomas Y.; Li, Ruo 53 2006 Preconditioning Markov chain Monte Carlo simulations using coarse-scale models. Zbl 1111.65003Efendiev, Yalchin R.; Hou, Thomas Yizhao; Luo, Wu An 50 2006 A mathematical framework of the bridging scale method. Zbl 1117.74056Tang, Shaoqiang; Hou, Thomas Y.; Liu, Wing Kam 32 2006 Improved geometric conditions for non-blowup of the 3D incompressible Euler equation. Zbl 1158.76305Deng, Jian; Hou, Thomas Y.; Yu, Xinwei 30 2006 A pseudo-spectral multiscale method: interfacial conditions and coarse grid equations. Zbl 1089.65110Tang, Shaoqiang; Hou, Thomas Y.; Liu, Wing Kam 21 2006 Coarse-gradient Langevin algorithms for dynamic data integration and uncertainty quantification. Zbl 1146.76637Dostert, P.; Efendiev, Y.; Hou, T. Y.; Luo, W. 17 2006 Level set dynamics and the non-blowup of the 2D quasi-geostrophic equation. Zbl 1173.76006Deng, J.; Hou, T. Y.; Li, R.; Yu, X. 12 2006 On global well-posedness of the Lagrangian averaged Euler equations. Zbl 1111.76006Hou, Thomas Y.; Li, Congming 8 2006 A 3D numerical method for studying vortex formation behind a moving plate. Zbl 1218.76034Hou, T. Y.; Stredie, V. G.; Wu, T. Y. 4 2006 A framework for modeling subgrid effects for two-phase flows in porous media. Zbl 1127.76064Hou, Thomas Y.; Westhead, Andrew; Yang, Danping 2 2006 Global well-posedness of the viscous Boussinesq equations. Zbl 1274.76185Hou, Thomas Y.; Li, Congming 190 2005 Geometric properties and nonblowup of 3D incompressible Euler flow. Zbl 1142.35549Deng, Jian; Hou, Thomas Y.; Yu, Xinwei 42 2005 Multiscale modelling and computation of fluid flow. Zbl 1134.76386Hou, Thomas Y. 8 2005 A level set formulation for the 3D incompressible Euler equations. Zbl 1107.76011Deng, Jian; Hou, Thomas Y.; Yu, Xinwei 2 2005 Multiscale finite element methods for nonlinear problems and their applications. Zbl 1083.65105Efendiev, Yalchin R.; Hou, Thomas Yizhao; Ginting, Victor 71 2004 Removing the cell resonance error in the multiscale finite element method via a Petrov-Galerkin formulation. Zbl 1085.65109Hou, Thomas Y.; Wu, Xiao-Hui; Zhang, Yu 51 2004 Multiscale numerical methods for singularly perturbed convection-diffusion equations. Zbl 1182.76902Park, Peter J.; Hou, Thomas Y. 12 2004 Homogenization of incompressible Euler equations. Zbl 1104.76054Hou, Thomas Y.; Yang, Danping; Wang, Ke 1 2004 Wiener chaos expansions and numerical solutions of randomly forced equations of fluid mechanics. Zbl 1130.76411Hou, Thomas Y.; Kim, Hongjoong; Rozovskii, Boris; Zhou, Hao-Min 1 2004 Multiscale modelling and computation of incompressible flow. Zbl 1181.76096Hou, Thomas Y. 1 2004 A mixed multiscale finite element method for elliptic problems with oscillating coefficients. Zbl 1017.65088Chen, Zhiming; Hou, Thomas Y. 142 2003 Numerical approximations to multiscale solutions in partial differential equations. Zbl 1027.65154Hou, Thomas Y. 6 2003 A nearly optimal existence result for slightly perturbed 3-D vortex sheets. Zbl 1094.76014Hou, Thomas Y.; Hu, Gang 3 2003 Wiener chaos expansions and numerical solutions of randomly forced equations of fluid mechanics. Zbl 1130.76410Hou, Thomas Y.; Kim, Hongjoong; Rozovski, Boris; Zhou, Hao-Min 3 2003 Analysis of upscaling absolute permeability. Zbl 1162.65327Wu, X. H.; Efendiev, Y.; Hou, T. Y. 74 2002 Multiscale domain decomposition methods for elliptic problems with high aspect ratios. Zbl 1003.65142Aarnes, Jørg; Hou, Thomas Y. 35 2002 Convergence of a boundary integral method for 3-D water waves. Zbl 1131.76339Hou, Thomas Y.; Zhang, Pingwen 12 2002 Singularity formation in three-dimensional vortex sheets. Zbl 1185.76172Hou, Thomas Y.; Hu, Gang; Zhang, Pingwen 4 2002 Boundary integral methods for multicomponent fluids and multiphase materials. Zbl 1046.76029Hou, T. Y.; Lowengrub, J. S.; Shelley, M. J. 65 2001 An efficient dynamically adaptive mesh for potentially singular solutions. Zbl 0986.65087Ceniceros, Hector D.; Hou, Thomas Y. 57 2001 ...and 51 more Documents all cited Publications top 5 cited Publications 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. 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